AA Odds Calculator for Windows 3.1 This program supports the playing of the Axis & Allies War game. It is intended to assist players in planning their strategies. It allows a player to examine possible alternative battle plans and analyze his/her chances of winning with the selected attacking and defending forces. It also allows a player to "step through" the battle using randomized dice rolls. This is a shareware product. If you find it useful, you should send a check for $12.50 to the author: Philip Hall 2102 Autumn Cove League City, TX. 77573 Compensating me for my efforts will encourage me to continue enhancements to this software, and (more importantly from your standpoint) provide those enhancements to you. Feel free to distribute copies to anyone else who might be interested (be sure to include this file). e-mail for problem reports and suggestions: PhilipHall@aol.com OK, so how do you use the thing. Installation: No special install required, simply extract the contents of the zip file into a directory where you want to keep the program and set up a windows icon to point to the executable file. The Main Menu options are "Battle" and "Exit". The Battle selection provides a cascading menu with three choices: Land/Air Naval Amphibious The intent of each of these should be obvious. Selecting one of these options will cause a screen to be displayed which allows the user to enter the number of units for attacking and defending forces. The Land/Air screen also allows the user to set the following options: TAAC - Take at all costs. The odds calculation will ensure that the last remaining attacking unit is a land unit. No Loss of Air - The odds calculation will only consider it a win condition for the attacking forces if no aircraft are lost AND the territory is captured. The result of using the Calculation function will be the same whether or not this option is selected but the results of using the TopTen function in the Execution window will differ. aa gun - indicates the presence of an anti-aircraft gun. (This option is also available for amphibious attacks) After entering the numbers and checking any necessary boxes, click on the Calculate button. The calculation process will then start. For average size battles, this will take less than a minute. For large Karelia style battles with 20+ units on each side, run time is around 3 minutes on my machine (486 DX33). Your runtime may be shorter or longer depending on your hardware. A math coprocessor helps immensely. The same calculation that takes 3 minutes on my machine takes 15 minutes on a SX33 (no co-processor). The probability that the attackers will win will be displayed when processing is complete. The number of seconds required to calculate the result will also be displayed. You can then change some or all of the numbers and run it again. Use the "Clear" button to reset all unit numbers to zero and start over. Use the "Done" button to return to the main menu. The button labelled "Execute" will cause a new window to be displayed which allows you to excute the battle with randomized dice rolls. Several options are available: OneRound: Executes a battle one round at a time based on randomized dice rolls, reports the number of hits by each side and displays the current status of each army. Complete Battle Executes an entire battle based on randomized dice rolls, reports the winner and displays the units remaining for the winning side. Exec 10K Executes the battle 10,000 times bases on randomized dice rolls and reports the number of times that the attackers win. This will give approximately the same results as the "Calculate" button on the set up window and will execute much faster for battles involving large numbers of units. TopTen Executes the battle 10,000 times and displays a list of the ten most commonly occurring results along with the frequency of each. Reset Clicking this button will restore the armies to their state before you started a battle. You should click on this button each time you select a new function. So that's about it - pretty simple on the surface. =============================================================== So how does it work? Can you count on the results? The Calculation algorithm looks at every possible roll of the dice and follows each path until one side or the other has been eliminated. As it does this, it accumulates the odds of that particular sequence of dice rolls and adds that number to the total probability of the side with remaining forces. The elimination of both sides is considered a win for the defenders. Assumptions: Lower cost units will always be removed from the board first (transports are removed before subs). TAAC orders modify this, obviously. Complicating factors: There is a non-zero possibility that a battle will go on indefinitely. The time required to look at all possibilities expands exponentially as the number of units increases so it is not feasible to really examine them ALL with today's desktop machines (of course ALL of them will never be evaluated because of the statement in the preceding paragraph). In order to deal with these complications and provide reasonable performance, I have had to make some simplifying assumptions. At the end of 6 rounds, if neither side has won, I assign the win to the side with the strongest force remaining (calculated by summing up the hit factors of remaining units). Additionally, I also terminate the evaluation of a particular path if the odds fall below .0001 and simply ignore that result. I arrived at these numbers as a reasonable compromise between accuracy and performance after considerable experimentation. I believe that the results are accurate at about the +- 2% level. I have done some evaluation of my predictions versus actual dice rolls for some small number of units and that figure seems to hold up. If anybody is inclined to perform similar experiments, please send results to PhilipHall@aol.com. I have found this software to be very useful in planning strategies. Just remember that a 90% win probability does not mean that you will ALWAYS win. The "Execute" algorithm is based on a randomized number generator which generates numbers for each dice roll. Units are removed from each side based on IPC value until the termination conditions are reached. Enhancements in Version 1.2: Display odds of Top Ten possibilities for units remaining at end of battle. (This really helps a lot!!) Support for super weapons To receive Version 1.2, send registration as described above. Enjoy!!