from the publisher of
The Columbus Book of Euchre
How would you play this hand?
|Presented here are archives of euchre columns by Natty Bumppo, author of The Columbus Book of Euchre, published on line.|
The A-K-10-9 loner
|My kings were squeezed, part 1
My kings were squeezed, part 2 (7/16/04)
Next: “Ya gotta believe!” (4/1/05)
“Nice stop” (8/5/05)
Not a stone idiot (9/6/02)
Not the perfect hand (6/14/02)
Odds & probabilities, part 1 (4/5/02)
Odds & probabilities, part 2 (4/12/02)
“Official” rules (10/02/09)
Order now, or wait for “next”? (2/19/10)
Order the right, and count on your partner (5/28/10)
“Ordering at the bridge,” part 1 (10/18/02)
“Ordering at the bridge,” part 2 (10/25/02)
Overriding the left bower (2/20/04)
The “perfect” hand (5/24/02)
Playsite, Pogo, and the St. Louis Browns (5/10/02)
A Polish “story” (6/21/02)
Power seat (12/5/03)
Probability chart (1/6/06)
Ratings, shmatings (11/7/08)
Redd Dogg riddle No. 8 (1/9/09)
Redd Dogg riddle No. 37 (6/10/06)
Redd Dogg riddle No. 7,000,000,005.5 (8/6/04)
Renouncing, reneging and revoking (6/19/05)
Review of a pretty old euchre book (9/2/05)
The Robin Hood of euchre (11/1/02)
Rules I (9/5/08)
Rules II (9/16/08)
Rules III (10/3/08)
Saving an ambushed loner (12/6/08)
Second hand low (12/13/02)
Setting up a king (1/16/04)
Shit happens (11/22/02)
Shouldn’t happen (my mistake) (11/29/02)
Shuffle, cut and deal (11/3/06)
Six-handed euchre (8/3/12)
So, which black ace do you lead? (3/26/10)
Stealing the deal: Is it “legal”? (3/8/02)
Stealing and stealing the deal (3/15/02)
“Stick the dealer,” part 1 (9/20/02)
“Stick the dealer,” part 2 (9/27/02)
Stone Idiots Nos. 12 & 35 (3/28/03)
Stone idiots Nos. 25 & 26 (6/4/04)
Table talk (7/1/11)
Ten o’clock scholars (2/6/04)
The ten of clubs (8/15/03)
The third-hand loner (12/3/04)
Throwin’ in the cards (5/3/02)
Trump to call (9/13/02)
Trumping a loner (4/11/03)
Trumping partner’s ace (7/4/03)
Trust your partner (7/8/05)
Trust your partner (if you can) (3/14/03)
A 20-card deck? (plus 1) (1/15/10)
Twenty-one card euchre (5/6/05)
Two bar’s ’n’ nothin’ else (3/6/09)
Two lessons . . . : Lead trump . . . (7/14/06)
Two (or more!) bowers in your hand (10/15/04)
Two points for nothing (9/3/04)
Video games (8/25/06)
Underplaying partner’s trump (5/21/04)
Wait for “next” (1/3/03)
Wait for “next,” vol. MDCCXIX (6/3/11)
What to lead (12/6/02)
When your partner fails to “donate” (11/4/05)
The why & how of “next” (8/16/02)
Why euchre is more fun than poker (3/16/07)
Win by two! (3/4/05)
Yahoo whores (10/7/11)
You have a partner (7/6/07)
“Double suited,” part 2 – July 5, 2002
The dealer picks up a club and holds A-
Assume further that the dealer had no good reason to turn down the club.
To me that’s axiomatic: Even if he holds the
jack of hearts and the A-K of clubs with the K-9 of diamonds, I think he must discard the
jack of hearts and pick up the 10 of clubs in most scenarios.
He has no defense to spades, and the discard and pickup make him two-suited with three trump.
The ace of hearts is led; the dealer’s partner is unable to trump, and the dealer takes the trick with the 10 of clubs. And now the question: Does he lead back his ace or king of clubs – to draw trump? Or does he lead the 9 of diamonds – to give his partner a shot, and perhaps to establish his own king? (I forbid him to lead the king of diamonds!)
This hand is not at all unusual. It is similar to a lot of other marginal trump calls. A cabal of euchre players – including a professional mathematician – spent several months on this question, and what follows is what we came up with.
For starters, the probability that the 9 of diamonds will draw the ace of diamonds is approximately, and not more than, three-fourths, which is the approximate probability that the ace is not in the pack. I say “approximate[ly],” and “not more than,” because of (1) the possibilities that the dealer’s partner or the third hand sloughed the ace of diamonds on the first trick, and (2) the possibility that the ace is not the lone diamond in the hand in which it is held, if any, and its use on the second trick would be futile or wasteful (i.e., someone trumped, or second or fourth hand takes the trick with the queen of diamonds).
The probability that the dealer’s partner holds the ace of diamonds is thus approximately, and not more than, one-fourth. But the probability that he will use it is less because of the possibility that the player on the dealer’s left will trump the 9 of diamonds.
And the probability that the player on the dealer’s left will trump the 9 of diamonds is not easy to calculate because it depends not only on his being void in diamonds, and on how many trump he has (if he has any), but on the rank of the trump he has (if any). Since only a 9 led, he might be smart to play second hand low and hold a lone trump on the chance his partner has the ace of diamonds; and he would be foolish to unguard a left bower in this situation. This all is based on an underlying assumption that each player plays his hand the best way possible for his team.
Now to the question of the probability that a trump lead will draw a bower:
The probability that both bowers are in the pack is 3/18 times 2/17 = just a little less than 2 per cent. Thus the probability that a bower is held by an opponent or partner is about 98 per cent. I would say that it is no more than 98 per cent because the club was not ordered.
The probability that a bower will be played on the dealer’s trump lead is 3 or 4 per cent less because of the possibility his partner has three trump with both bowers, or the left bower guarded by one smaller trump. And the probabilities that it will be used by partner or opponent, of course, are less than one-third of the remaining 94 per cent and about two-thirds of that, respectively, or about 25 per cent and 63 per cent, respectively (“approximately” again, of course, because by the time the trick gets to the fourth player, the jig is up; he knows what to do. The reason the dealer’s partner is less likely to trump than an opponent is, of course, that the dealer has led the ace of clubs; and his partner will not lay the left bower on that if he has it guarded).
But other variables that must be considered are (1) whether both bowers are out (probability about five-sixths), (2) whether both will fall on the dealer’s trump lead if both are out, and (3) the relative positional strengths (opponent gets to play last), etc. etc.
All of which makes one wonder whether the empirical approach might be more efficient than mathematical analysis – i.e., play a statistically significant sample of hands twice (once each way) and see what happens.
Harvey Lapp, webmaster of Euchre Central (and “Ask Harv” fame), posited:
|“I would (by instinct) lead the 9 of diamonds.
I also believe that it is the correct call mathematically because there seem to be more
possibilities to succeed by getting the off suit out there.
The perfect scenario would be your partner’s having an ace of diamonds that walks
and a suit lead back that you can ruff.
Making the defenders spend a bower stopping the 9 of diamonds would be probably second
best. The king of diamonds is a nice card
for an end play.
“My friend Henry and I tried a few duplicate style samples of the hand. As with any common hand in euchre, we found that almost anything is possible. Sometimes the maker won and sometimes he got euchred. We tried leading trump and throwing off, but there seems to be no definite answer. I would simply guess that you have a 55 to 60 per cent chance of making a point with the hand, with the play siding in favor of leading the 9 of diamonds.”
|Our mathematician – my little brother the Ph.D. at Motorola, who tells engineers where and when (and how high) to jump (we call him “Dr. Math”) – mused as follows before digging in:|
|“This is reminiscent of what happens to me when I contract to model some
gizmo at work. I always think the model
will be relatively simple. Then, as the
people I contract with start filling me in on gizmo details, I realize how complicated
the model must be. The result for me is always
overly optimistic deadlines that I can’t meet.
“I can see the potential for this problem to grow in complexity very rapidly. And I don’t think we can get a definitive answer soon.”
The opponents’ holding that would most favor leading trump would be an unguarded bower
in each opponent’s hand. And the holding
I most easily envision as almost requiring a trump lead is an unguarded bower in each
opponent’s hand and the ace of diamonds also in one of the two opponents’ hands.
But a 9 of diamonds lead will work even against that if the dealer’s partner can
trump the diamond and neither of the opponents can or does, or if it is the right hand opponent
who has a lone ace of diamonds and the left hand opponent lays down a bower.
But what is the probability each opponent will hold an unguarded bower? If the probability is infinitesimal (definition: Significantly less than 5 per cent), then my conclusion is either (a) lead the 9 of diamonds, or (b) it doesn’t make any difference.
I would have liked to have withheld calculation of the probabilities of the dealer’s partner’s holding as long as possible, but ultimately we could not. E.g., the probability that his partner has a bower is almost 4/15, but a little less, since he didn’t order (I do not factor in the knowledge that the lead opponent holds or held the ace of hearts because only an idiot opponent will lead a bower in this situation). The probability the dealer’s partner has the ace of diamonds is about the same – less than 4/15 because he didn’t order, but a little closer to 4/15 because it was not led.
I e-mailed these thoughts to Dr. Math just to get his juices flowing, and he got definitive. He replied:
|“The probability that neither opponent has a guarded bower is 57 per cent
– which means that 57 per cent of the time, a trump lead will leave the dealer with the
“With that exercise complete, the probability that both opponents hold unguarded bowers (“simultaneous unguarded bowers”) is fairly easy: There are two classes of pairs of opponents’ hands – right bower or left bower in West’s hand. Assume West has the right. The rest of West’s hand is formed by drawing three cards from eight (since none can be a trump). This makes C(8,3) such hands. Then East’s hand is formed by drawing three cards from a deck lacking both trumps and West’s other three cards. This makes C(5,3) hands. So we have C(8,3)C(5,3) pairs of hands with the unguarded right in West’s hand and unguarded left in East’s. Since we have divided the totality of pairs of hands with unguarded bowers into two equally sized classes, the number of such pairs is 2C(8,3)C(5,3). The total number of pairs of any kind is C(15,4)C(11,4), so the probability of simultaneous unguarded bowers is 2C(8,3)C(5,3)/[C(15,4)C(11,4)] = 0.0025.
“Or one-fourth of 1 per cent. Definitely infinitesimal.”
Yeah, that’s infinitesimal. And now it was
all making sense.
And we were back on the precipices of intuition and subliminal perception, as in, “Did the guy on my right raise his left eyebrow, or did I just imagine that?”
Because even though a trump lead would establish high trump in the dealer’s hand 57 per cent of the time, it would do nothing to establish his king of diamonds; and it would guarantee him only two tricks – the one he already had taken with the 10 of clubs on the first lead, and the one he eventually would take with the king of clubs. And it could jerk an unguarded left bower or other lone trump from his partner that his partner could have trumped the 9 of diamonds with.
The quest went on. And it brought the kicker from Dr. Math:
|“I have found that there are few mathematical solutions, but often mathematical guidelines. We could do better by doing some behavior modeling, but our answers would be only as good as our assessment of the behavior. In the engineering world, where I have served for almost 30 years, I have found that the best I can do is put the engineers in the ball park. They do the rest by trial and error. More than two decimal points of accuracy is wasted compute time.”|
OK. We were in the ball park.
Time to play.
As Dr. Math indicated, the question whether to lead the nine of diamonds or a club defies precise mathematical analysis. So while I was corresponding with Dr. Math and Harvey Lapp and others, I was also conducting empirical research – playing hand after hand, both ways, time and again, to see what happened (this was before I discovered Gerry Blue’s Euchre Laboratory. I did it with a real deck of cards, on the kitchen table).
And here are the results: I played 30 samples, each way (60 hands in all) – once with a 9 of diamonds lead, once with a club lead. Playing it “right,” I had 26 winners; I was euchred only four times. Of the 26 winners, however, five depended on leading the 9 of diamonds, and four depended on leading trump (on the other 17 it did not matter). Not real conclusive. We are still looking for volunteers to “go to the ball park” (i.e., the Euchre Lab!) and play 100 hands (twice each; 200 all day).
Now let’s do some really simple math: If you played those 30 hands only one way (i.e., leading the 9 of diamonds or the club), you’d be four or five short of 26 winners (depending on which lead you chose). So, you’d have at least 21 winners, maybe 22. Let’s call it 21-and-a-half.
Almost three-fourths of the time (21.5 divided by 30 equals 71.7 per cent) you’ll be glad you picked up the club for a two-suited shot at a point or two. That's significantly even better than the 55 to 60 per cent success rate predicted by Harvey Lapp and friend. Even if you are euchred 28.3 per cent of the time (8-1/2 out of 30), you are points ahead even if you score only one point every time you are not euchred. And sometimes you will score two.
In the midst of this extended query, I submitted the hand to Joe Andrews for publication in his MSN Zone monthly euchre column. Joe published it (July, 2001), but he missed the bus: He didn’t even get to the ball park! No chance to get in! Joe said you should not pick up the club!
That is absolutely incorrect. The dealer must pick up the club. Picking it up makes him two-suited with three trump. Mathematical analysis and experience both indicate that you will score (which means also, not get euchred) more than 70 per cent of the time if you pick up the club.
And if that’s not enough, there is another, perhaps even more compelling reason to pick it up. If you don’t, you are a sitting duck in “next,” and likely for a loner.
It is important to recognize the power of the deal (Joe seems not to understand this). The dealer’s position in trump is more secure than any other player’s: No one else felt secure enough to order the dealer up on this hand. The danger of finding both bowers on your left lurks, yes; but that’s another good reason not to lead trump: Make the opponent use one of his bowers on your nine of diamonds if you can.
[second of two parts]
Natty Bumppo, author,
|“Double suited,” part 1 – June 28, 2002|
We know that it means holding a hand containing only two suits, and it can be pretty
valuable. My friend Ron told me that if, as
dealer, he holds the ace, king and 10 of diamonds, the queen of clubs and the 10 of hearts,
and he turns up the 10 of clubs, he will pick up the 10 of clubs and discard the 10 of
Well, I don’t think so – unless your opponents have six or seven points and could go out on a loner – or you see your left-hand opponent, who never has managed to hold a poker face, drooling and panting, waiting for you to turn down the heart. Or maybe you are getting your butt kicked 9 to 2, and you have to try something outrageous just to shift the momentum (but if that’s the case, why not go alone with that Q-10 of clubs?!).
Ron made a pretty good pitch, and he’s a good player (58 per cent winning percentage on Yahoo!, with the big boys, last time I looked); but I took his proposition to Gerry Blue’s Euchre Laboratory to test it. I played Ron’s scenario 100 times – playing the opponents’ cards optimally but without taking advantage of the X-ray vision the Euchre Lab gives you (and I threw out the hands on which an opponent obviously would have ordered up the club). These were the results:
|On 36 of the 100 hands, Ron made a point picking up the little club; and on
13 of the hands he made two points – i.e., he scored on 49 hands, or
almost half of them – and he scored big more than an eighth of the time.
It means also, however, that he got euchred 51 per cent of the time.
But also he stopped nine loners held by the opponents, including two hands on which he scored two points – those were 6-point turnarounds! Ron was euchred on the other seven stoppers, saving his team 2 points on each hand.
Also he stopped one lone hand his partner would have made: That one cost his team 3 points.
In sum, Ron scored a net of -23 points in the 100 hands (that’s minus 23, or an average of nearly a fourth of a point lost every time he picked up that 10 of clubs).
Being “two suited” gives you some advantages and a lot of flexibility, but it’s
not everything (this is not to be taken as an endorsement of John Ellis’ book!).
Those nine opponents’ loners stopped out of 100 hands still give Ron a pretty good argument for picking up, however, when his opponents have 6 or 7 points – it’s the Bloomington corollary (see pages 13 and 35, The Columbus Book of Euchre [2nd ed.; pp. 13 and 34, 1st ed.]). And they might give him a good argument for picking up when his team has a big lead to protect – like 8 to 1 or 9 to 2 or 3 – that’s the Bubinski (pp. 13, 34-35, 2nd ed.).
I made one other interesting observation, on which I did not take notes: A few of the euchres (I did not count them) depended on a bold opening trump lead by the left-hand opponent – something he should rarely do. This observation either gives Ron’s weak pickup a little better odds, or lets some of the air out of my recommendation not to lead trump against the opponents. But there weren’t enough euchres depending on bold trump leads to give that recommendation a flat tire. Another study may be needed.
There was one potential euchre that depended on the left hand opponent’s leading a lone ace of trump from a holding of ace of clubs, ace-king of hearts and queen-nine of spades. Such a lead normally would be so stupid that I just did not let him do it; any other lead would have given Ron a point, and I gave him the point. ("Oh?" you say. "I would have led the ace of clubs!"? Go on. Lead it. That’s stupid. That’s my story, and I’m stickin’ to it.)
[first of two parts]
Natty Bumppo, author,
|A Polish “story” – June 21, 2002
Nonetheless, we were up 8 points to 6; I was dealing, and “liywya36” ordered a right bower into my hand – which was good for one of four tricks “nizoski” and I took! (“Liywya36” did have an unguarded left bower, but that’s not what she took her only trick with.) Score 10 to 6, our favor. And “liywya36’s” partner typed:
And I got booted, by unanimous vote of the three other players (“Asshole” was the explanation given on the boot message line). They can do that on Pogo, you know, in the middle of a game, rated or not. They can boot you for having a sense of humor, or for not having a sense of humor. They can boot you for being smart, or for being “dumb” (or for being “smart”). They can boot you for being slow, or for being “fast.” They can boot you for talking too much, or for not talking enough – e.g., for not saying “ncp,” “nsp,” “typ,” etc., etc. I’ve seen it tried. I once got booted from a game on Pogo for being dumb – i.e., for not “chatting” at all (“Doesn’t talk” was the reason given on the message line).
No big deal in this case, you say? Game was over? We had won? Not quite! Turned out, it was an 11-point game! Talk about Polish! (Nah, actually that’s English – and Pennsylvanian. Not even tolerated on Yahoo!) At least that explained “liywya36’s” order – apparently she was intentionally giving up a euchre to prevent my going out on a loner.
I tried to re-enter the game but was booted again immediately, before I could play a single card, or even apologize (which I would not have anyway, of course). So I monitored the game, watched a series of three computers and two real players occupy my chair, and watched “nizoski” gradually lose the game, 11 to 10 (and my rating took a dive with his, of course. That’s the way it works on Pogo).
Well, OK – perhaps my remarks were not “politically correct.” But in many respects I was more “Polish” than “nizoski.” I speak Polish; my wife is Polish (“off the boat”) and does not speak English, and I have a Polish stepdaughter and two Polish grandchildren living in Poland. The other three players had no way of knowing any of those facts but the first, of course; but it had to be obvious to them that I was the only one at the table who knew how to speak Polish. Didn’t all that give me a little license?
|Not the perfect hand – June 14, 2002|
| And the webmaster, Gerry Blue, asks
everyone, “How would you play this hand?”
It is subtler than most hands heading euchre web sites. Gerry doesn’t tell us what was turned, but if we assume it was a heart lower than the right bower, I’d say:
At first hand I pass and wait for a chance to call next (or to euchre the dealer if he picks up).
At second hand I order into my partner’s hand only if we have 8 points or 9 (let him pick it up, for a loner, if we have less; I have “next” covered). If the opponents have a substantial lead, I order and go alone. If the score is close or we have a comfortable lead, I pass.
At third hand I keep my mouth shut: Too good an opportunity to euchre the dealer if he picks up; too likely I’ll get euchred or queer my partner’s “next” call if I order.
As dealer, I pick up and go alone (unless we have 8 or 9 points).
Second round (hearts down):
At first hand, I call next (diamonds) and lead the 10 of clubs. If my partner does not have the ace or a good king of clubs to cash, or a left bower to ruff with sometime in the hand (or another ace or good king off suit that avoids getting trumped), I hope my left hand opponent takes a trick to give me an end play with my right-ace. I am playing for one point, and no more. I need help; I don’t want to bleed my partner’s unguarded left bower if that’s all he has (and, with hearts down, he is more likely to have it than the opponents are), and I am not about to give the opponents an opportunity to go alone in black.
At second or third hand I pass: Too easy to get euchred, too good a chance to euchre the opponents.
Fourth hand is moot: Hearts would not be down.
Those were my “off the cuff” remarks in anwer to Gerry’s question, without application of probability theory or trial and error, based on “Double’s” principle: No time for analysis. But I stood ready to defend all of it. Those were my stories, and I was st-stickin’ to ’em!
But there did come fierce argument from Ryan (“Lead the Right Bower, Damn It!”) Romanik, who stated in regard to my suggestion to lead the 10 of clubs if going “next” in diamonds:
“Disagreed. Right bower lead is ‘best by test.’ If the club is going to find your partner’s ace, it will do it better after all unprotected trump are out of your opponents’ hands. Besides, although you fear the unprotected left in your partner’s hand, remember that since you hold only two trump, the probability that his left is protected soars.
“Furthermore: If your goal is your partner’s ruffing your lead with an unprotected left, you’re better off leading a heart, in my opinion. Four hearts are gone (queen and 10 in your hand, one turned down, and the jack ain’t a heart).”
The problem with Ryan’s reply is that, although he said “best by test,” he did not put it to the test. I did. This hand does not lend itself easily to mathematical analysis; so I took it to Gerry Blue’s Euchre Laboratory and gave it 100 revolutions times three: Once each with a 10 of clubs lead, once each with a heart lead (the queen and 10 are equal in the same hand, since the jack – wherever it may be – is the left bower), and once each with a “Lead the Right, Damn It!” lead. That’s 300 hands played (100 times 3; count ’em) all day (actually it took several days!). And I threw out all hands – “reset the scenario” – on which it would make sense for the dealer to pick up the heart that was turned.
First of all, on more than two-thirds of the hands (69 out of the 100) it did not make any difference what was led: All three ways the maker’s team scored either one point or two points or was euchred.
The broader results: The club lead made a net of 51 points; the heart lead, a net of 45, and the right bower (damn it!), a net of 29 points.
The club lead made 1 point 69 times, made 2 points 11 times, and got euchred 20 times: 69 plus 22 minus 40 = 51.
The heart lead made 1 point 63 times, made 2 points 14 times, and got euchred 23 times: 63 plus 28 minus 46 = 45.
The right bower lead (damn it!) made 1 point 59 times, made 2 points 13 times, and got euchred 28 times: 59 plus 26 minus 56 = 29.
I think it is interesting to note that the offensive totals – i.e., 1-point and 2-point scores combined – were equal for the club lead and the heart lead: 91 points. To me this says that when the heart lead worked, it generally worked better. But it didn’t work as often – 80 to 77 in favor of the club or, to put it the other way, the heart lead got euchred three more times. Even without these results from 100 samples, the reason I lead the club instead of the heart is that it gives my partner two chances: To take it with the ace or king of clubs, or to trump it. I don’t expect the heart lead to survive all three other hands; and since the dealer turned down a heart, I consider him the most likely player to be able to trump it; and he’s sitting in a position to overtrump my partner, or to hold back a trump if my partner plays a bigger trump than the dealer holds.
And I am not at all impressed by leading from a right-ace trump tenace when that is all the trump you have, and you have no aces outside. The right bower lead, like the heart lead, scored more 2-point marches than the club lead did. But it scored only 72 times or, to put it the other way, it got euchred a lot more. “There was a little girl, who had a little curl, right in the middle of her forehead . . . .” This seems to be a trump combination begging to be reserved for end play.
OK, I’ve played enough hands at the Euchre Lab! Lead the 10 of clubs, damn it! That’s my story, and I’m stickin’ to it!
Natty Bumppo, author,
P.S. If it had been a diamond turned down, on second round:
At first or fourth hand, hearts alone.
At second or third hand, hearts with help.
Hearts, any of the four hands. Alone if we really need it, from any of the four positions – depends on the score.
That’s my story, and I’m st-stickin’ to it!
|B Woods’ loner – June 7, 2002|
B held the right, king and nine of hearts and the king and ten of spades.
He took the first trick by ruffing a small diamond with the nine of hearts, and the second by
leading the right bower – catching only the queen and ten of trump.
No spades had shown yet.
Now what to do?
The poll results:
0% B should lead the king of hearts
I voted for leading the ten of spades. I had the advantage (or misfortune) of having played this hand with B Woods, as his partner, and watching him get euchred by leading the king of spades, costing us the game. Before I get to the reasoning behind my vote (yes, there is more than pure emotion), let’s take a look at the other answers.
Having suffered the euchre and the loss with B, I cannot fault the respondents who voted that B should not have gone alone and voted that his partner should shoot him – particularly the latter.
But I don’t really fault B’s going alone. It was a fair chance to win in a heartbeat against the opponents’ 8-to-6 lead. If B’s right bower had dropped the left and ace of trump – or just either one of them – the king and ten of spades would have looked pretty good, particularly in light of B’s right-hand opponent’s having elected not to go “next” with spades.
And it was a reasonable shot at just a point, to keep the third hand from going out in diamonds or spades.
As it happened, B’s lead of the king of spades drew the ace from the opponent on his left; that opponent then led the ace of trump to his partner’s left bower (taking B’s king of trump down with it), and the partner on B’s right then took the euchring trick with the queen of spades (over B’s ten).
There are other ways the disaster could have occurred: For example, the jack of spades would have worked as well as the queen; or the opponent who cashed the ace of spades might have had the jack or queen of spades himself to lead back (or even the nine to be trumped by his partner); or he could have had the left bower to lead, taking B’s king of trump, and then, with or without his partner’s help, cashed diamonds or clubs; or he could have led a club or a diamond to his partner’s trump and the partner could have led the nine of spades back to the first opponent’s trump, etc.
The point is, B had to know he was in trouble when neither the left bower nor the ace of hearts fell to his right bower. At that juncture he had to forget about the loner and concentrate on saving a point (he could still get lucky, but he had to keep his eyes on the prize – the game, and staying in it).
If he had led the king of hearts, he would have had to drop both the left and the ace on one trick, or hope the opponents had only one and not the other, and hope they would lead spades – twice, if they have the ace of spades. If B dropped only one of the two bigger trump with his king of hearts, there would be a fair chance the guy who played it had the other, and no spades, or the ace of spades, or that his partner had the ace of spades, etc. Scratch king of hearts (no one voted for that).
I think B maximizes his chance of saving a point by leading the ten of spades. That forces the ace of spades if it’s unguarded, or guarded only by the nine, making B’s king good if the taker eventually has to lead the nine or his partner winds up with the fourth trick and nothing but a spade to lead. And if the opponent on B’s left is void in spades, he might forget “second hand low” and waste his ace of trump on the ten of spades in his eagerness merely to stop the loner (B’s call could have been a “lone bluff”: See page 47, The Columbus Book of Euchre (2nd ed. The left-hand opponent should be shot, of course, if he plays the left bower on B’s ten of spades).
If the ace takes B’s ten of spades and the opponent leads the ace of trump (as happened), B’s king of spades might have saved the day (if the left bower was led, though, school was out, of course – as it would be if the opponent took the ten of spades with the jack or queen and had the ace to lead back). If the opponent leads another suit his partner cannot trump, B prevails with his king of trump.
The king of spades lead works if both opponents have spades without the ace. The mathematical probability of that is only 8/18, or 44 per cent, but realistic odds are closer to 50-50 given the right-hand opponent’s election not to go “next.”
The king of spades has a fair chance to work if it forces an opponent to trump – but that works only if the opponents have only one trump, or have both but no opportunity to draw or overtrump B’s king of hearts, or have to lead the nine of spades back to B’s ten.
All I am saying is, leading the ten of spades is more likely to set up the king as a winner than the king is to set up the ten. The ten is almost as likely as the king to force a trump. And the ten will not suggest that you have another spade to any but a sophisticated opponent; so it gives a fair chance of getting spades led back.
I think the king of hearts is the second most reasonable lead, on the hope the left and ace are in partner’s hand or the deck, or that someone will eventually have to lead to the king of spades. It is a lot to hope for the spades to take two tricks even if you get the trump out first (i.e., it was a “long shot” loner in the first place), and it is just too much to hope that both the kings of hearts and spades are good when you have not seen the left or ace of trump or a single spade after two tricks.
But I am going to let Gerry Blue, the EuchreScience webmaster and inventor of the Euchre Laboratory – where this hand is set up for you and you can play it out – have the last word. He voted for the king of spades lead, and would again. He voted also that B should not have gone alone.
Gerry agreed that there was a reasonable shot at one point, “especially with help. Pretty decent shot at two points with help. That would have tied up the game, and then while the opponents are distracted by your berating B for not going alone, he’s stealing the deal.”
“I toyed with leading the ten of spades but decided on the king because I think the ten is unlikely to force out the ace of spades. If I’m an opponent and B leads the ten and I hold the ace-queen, I’m going to play the queen even if I sit to B’s left, since he’s going alone. I don’t have to beat my partner, just the ten. That leaves me with an ace still in my hand, which always feels good. I’ve stopped the loner and am now shifting gears to focus on the euchre (and the game).
“And if I’m on the left and void in spades, I’m thinking B’s sweating if he’s leading an offsuit ten in a loner; so I’ll throw off and look for my partner to take the trick with a higher spade or a trump. Then I’ll have the end play on the next trick. If, however, B leads the king, I have to seriously consider playing my ace of trump if I have that and not the left bower. My primary goal is to stop the loner.
“The ten is almost as likely as the king to force a trump but not quite. When I put myself in the shoes of the player to B’s left, I have a much different reaction to a ten than I do to a king. The ten indicates to me that B’s in panic mode and worried about getting euchred, while the king gives me the impression he doesn’t have the left but probably does have the ace or king of trump (but not both, or he would have led one of them).”
There are too many variables here to pin this hand down with mathematical probabilities, and you can argue with us and our reasoning all you want. I love to argue. It’s my job.
But you can’t argue with B Woods. He’s dead.
Natty Bumppo, author,
|The “perfect” hand – May 24, 2002|
Harvey Lapp, Euchre Central
webmaster and author of the “Dear Abby”ish euchre advice column “Ask Harv,” forwarded the
following query to me:|
“Here is a question I received that I also would be interested in finding out the answer to. Perhaps Dr. Math knows?” [Dr. Math is my brother the mathematics Ph.D. at Motorola who tells the engineers to jump, and how high.]
A . . . A . . .
Well, I said, shucks, Harv, I think I can do this without Dr. Math (oops!
Thought I could! But I ran it by Dr. Math first,
and he caught a mistake I made. Another mistake
was caught July 21, 2003, by a reader, Eric Reid; and the original of this column
has been revised to take his correction into account.
Here is the corrected poop).
Start with any jack: The probability of getting a jackless hand is 20/24 times 19/23 times 18/22 times 17/21 times 16/20 equals 36.48 per cent; so the probability of getting a jack is the complement of that, 63.52 per cent (another way to look at this is that if you hold a hand without a jack, that’s fairly unlucky).
Now we need the other jack, same color. Four chances out of 23, 4/23. So, the probability of holding both bowers – if their color becomes trump – is 4/23 of 63½ per cent equals 11.05 per cent. Not so rare – a little better than one in ten (but keep in mind, for more than three out of four of the scenarios depicted below, it depends on everyone else’ keeping his mouth shut – i.e., not ordering or calling trump before you get the opportunity. Not presently practically calculable, even in the 21st century).
And on down:
|Ace of suit, three out of 22; all three, 3/22 of 11.05 per cent
equals 1.5 per cent (thus you have about one chance in sixty-seven of getting the top
three cards of a suit).
King of suit, 2/21; all four, 2/21 of 1.5 per cent equals 0.14 per cent – (one chance in 714 of getting the top four).
And queen, 1/20; all five, 1/20 of 0.14 per cent equals 0.007 per cent – i.e., less than a hundredth of 1 per cent, or a little less than one chance out of 14,000 hands of getting a “perfect” hand (without consideration of the suit turned or another player’s making trump. N.B.: The original calculation, before Mr. Reid’s correction, was 0.009 per cent, or one chance in a little over 11,000 hands).
|But let’s back up a little. You don’t need the king or queen for a “perfect” hand. Both bowers and ace and any two other trump constitute a perfect hand: Played correctly (i.e., ruffing with a bower or ace if it is necessary to ruff), such a hand cannot fail to take all five tricks, from any position. So:|
|Fourth trump, 4, not 2, out of 21:
4/21 of 1.5 per cent equals 0.29 per cent – i.e., there is
about one chance in 266 hands of getting the top three cards plus one in a suit.
Fifth trump: 3/20 of 0.29 per cent equals 0.043 per cent – i.e., the probability that you will get a “perfect” hand (but not necessarily a royal flush) is once in every 2,323 hands (again, without consideration of the suit turned or another player’s making trump. N.B.: The original calculation, before Mr. Reid’s correction, was 0.06 per cent, or once in every 1,771 hands).
Now, that does not seem amazingly rare to me, and especially considering this:
A typical game consists of ten hands or more (it would take Dr. Math to
give us a mean of hands per game, but consider:
Three hands is the minimum for a game, and that is quite rare; nineteen is the maximum,
and that is probably even rarer. And it all
depends on the aggressiveness of the players, which is not calculable except statistically:
What does it take to get them to go alone? How
willing are they to risk being euchred?).
Let’s take 10 for a conservative average of hands per game.
If you play ten games of euchre a day (not an awful lot for a euchreholic, particularly for an internet euchreholic), that’s a hundred hands a day. At that rate you will get a “perfect hand” every 23.23 days – i.e., roughly once every three weeks.
If your correspondent still insists on euchre’s version of a “royal flush” (i.e., two jacks, no ten and no nine), he’ll still get his “perfect hand"“ once every 140 days, or nearly three a year.
Now, just for fun and nausea, let’s revisit that “perfect hand” one more time:
Actually, only the player to the left of the dealer can get a “perfect” hand, because of the possibility of sabotage – intentional or accidental – in the making of trump (i.e., someone else’ ordering or calling before you get the chance).
And because the player to the left of the dealer has the lead, all he needs is either (1) the two bowers and ace and any other trump plus a suit ace, or (2) the two bowers and any three other trump. Those – held by the player left of the dealer, and only by that player – are the real “perfect hands.” But he needs also the right suit turned.
The combined probability of J-J-A-x-x (all trump) and J-J-A-x + A (four trump plus outside ace) – with the probability that the dealer will turn a card of the desired suit factored in – is 0.00707 per cent, or once in every 14,144 hands – once every 141 days at ten games a day; you’ll get about two-and-a-half such hands a year.
But then you have to divide by four because you sit to the left of the dealer only a fourth of the time. That makes the probability 0.00176 per cent, or once in every 56,818 hands. By this definition you will get a “real” perfect hand about every 568 days – i.e., about every year-and-a-half (if you play ten games of euchre every day for a year-and-a-half!).
[Caveat: Some of the decimal numbers above are rounded slightly; so you won’t get the exact results I got if you crunch them.]
Natty Bumppo, author,
P.S. Where does one give “speeches” on euchre???!!!
|Leading before the discard:
The “Muncie ploy" and the "Brownstown maneuver" – May 17, 2002
The “Muncie ploy” – pages 19, 50-51, The Columbus Book of Euchre (2nd ed.) – consists of leading before the discard, to prevent the dealer’s calling alone in time (once play begins, it is too late to declare alone).
The “Brownstown maneuver” – pages 13, 38, 51 (see also the New Appendix to The Columbus Book of Euchre, on line) – is the same thing by the dealer’s partner when the third hand has declared alone – to give the dealer an idea what to discard. Conversely, the dealer should wait for the lead before he throws off.
Ryan Romanik wrote from Michigan:
Some of your ploys seem a little shaky as far as being actually legal according to the rules of euchre. For example, I had a hard time convincing my playing group that the Brownstown maneuver was actually legal, until I found the clause in the “official” rules that if a card is led out of turn, it is placed face up, etc.
My question is: Is there similar justification for the Muncie ploy? In other words, why is it that just because you’ve led out of turn I lose my opportunity to call alone? Since the lead is out of turn nonetheless, why does it move the dealer from the “calling trump” stage to the “discarding” stage?
Natty Bumppo replies:
First of all, you have hit upon some of the differences between the way euchre is played in Michigan and the way it is played in Southern Indiana! But seriously:
As for the Muncie ploy, you should have no trouble finding a rule – or at least a consensus – that a loner must be declared before the first card is played. See page 141, Official Rules of Card Games (71st ed., United States Playing Card Company, Cincinnati, 1990).
I, too, have had trouble convincing my friends of the legality of the Brownstown maneuver. In fact, in the circle I play in, my house (just outside Brownsville, Ky.) is the only one in which the “maneuver” is allowed.
But both ploys are “legal,” and the reason is that neither is “illegal.” Neither of those ploys is a “lead out of turn.” It is the leader’s “turn” to lead, in both instances. He just leads before the discard. You will not easily find a rule requiring the discard to be made before the lead, or requiring the leader to wait for the discard (you certainly won’t in the Official Rules of Card Games).
And, just like drinking Postum, there’s a reason: As for the Muncie ploy, it is normally not to the leader’s advantage to lead before the discard. Normally, it is greatly to his disadvantage. So, it does not need a rule of prohibition.
And so, then, why shouldn’t an alert player in the lead take advantage of the sloth or ineptitude of an unalert dealer? After all, the dealer has an absolutely peremptory antidote – he merely declares alone before he touches the turned card (or before he calls the suit, if on second round). That’s the “Milroy squelch” (pages 19 and 51).
The Brownstown maneuver likewise is not a “lead out of turn.” And it is legal simply because it is not prohibited. It has nothing to do with the rules regarding “leads out of turn.” (Obviously, it took some smart ass lawyer to figure this one out. Guess what the author’s day job is.)
Natty Bumppo, author,
|Playsite, Pogo, and the St. Louis Browns
– May 10, 2002
To the best of my knowledge, Playsite never had the TRAM option. They have the option, as you know, of “auto play” if there’s only one legal play you can make.
I prefer Playsite. None of the euchre sites on line has all my favorite options; but, all things considered, Playsite appeals to me the most. I like the user interface at Pogo the best, but I’m not crazy about their ranking logic. It seems to be based on the number of games won versus the games played, where Playsite bases the change in your rating on the rating of those you beat. I also like being able to go alone if my partner orders up the right when I’m the dealer. I suppose I like a few of the fringe rules such as “shaft the dealer” and defending alone. I also like being able to select the card I intend to play before it’s my turn. But I do wish Playsite didn’t force everyone to leave the table and create a new one after each game, and I also wish watchers could kibitz.
Gerry Blue, inventor, the Euchre Laboratory
Natty Bumppo replies:
Thanks for your critique. It seems that we are in agreement on many features of both Pogo and Playsite.
Playsite did have TRAM, I am pretty sure, when I first encountered it four or five years ago. I like the “auto play” feature, but I just cannot get used to that retarded requirement of deselecting the card picked up before you can select one to discard.
And I don’t like Playsite’s “go alone” option, that not only allows a dealer to save a loner from a “non-Canadian” partner, but also allows one to defend alone on an ordinary call: That discourages the “Columbus coup” – ordering or calling with the intention of getting euchred, to pre-empt an opponent’s loner.
It might be acceptable if it would give the maker four points if he does not get euchred, but it doesn’t. It would be acceptable if it were a game “option,” but it’s not; it’s standard on Playsite. Pogo, to its credit, at least makes “defend alone” optional; and Yahoo!, to its greater credit, does not countenance “defending alone” at all. The only time defending alone makes sense in traditional euchre is when the maker is going alone; and none of the sites gives you that option.
I agree that Pogo has the friendliest and most logical user interface – among Yahoo!, Playsite and Pogo, for example, only Pogo makes it clear when someone is going alone. Pogo has the friendliest graphics also (maybe this is part of the same thing), and it is much easier to get a game started on Pogo than it is on Yahoo! Maybe these are the basic reasons I generally prefer to play on Pogo, even though I pan it severely on Borf Books’ Euchre links page and recommend Yahoo!
But Pogo’s allowance of “booting” by unanimous vote of other players (all of whom may be ignoramuses) is even more annoying and frustrating than the card deselection requirement on Playsite.
And the rating systems on all the sites are flawed. Pogo’s works like Yahoo!’s the best I can tell (one of them copied it from the other, and so did Playsite; I forget who had it first): The main consideration is one partnership’s average of ratings compared to the other’s: The higher rated partnership will gain less for a win, drop more for a loss, and vice versa.
The only way the number of games played comes in is that it takes a while to work your way up from the initial low rating. I would have no problem with that if that were all there was to it. The number of games played is not a ratings factor in itself. It goes back to the comparative rating factor I disapprove of: You have played few games; therefore you have a low rating; therefore you will gain more if you win than you will lose if you lose, and your higher rated opponents will lose more if they lose, gain less if they win.
The purpose of weighting results (on the basis of comparison of the two game partnerships’ average ratings) is commendable – to keep players from enhancing their ratings by continually beating up on incompetents – but it just doesn’t work fairly; and it discourages mixing players of different levels. How is one to get ahead if he can’t get into a game with other good players (or rig his rating with mutually consenting “lambs and lions” teams)? Just dumbing down the system to equal additions and deductions for wins and losses, regardless of the relative rankings, would be fairer in the long run.
Let’s think about it. Regardless of what happened in the past, the New York Yankees and the St. Louis Browns started even every April. And even in September, when the Yankees were always in first place and the Browns always in last place, if the Browns beat the Yanks they would not gain more than a game on them in the standings, and the Yanks would not lose more than a game. So, what’s with Yahoo!, Pogo and Playsite? They know better than the American League? Give us a break!
Natty Bumppo, author,
|Throwin’ in the cards – May 3, 2002
I’ve been taking an interest in euchre psychology – i.e., watching my opponents and partners’ reactions etc. to their cards and to other players, and factoring them into my decisions. And recently I had a thought about “throwing in the cards.”
Normally when I’m playing serious euchre with my friends, we play pretty fast. And when someone has cards in his hand that will dictate the outcome of the hand, he’ll “toss ’em in” – and we’ll get on with the next hand.
But playing in a local tournament it occurred to me: If you always do that, an attentive opponent will notice and adjust accordingly. My attentive opponent will know, say, when I don’t throw in my right bower after my partner and I have taken two tricks and our opponents have one, that I don’t have it; and that’s a fact he can take into consideration in the remainder of the play.
“Throwing in the cards” is real life’s equivalent of “TRAM” (you do know “TRAM,” don’t you? It’s the acronym of “The rest are mine,” the automation feature that “swooshes” the cards on Pogo when the outcome of a hand is determined). The failure to “swoosh” sometimes tips a hand, too, as pointed out in my critique of euchre on line on Borf Books’ euchre links page.
Ryan gives us a good example. If his opponents have taken the third trick after he and his partner have taken two, and he does not immediately claim his third trick if that is his wont, the opponents can lead trump with abandon, on the assumption that one of them has the “boss” – to capture the remainder of Ryan and his partner’s trump (if Ryan’s partner has the boss, school is out anyway; the opponents lose nothing by their boldness).
But another reader, David Lin, pointed out on July 21, 2003, that that is the defenders’ correct assumption anyway, with the trick score 2 to 1, whether or not the maker “throws in” the cards – the defenders have to have the “boss” at that point to score a euchre.
But the failure to “throw in,” if that is customary, is encouragement for one opponent to ruff low on the fourth trick on the assumption that his partner has the fifth trick locked up with the boss.
“Tipped hands” are rare, however. The main reason not to “throw the cards in” (which my buddies and I do all the time, by the way!) is that it may prevent an audit in the event of a dispute (who took what?). So it is a particularly bad practice in tournament or money play, or when players are drinking too much (which my buddies and I do all the time, by the way!).
So, yes – play it out.
(The remedy “to play out every hand” reminds me of my admonition either to sort your cards constantly or never to sort them at all: See “Don’t sort your cards,” p. 41, The Columbus Book of Euchre, and at the New Appendix on line.)
Natty Bumppo, author,
Ryan gets in the last word (almost):
Another reason not to “toss ’em in” or “TRAM”: It doesn’t give your opponents enough chance to renege. Sure, serious players shouldn’t make that mistake; but they do, and if you’re playing with and against people who can’t even hold their cards straight, there’s a 2-to-1 chance the reneger will be your opponent (not to mention that nitwit opponents might not catch your partner reneging anyway!).
Good point! Same reason you sometimes defend alone against a loner when you have one sure trick but not much chance at another: If the loner reneges, you get 4 points. Page 38, The Columbus Book of Euchre.
Natty Bumppo, author,
The A-K-10-9 loner revisited – April 19, 2002
A critic wrote in response to last
week’s column, “The odds that the
bowers both are not in your oppo-
nents’ hand are 8/18 times 8/18 =
.198 or about 20 per cent.”
My adviser “Dr. Math” says that the probability actually is 8/18
times 7/17 = 18.3 per cent (which is the complement of the 81.7 per
cent probability he gave that the opponents have a bower).
In other words, the critic has given my A-K-10-9 loner a slightly better chance of success
than I did.
We are not in serious disagreement on the math. I disagree only with the critic’s conclusion that going alone on this holding is risky and likely to be wasteful. The probability of getting euchred when you hold four trump headed by the ace or left bower is infinitesimal, and the probability your partner can help you is even slighter (here I included in the calculation the no small likelihood your partner can even hurt you, by trumping the first trick and leading back a suit on which you can be overtrumped).
The critic inlcuded in his discussion the possibility and probabilities of throwing a loser on partner’s ace; but the hand I posited included an outside ace – it did not have any “losers.”
The score does make a difference, as he said. I have pointed out consistently that there are loners worth attempting at 6 points or fewer, but not at 7, and that there are risks you must not take when your opponents have 8 points. There are other considerations of score, numerous enough to merit entirely separate discussions.
But there is no real risk of being euchred in the four-trump hands that were posited (a four-trump holding headed by a king is another matter).
The critic said my remark “Lead next against a loner” was “way too simple,” and he is right. I just threw that in to make a minor point as briefly as I could. What to lead against a loner depends on what else you hold, whether your partner gets to play behind the loner on the first trick, whether your partner was ordered, and a few other things, and is another subject best left to separate discussion – as are other subjects raised, including why not to turn down a bower, and when to “swing for the fences” with a lone king of trump.
The critic and I agree on a lot more than we disagree on – e.g., as he responded to his own critic (and I am paraphrasing): If you like to play euchre just for fun and socialization, without thinking about what you are doing, that’s OK – but not in the advanced lounges.
Natty Bumppo, author,
Just an opinion on your recent es-
|Natty Bumppo replies:
I agree that Ron should have taken the dealer’s ace of trump with his guarded left bower; but I do not agree that ace, king, 10 and 9 are not enough to go alone on – regardless of partner’s pass. This is timidity of the type voiced by Tom Gallagher and Joe Andrews.
It’s more than plenty to go alone on. See pages 44-46 of the Columbus Book of Euchre, which include several scenarios in which to go alone on marginal holdings (even with a lone king of trump, which I have done, successfully, more than once). It takes special circumstances in position, score and configuration; and it is important to have a pretty sure point if you don’t sweep.
And an intelligent partner, sitting opposite the dealer, will sit on a marginally good hand – even a hand with a bower – for the very purpose of preserving his partner’s opportunity to go alone. This is the strategy behind the Canadian rule that requires the dealer’s partner to go alone if he orders up at all.
It is the strategy also behind my own double-edged precept (1) never to order a bower to your partner (unless you are going alone yourself) and (2) never to turn down a bower (unless you have all three other suits stopped. The first precept does not apply, of course, when you have 8 or 9 points; and the second does not apply when the opponents have 8).
Natty Bumppo, author,
I didn’t mean to imply that the dealer couldn’t or shouldn’t have gone alone with that hand, but only that Ron should have assumed that the dealer had the right and should have taken the first trick to stop the loner.
I will add that my response was largely based on the score given (5-4), and on the rules my group plays under: No matter who orders trump, the dealer has the option of playing alone. I have been playing that way for 5-6 years, and that influenced my response with reference to the dealer’s partner’s passing.
If I were dealer, I would not have gone alone with the hand presented. I am not a college professor, nor a statistician. But I’ve been playing for some 45 years, and somewhere deep inside are the probability factors and percentages (without necessarily recognizing them as such or being able to recall them as a specific number), as well as a bit of experience and intuition. My internal probability “experience” says that the dealer’s chances of making that loner are very, very slim, and at or nearly equal to his chance of getting set. And, at a score of 5-4, he should have taken his partner with him. On the other hand, if the score were a wider margin, such as 6-3 or 7-4 or less, going alone would probably have been worth the risk. At that point, getting set still leaves the dealer’s side with score advantage.
Well, let’s analyze that, mathematically. Let’s use the same approach we used last week on Gerry Blue’s five-trump hand headed by a left bower.
The proposition is that the dealer has picked up the turned card and holds four trump headed by an ace, with an ace off suit. It makes a difference whether the off ace is next or not (better if it isn’t); but, just to make the loner a little more difficult, let’s give the hand the ace in next.
Now: I say the probability the opponents have at least one of the two bowers is 2/18 + 2/16 + 2/14 + 2/12 + 2/10 = 74.56 per cent.
But my brother, Dr. Math, the Ph.D. who tells engineers at Motorola where (and when) to get off, says it’s not that simple, and that the probability is 81.7 per cent. And I’m going to take his word for it! Not because I love him, but because I respect him.
So, for starters, the probability of making the loner is a little over 18 per cent – I never promised you a rose garden, but – not bad odds, in my view, considering (a) the virtual certainty of scoring 1 point, (b) the small likelihood your partner could help you score 2, (c) the possibility your partner could even hurt you by taking the first trick and leading back a suit the opponents could overtrump you on, and (d) the payoff if you make the loner – which we will get to.
Then factor in the possibility the ace off suit gets trumped. The lead player would have to have a card in next, and his partner would have to be void. The probability of the void is 14/18 x 13/17 x 12/16 x 11/15 x 10/14 = 23.37 per cent, and the probability the first partner has one to lead is the complement of that, 76.63 per cent. The probability it can happen, then, is the product of those two probabilities, or 17.91 per cent; and that also is approximately the probability it will happen if the lead opponent has any sense (“Lead next against a loner”).
But you don’t add that 17.91 per cent to the 81.7 per cent probability that your opponents have at least one bower, because the two scenarios are not mutually exclusive. What you do is reduce the 17.91 per cent to 3.28 per cent, by multiplying the 17.91 per cent by the 18.3 per cent probability your opponents do not have a bower, and then add the 3.28 per cent to the 81.7 per cent for an 84.98 per cent probability that your opponents will stop the loner – meaning that your probability of making the loner is just a little over 15 per cent.
Other variables, not determinable by math, obtain: How good are the other players? Is either of them distracted – perhaps worried about whom his wife is with? I am very pleased with a 15 per cent probability of making the loner, considering everything, of which there is more to come.
Now, let’s consider the probability of getting euchred. That would require:
1. That the opponents have both bowers. The probability: 10/18 x 9/17 = 29.41 per cent.
2. That the opponents will be able to play the bowers on separate tricks. The probability that either opponent has two trump (i.e., a guarded bower) is 15/18 x 8/17 = 39.2 per cent. This also is the maximum probability that both bowers will not fall on one trick (accidents can happen) even if the opponent’s partner has the third trump, the probability of which is 5/16 of that 39.2 per cent = 12.25 per cent (which also is the probability the opponents hold all three trump against you). The probability that both bowers are in one opponent’s hand is 10/18 x 4/17 = 13.07 per cent. Since these lower percentages are included in the 39.2 per cent, the 39.2 per cent will be the factor used.
3. That the opponents trump your ace of next (17.91 per cent, as we saw above) – and that they don’t have to use a bower to do so: So, cut that 17.91 per cent by a factor of 10/18, to 9.95 per cent.
The upshot: 29.7 per cent times 39.2 per cent times 9.95 per cent equals a probability of 1.16 per cent of being euchred – just slightly over one in a hundred, if you prefer not to think in percentages.
Your experience says the dealer’s chance of making the loner is slim and nearly equal to his chance of getting set? Looks closer to 15 to 1 in favor of the loner to me. And a pretty sure point, with or without your partner (who, as I pointed out, is as likely to hurt you as help you).
Now, as we did with Gerry Blue’s 5-trump hand a week ago, let’s look at the payoff if we take all five tricks: There is only a 100 per cent bonus if you march with help (2 points as opposed to 1, or 1 extra point); there is a 300 per cent bonus if you march alone (4 points instead of 1, or 3 extra points). That’s 3 to 1.
I will take a 3 to 1 bet with 3 chances in 20 to make it (15 per cent) – and less than 2 chances in 100 of losing it (i.e., getting euchred) – one hundred times out of a hundred (as Gerry Blue might say).
And I don’t care if my opponents have 8 points. If they have what it takes to euchre me, they have what it takes to euchre me and my partner together. They’re just not going to euchre me with only one bower.
[second of two parts]
Natty Bumppo, author,
Odds & probabilities, part 1 – April 5, 2002
I am always impressed by Natty
Natty Bumppo replies:
Ha! Ha! Thanks, Carl! One at a time! I have no master list.
There’s a three-page table of “euchre odds and percentages” in Joseph P. Wergin’s book Euchre According to Wergin – but as I have pointed out elsewhere, although it seems arcane, it’s merely simple probability theory taught in freshman math. Tom Gallagher’s book also contains stats and tables, but a number of them are wrong.
Natty Bumppo, author,
Gerry Blue, EuchreScience webmaster, wrote:
This reminds me of an exchange I had a couple of years ago when I first started playing on line. I was the dealer and went alone on a hand with five trump, left high. One of my opponents was amazed that I would be so stupid as to attempt to go alone without the right bower.
I suggested to her that the odds were pretty good that the right was in my partner’s hand or buried. She insisted that the odds were 2 to 1 against that.
There are 24 cards in the deck, and there were 18 unaccounted for – three buried (I had seen the fourth in the pack because it was my discard), five in my partner’s hand, and ten in the opponent’s hands. I’m no mathmetician, but it seems to me that the odds are 5 to 4 (10 to 8) that the right is in one of my opponent’s hands. The odds are against me, but just barely. Since there is absolutely no way I can get euchred with five trump, it seemed like a pretty sure bet to me – a bet I’ll jump on 100 times out of 100 (my loner attempt was successful, by the way. And the woman said I was lucky!).
Gerry Blue, inventor, the Euchre Laboratory
Exactly, Gerry: Odds 5 to 4. Translated to probabilities, that’s 55.5 per cent your opponents have the right bower (10/18), only 27.75 per cent your partner has it (5/18. This is what I mean by “freshman math”).
And your partner cannot help you even if she has the right bower. So you are effectively going alone whether you call it alone or not. In fact, your partner can even hurt you if you leave her in – by taking the first trick and leading a suit an opponent can overtrump you on.
So you’re right. Me, too – one hundred times out of a hundred I’ll go alone on five trump with the left, and ninety-nine times out of a hundred even when I don’t have either bower. Still no way to get euchred. (The time I won’t go alone – besides when I have 9 points – is when I know my opponents have the left bower and my partner has the right – i.e., some cards have been exposed; maybe the turn card was one of them).
Yes, your probability of taking all five tricks is less than 50 per cent. But if you have the left bower, the probability of getting help from your partner is less than zero. And if you don’t have the left bower, the probability of getting help from your partner still is not even 17 per cent (10/18 probability opponents have left bower times 5/17 remaining probability your partner has the right bower = 16.33986 per cent).
Now, compare those probabilities to the potential bonuses: Only a 100 per cent bonus if you march with help (2 points as opposed to 1), to 300 per cent if you march alone (4 points instead of 1). That’s 3 to 1 – and I will take a 3 to 1 bet with a less than 17 per cent chance of failure one hundred times out of a hundred!
[first of two parts]
Natty Bumppo, author,
Borf Books http://www.borfents.com
[NEXT: Why probabilities dictate going alone with ace-high trump in “Dumb’s” hand in “Dumb and Dumber.”]
|“Dumb and Dumber” – March 29, 2002|
Ron, on my right, holds left-queen of
trump (i.e. the jack of hearts and queen
of diamonds), the queen of clubs, and
the king and ten of hearts..
Ron’s partner leads the king of spades, Ron sloughs the ten of
hearts, and I take the trick with the nine of diamonds.
Dyslexic, vision-impaired, drunk, and otherwise impaired with attention deficit disorder (i.e., thinking it is the left-ace I hold, not the right-ace), I lead back the ace of diamonds.
And Ron, thinking I don’t have the right bower, and hoping to euchre me, ducks with the queen (unguarding his left bower).
I then lead the right, taking Ron’s left, and cash my clubs for four points.
1. Was Ron a stone idiot for unguarding his left bower?
2. Was I “brilliant” (unconsciously, ha! ha!) in getting Ron to unguard his left bower?
Natty Bumppo, author,
Ryan Romanik said:
You left out a vital piece of information: Did Ron’s partner follow suit on your trump lead?
If so, Ron’s partner might have been holding back the right bower in hope of euchre – and by not following the maxim “Take tricks, idiot,” Ron may have queered a euchre.
But if his partner did not follow suit on the trump lead, Ron’s reasoning was sound. When making educated guesses about a good player’s hand, you must assume best possible play. Ron assumed you had ace-high trump, he hoped your trump were only three (and he was right about that), he hoped his king of hearts was good (and he was right about that if you led a low trump back to him), and he hoped his queen of clubs was good or his partner had the ace (wrongo, bongo; but nice try, Ron).
Now, were you brilliant? Probably not! However:
In chess, you are taught to play the board, not the player. Not so in euchre. A ploy to get Ron to drop his guard would be sound if (a) you knew or had good reason to believe he had a guarded left (maybe he didn’t hold his cards back? His left eyebrow twitches whenever he holds a guarded left against a loner?) and (b) you are familiar enough with his play that you know he will duck your ace of trump.
Agreed: If Ron’s partner plays trump (other than right bower), Ron has to take the trick.
And we need to give Ron a little credit for knowing his opponent, too: He knows I won’t hesitate to go alone with ace high trump.
But I know he knows that, which gives me greater justification for my “countersandbag” lead (can we call it that?)! Uh, oh, it’s gettin’ sorta slippery here! How many angels can dance on the head of a pin?
The noted euchre webmaster “Double” says:
I guess the reason I don’t usually partake in questions and answers in euchre is because there are so many variables that often it’s not a case of right or wrong but a case of being able to dissect every variable, determine the odds, and then make a decision as to which play or strategy was the correct one. By the time this old “stoner” gets done doing this, he could have played two games and either had his female opponents’ clothes halfway off or money in his pocket! Hindsight is 20/20, and “if” is one of the largest words in the English language; and one of my region’s favorite sayings is, “We know that now, don’t we?”
Sometimes making a “stupid” play work will earn the favor of Lady Luck, causing her to switch sides; and when that happens, it’s brilliant.
But, what’s the score????
Ron is a stone idiot if the loner ends the game. In that case under no circumstances should he have unguarded his left bower. If the score is Ron and me 7, 8 or 9, and you and your partner 6 or 7, then my friend Ron just bought himself an introduction to my friend “.38,” who resides inside my left boot waiting for thugs and the criminally stupid.
But if it was a last ditch effort to turn the game around, that’s another story. Sometimes you just have to try to make things happen. If the score is 7 to 0 or 7 to 1 against Ron and his partner, why not try to dazzle Lady Luck with something brilliantly stupid or stupidly brilliant that actually has a chance of working? If it fails – as it did, in this case – Ron gets the ass-kicking over with a little quicker, and you can start afresh.
Double, “There is no other card game”
Good point. The score in this game was 5 to 4. I agree that if we’re behind, say, 7 to 1, there might be more justification for my “countersandbag”; and if Ron’s team is behind 5 to 1 or 7 to 1, there might be more justification for his sandbag.
Yes, I said 7 to 1. Even when my partner and I could go out with a loner, if Ron and his partner are that far behind. No big loss, as you say; it gets the ass-whoopin’ over with, and – there would be a huge psychological value in a euchre at that score, that might last well beyond that game itself.
But not at 6 to 1. At 6 to 1 it’s on the margin: My bonus for a lone march is a time-and-a-half greater at 6 (300 per cent) than at 7 (200 per cent), and Ron’s partner is much less likely to forgive him for letting me go out from 6 than for letting me go out from 7.
By the same reasoning, my going alone at 6 is likelier to be riskier, and at 7 likelier to be a sure thing. But by leading the ace I did not play it like a sure thing, giving Ron additional reason to believe he can euchre me. At 7 to 1, I don’t think I should go alone in the first place on that hand.
You was absolutely brilliant in taking the guarded left – which, by the way, to me is damn near as good as winning the game. When Edmond penned the rules, he didn’t mention that if you take a guarded left out of someone’s hand you automatically win the game because he knew there were guys out there like Ron who are capable of playing above the game.
Double, “There is no other card game”
Ha! Ha! Funny way to spell “brilliant”: S - T - O - N - E - D.
What about the probability the left will be unguarded? Approximately 5 in 9 times it will be in their hands, and the chances of its being guarded are not exactly extraordinary, since you know where three of the trump are. Plus, factor in the chance of your bluff’s failing.
The probability of either Ron’s or his partner’s holding a guarded left is 13.07189 per cent, to be exact (10/18 x 4/17). Not “extraordinary,” but substantial.
The probability my “countersandbag” fails is pretty high – 86.92811 per cent (100% minus 13.07189%) times the psychological probability Ron will decide not to sandbag (a probability we may not be able to calculate without access to his privileged psychiatric treatment records). All day, I would say, the probability the countersandbag will fail is in the neighborhood of 75 to 86 per cent (and probably closer to 86 per cent). This is the “dumb” of “dumb and dumber”!
Which brings back Double’s deeper and longer term psychological considerations. Let’s say Ron has been sandbagging and undercutting my ass all day, and becoming quite boastful (and obnoxious) about it. This is my opportunity to neuter him – to shut him up for good, even. Maybe worth the risk. If it doesn’t work, no big deal – it’s merely another coup for Ron.
Gerry Blue, EuchreScience webmaster, asks only:
Did Ron get up off the floor yet?
Gerry Blue, inventor, the Euchre Laboratory
Lucky fella! Billy forgot to load his pistol.
Pontificators like the ubiquitous Joe Andrews will tell you that they know how to play this hand, and they will tell you how to play the hand.
Philosophers like Ryan Romanik, Double, and Gerry Blue will tell you that they don’t know how to play a hand like this without knowing the score and without knowing with whom they are playing.
Natty Bumppo, author,
|Euchre on line
– March 22, 2002
I was introduced to euchre while going to school at Michigan State and have missed it terribly since moving back to California. There’s not a lot of euchre players out here. I’ve tried to teach my wife, but wives seem to be unteachable. When the internet began to blossom and I discovered euchre on Excite (now Pogo), I was hooked.
But I’d prefer to sit at a real table with real people, and steal the deal, and renege, and kick my partner when he trumps my ace, and . . . and . . . and . . . . But I’m stuck with watered down gaming on line for the time being. There’s a group of transplanted Midwesterners that get together in San Francisco occasionally, but I just can’t seem to get fired up about driving an hour-and-a-half through Sonoma, Marin, and the City to play a few games.
Gerry Blue, inventor, the Euchre Laboratory
Natty Bumppo, author of The Columbus Book of Euchre, replies:
And . . . and . . . and . . . flailing elbows! Skewing the markers! Spilling beer on claimed loners!
Euchre on line is fine, but – see the comments on my Euchre links page.
I feel your frustration in looking for a “table” game in California (if we were talking about hearts and my name were Bill Clinton, I would “feel your pain”). It’s not easy to find a game of euchre here in the South, either, where the hoi polloi think Rook is a form of bridge (the sophsticates play spades).
Perhaps you should move to L.A. A friend of mine described it as “not really a city – it’s a collection of Midwestern towns.”
And as for wives, maybe you just need a new wife! My lovely second wife did not know how to play euchre before we married but was a good bridge player. She learned euchre so well that she remains, even these many years after my lovely second divorce, the best euchre player I have ever known.
Natty Bumppo, author,
|Stealing and stealing the deal
– March 15, 2002
What you and Wergin have written – that the deal is final and unappealable once the card is turned – is the generally accepted rule in Michigan. However, some guys I play with insist that, even though the deal has been “stolen” (or, perhaps, just “misappropriated”), the rotation of whose “actual” deal it is hasn’t changed. Therefore, if you deal one hand early, you get the next deal, too. To me, this is absurd.
This is not merely absurd, it is fascinating! But the rules I have cited belie such an interpretation: The general rule still is, the deal rotates clockwise. A “statute of limitations” – the rule that excused the first theft – operates only negatively, not positively: I.e., it does not confer a benefit upon the miscreant in addition to sparing him the penalty for the infraction he has committed. Another way to rebut your friends’ interpretation would be to invoke another “natural statute” (as the Official Rules of Card Games might call it): “Two wrongs don’t make a right”!
Not only does their principle of “preserving the original rotation” blatantly point out that you stole the deal when you reclaim it immediately (and thus multiply your chances of getting caught the next time), but it also makes possible an incredibly powerful ploy for a deck thief. Say you steal the deal and get away with it but no one mentions it, and you pass the next deal as if no theft occurred. Now the “actual” deal is always one off the deal being dealt. Then on the apparent last hand, if the deal does not fall to you or your partner, you declare your prior theft and declare all the intervening deals “stolen” (or “innocently misappropriated,” ha, ha) as well, and claim the last deal. And of course a riot ensues.
Even more fascinating! While I disagree with these guys’ interpretation of the rules, as a lawyer myself I must admire their imaginative and creative manipulation of the rules. I cannot categorically say they are wrong – that would take a Euchre Court of the Highest Resort. But, as you suggest in the words “And of course a riot ensues,” their interpretation rather defies the major premise of a statute of limitations, which is to bring finality to the consequences of an untoward event.
Your friends do not seem to me to be “real lawyers” – they seem more like Slobodan Milosevic defending himself!
I insist that the deal passes to the left, regardless of whether the deal was stolen or not. It looks like no salvation can be found but to offer this argument and persuade people to clarify their house rules.
The only salvation – besides what I have offered in the general rule that the deal rotates left, and the notion of “laches” or “statute of limitations” that excuses a theft once the card is turned – is more specific legislation, which means more legislation, which I find – whether in Congress, the state legislature, the county commissioners, the city council, the school board, or the board of trustees of the local YMCA – generally dangerous. Because the more you address specifically, the more you leave unaddressed specifically, and the more you have left to address specifically, and the more “law” you wind up with that no one can keep track of without an extremely competent and expensive lawyer, and that an even more competent and expensive lawyer then can shoot down. It is for the same reason I find a 3-page contract generally preferable to a 307-page contract, whatever the subject matter. Excessive specification amounts to a denial of “common sense” (of which there is no such thing anyway, Professor Nekam would argue, and correctly; but still it’s a nice and useful concept), and a manifestation of distrust of the judicial process (which, I must admit, however, is not always or universally unjustified).
It all reminds me of my definition of God: “God is everything we do not know or understand” (cf. Deut. 29:29, King James version). Science teaches us that the more we learn and understand, the more we know is out there that we do not know or understand. Therefore, by this definition alone, God is greater every day. This definition is brief; it’s as good as any; it’s delightfully unspecific, and it’s probably valid and sufficient for all religions, as well as for atheists and agnostics. Perhaps it is even ecumenical.
Natty Bumppo, author,
|Stealing the deal:
Is it “legal”? – March 8, 2002
The “illegality” of “stealing the deal” is inferred from the general (and often unwritten) rule that the deal passes clockwise: For example, in Official Rules of Card Games (71st ed., United States Playing Card Company, Cincinnati, 1990), at page 11, in a chapter titled “General Rules Applying to All Card Games,” there is a section headed “Rotation” stating, “The right to deal, the turn to bid, the turn to play, all rotate clockwise, that is, from each player to his left-hand neighbor.”
This is a convention so basic that it is usually not found in the rules to a specific game, and it is not found in some “Hoyle” encyclopedias at all – e.g., not at all in Morehead and Mott-Smith, Hoyle’s Rules of Games (2nd rev. ed., Penguin, New York, 1983 – and not at all in several books I have looked at specifically on bridge, hearts, pinochle and poker. It is stated, however, in The Columbus Book of Euchre, and in Gary Martin’s Euchre: How to Play and Win and Thomas A. Gallagher’s Winning at Euchre.
The “legality” of “stealing the deal,” then, arises from a notion of a “statute of limitations,” as it is termed in Official Rules of Card Games, at page 13, in a section headed “Condonement [sic; they mean ‘Condonation’] of an Irregularity,” which states:
“The laws of different games vary widely in the penalties
“Custom has fortified at least the following ‘statute of
“Procedural error in shuffling, cutting, or dealing (not
“Many games place a greater limitation upon the time
Statutes of limitations are found in both the civil and the criminal laws of states and nations, of course, and are based on a desire for finality. In some jurisdictions even felonies (such as grand larceny) have limitations.
The problem with cards is, you will rarely find such a “statute“ – a legislative or codified rule or law – of limitations, either in general rules or in rules to a specific game. It is largely a matter of custom, or “house” rules.
And, as one of my more respected law professors once pointed out to me – quite persuasively – there is no such thing as “natural law” (except in science, e.g., the “law” of gravity). So the above citation of a “natural statute“ is out the window, as far as I am concerned. What we are really dealing with is not a “statute“ of limitations, but a legal doctrine called “laches,“ which is to the common law, or case law, what a statute of limitations is to statutory law. At some point enough is enough – in love, war and card games; and well settled principles evolve, even in the absence of statutes, as to what or when is enough.
In most card games, not just in euchre, it is customary to accept a deal regular in form. In The Columbus Book of Euchre I have merely stated this custom in statutory form: I have “enacted” a “statute of limitations” on the deal, at page 23 (2nd edition; page 24 in original edition), that you will not find in most printed rules of card games: “Once the card is turned, the deal is official.” I.e., if the wrong guy dealt, it’s too late to complain about it now (the paragraph does go on to explain that misdeals in the number and nature of cards – e.g., markers in the deal – still can be called before the next deal is completed.)
Interestingly, Joseph Petrus Wergin, whom I have harshly criticized elsewhere for being too stodgy, agrees with me. At page 113 of Euchre According to Wergin (Huron Press, Madison, Wisc., 1990), he states, “If a deal is made out of turn and the mistake is discovered before the dealer has turned the starter card, it should be redealt correctly. . . . If the error is not discovered until after the starter card is turned, the deal stands.”
Now, of course, not everyone plays this way. Some players consider such ploys as the “Brownstown maneuver” (Columbus Book of Euchre, pp. 13, 15, 38 and 51), and intentionally dealing out of turn, so dastardly that they will banish the miscreant from the table, even exile him from their houses; some will even shoot or stab or strangle him.
But, either you have a definite “limitation” or you do not. And if there is a better one than the turn of the card, what is it? The turn of the card is more definite than the Official Rules’ “natural statute of limitations . . . Stands after all players look at their hands.” It avoids argument over who has and has not looked at his hand, and it thwarts the dilatory tactic of deliberately not looking at your hand while trying to remember whose deal it is.
The later the limitation, the weaker the memory, the fiercer the argument about whose deal it was. This is a second reason for laches and limitations: They not only give an event or series of events finality, but also they require prosecution while witnesses’ memories remain fresh (or, at least, before they have become unconscionably stale).
And if the rule is not available to the dishonest, then neither is it any good for the honest. It’s like the 4th and 5th Amendments and other civil rights: Of course they are invoked by criminals. But they do not exist for criminals, as the “law and order” wailers howl. They exist to protect honest guys like you and me from overbearing police.
Again, Wergin agrees, page 7: “Enforce every rule impartially and don’t make any exception or the card game will become a farce.” *
Natty Bumppo, author,
* Wergin is a notorious
stickler for “honesty,” how-
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