Aerial Attack wrote:Aerial Attack wrote:8 vs 10 is the first true 50/50 battle (you feeling lucky, punk?).
This bit doesn't work. Use some Markov chains with those probabilities above, and you get these, assuming that the attacker continues to attack until he wins or has 1 army left, his odds of winning are:
50% with 6v5
39% with 6v6
29% with 6v7
63% with 7v5
52% with 7v6
.
.
35% with 8v10
Got Excel? Use these basic rules to figure your own odds, or modify them to figure new odds, say if you want to: stop if you get down to 3; stop if you have less than the defender; have a certain number left over; etc.
If you have 4 or more armies, say A, and your opponent has 2 or more , say B, then your odds of winning (P[A, B]) are 0.3921*P[A, B-2] + 0.2863*P[A-2, B] + 0.3216*P[A-1, B-1] . That is, you'll win AvB if you win two in the first roll and you can win AvB-2 or you lose two in the first roll and can win A-2vB or you win one, lose one and can win A-1vB-1. If you understood that, you can reckon the odds of winning with less than 3 or against 1 defender, then fire up a spreadsheet and generate odds for any size.