In the meantime, here's an interesting fact that we'll be making use of in the update: any completely average (looking at the mean outcome) Axis and Allies battle with A attacking units and B defending units terminates in at most:
ceil(log[5/6,1/(max(A,B))])
turns, where log[b,a] is the logarithmic function to base b. Derivation:
Worst case, every unit makes 1/6 hits on average, so:
max(A,B)*(5/6)^n < 1
is the termination condition, because when the largest army has less than 1 unit left the battle is over. Rewrite in logarithmic form and take the ceiling of n because the number of steps must be an integer.
So for instance, if you have two armies with 100 units, the maximum number of turns the ideal battle will take is ceil(25.253...) = 26 turns. One caveat: this doesn't account for capital ships (battleships, and also carriers if you're playing 1940+) and non-firing units.
3 comments:
very cool. Looking forward to the update!!
hi there,
i was hoping to test your calculator before purchasing, is there a web based version?
are the 1940 rules fully implemented?
can you adjust the order units/ hits will be taken? this is very important in the 1940 game, as taking "free hits" on battleships and aircraft carriers is from automatic now.
also, what about territory takes where one is willing to lose planes to keep ground units alive?
are the updates free or discounted, or do they require a full purchase?
many thanks for your time.
rockrobinoff[at]gmail.com
@anonymous
No, there is not currently a web based version. The 1940 rules are fully implemented, and the sim automatically takes "free" hits on battleships and carriers first.
Updates are free!
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