Probability chart
January 6, 2006
The newest toy on the internets euchre block is a chart of the probabilities
of who will win at any given score.
It
was created by Fred Benjamin, known on line as Sword_4_hire.
It suggests, for example, that:
*
The dealers team has a probability
advantage over the other team of 51 per
cent to 49 per cent at all tie scores up to 5 to 5, and of no better than 54 to
46 at 8 to 8, but a whopping advantage of 65 to 35 at 9 to 9.
*
You still have an 8 per cent chance of
winning the game down 8 to 2 (if
youre dealing its only 7 per cent if youre not).
*
Up 9 to 6 without the deal, your probability
of winning is 82 per cent:
Is it
worth a safety [donation] to preserve the good odds?
Your probability
of winning at the next hand, ahead 9 to 8 with the deal, is still a
strong 72
per cent.
The chart is not gospel:
Its
based on Freds notions of what good euchre play is.
He taught a computer how to play; ran 10,000 simulations for every possible hand
from 0-0 to 9-9, and collected data indicating that generally, among equally matched
good players (i.e., four Freds):
*
The dealers team would score 1 point 45
per cent of the time,
*
The opponents would score 1 point 17 per cent
of the time,
*
The dealers team would score 2 points
(either by marching or
by euchring the opponents) 16 per cent of the time,
*
The opponents would score 2 points (either
by marching or
by euchring the dealers team) 12 per cent of the time,
*
The dealers team would score 4 points (a
lone march) 5 per
cent of the time, and
*
The opponents would score 4 points (a lone
march) 5 per cent
of the time.
I think thats 100 per cent.
Add
em up.
These percentages are
altered at scores including 8 or 9 points because of the lesser value of going alone
at 8 or 9 and the lesser value of scoring a euchre at 9.
Freds software (which I think he'll share with you; you can e-mail him at fastfredy0@yahoo.com) allows you to alter those
percentages if you disagree with them or if you wish to pit duller players against brighter
players.
So what good is this?
Well, for example, say you are the dealers partner and down 7 to 2, and want to
know whether a long shot loner attempt is a good idea, to get back in
the game.
Down 7 to 2 and dealing,
according to the chart, you start with a probability of only 14 per cent of winning
the game.
Lets say you have four aces and king of hearts, and your partner turns the jack
of hearts.
You have a great shot at a
point, which would put you down only 7 to 3.
Or do you order your partner to pick it up and turn it down, going for a
loner to put you down only 7 to 6 in the game score?
First you do the arithmetic of the hand.
Fred doesn't give you this, and neither does his chart.
You actually have to play the particular hand (or ask Fred, or find another simulator).
But lets say you play 15 samples of this hand going alone and the same 15
samples not.
Fred did that and, going
alone, scored one point eleven times (+11), made two lone marches (+8), and got
euchred twice (-4), for a net score of 15.
Going with partner he scored one point 11 times (+11) and marched four times (+8), for
a net score of 19.
So far that seems to be a strong argument for not going alone, doesn't it?
A net score of 19 is 27 per cent better than 15.
But before you buy that argument, look at the probabilities of winning (not net
score) at resulting scores after playing the hand alone.
First, look at the probabilities of getting to certain scores on that hand:
7-3
73% of the time (11/15), scoring a point;
7-6
13% of the time (2/15), scoring a lone march, and
9-2
13% of the time (2/15), getting euchred.
Then look at the probabilities of getting to certain scores playing with partner:
7-3
73% of the time (11/15), scoring a point,
and
7-4
27% of the time (4/15), marching
[9-2 i.e., getting euchred has been found improbable].
The opponents have the next deal.
According to the chart, your probabilties of winning against dealing opponents are:
at 7-3
16%
at 7-4
22%
at 7-6
39%
at 9-2
3%
Thus the total chances of winning on the given hand, down 7 to 2, including the
probabilities on the next deal, are:
Going alone:
7-3:
73% of 16% = 12%
7-6:
13% of 39% = 16%
9-2:
13% of
3% =
0%
The total probability of winning, going alone on the given hand the sum
is 17 per cent.
With partner:
7-3:
73% of 16% = 12%
7-4:
27% of 22% =
6%
[9-2, again, discounted].
The total probability of winning, going with partner on the given hand the
sum is 18 per cent, not significantly better with such a small sample.
And Fred reports that he has since run more extensive simulations that indicate an approximate
3 per cent advantage in going alone with that hand.
The above, I hope, shows you how to apply a particular scenario to the chart.
I ran an experiment of my own 20 hands in Gerry Blues Euchre Laboratory,
going alone with only the king of hearts in trump, backed by the three suit aces and the king
of spades (again, down 7 to 2 with jack turned to my partner).
Applying the results to Freds probability chart, I was convinced that you might as well
go alone with a lone king of trump in that situation.
The odds of winning are about the same as with taking partner along, and youll sure
amaze your friends, astound your relatives and piss off your opponents if you march alone
with a lone king of trump.
If you get euchred,
so what?
You can toss it off, saying, Ah, what
the hell, we were losing anyway.
Although this chart wont do you much good in the heat of a game, youll probably
find it fun to play with, and useful in confirming and debunking some of the
intuitive notions you have about what are and are not good moves.
But lets not get carried away just yet.
Euchre is not bridge is not chess.
I
have yet to meet a tinhead that plays well.
Perhaps Fred has one to offer Yahoo or Pogo.
Natty Bumppo, author,
The Columbus Book of
Euchre
Borf Books
http://www.borfents.com
Box 413
Brownsville KY 42210
(270) 597-2187
[copyright 2006]
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