I recently received a negative review for my Ancient Isles of Kjeldor map, and one of the criticisms is that 4v4 dice are actually worse odds for the attack than 5v6, which is contrary to what I post in the board's description. I don't believe this is correct, but I thought I would ask some of the more sophisticated probability folks out there for an expert opinion =)

Clearly, if I'm wrong, I need to update the board.

Of course, you're not wrong. There are nice sophisticated formulas out there, but my trusty brute force program gets the same answer

4v4: 0.3066 defender loses 2, 0.3477 split, 0.3457 attacker loses 2 for a 1.081 to 1 defender edge.

5v6: 0.2400 defender loses 2, 0.3480 split, 0.4120 attacker loses 2 for a 1.415 to 1 defender edge.

Thanks Hugh

Hugh wrote:

Of course, you're not wrong. There are nice sophisticated formulas out there, but my trusty brute force program gets the same answer

4v4: 0.3066 defender loses 2, 0.3477 split, 0.3457 attacker loses 2 for a 1.081 to 1 defender edge.

5v6: 0.2400 defender loses 2, 0.3480 split, 0.4120 attacker loses 2 for a 1.415 to 1 defender edge.

 Explaining the "edge" numbers for anyone that's interested (I was)..

Attacker loses (2)3457 + 3477 = 10,391 units for each (2)3066 + 3477 = 9609 units defender loses, yielding a 1.081 to 1 ratio in favor of the defender.

I find it interesting the 5v6 numbers tell us that attacker is almost 2 times more likely to lose 2 armies than defender.