Friday, September 11, 2009

Wolf Claws Mathhammer

Warning! The interpretation of the tabular data below is thoroughly wrong. I'll clean it up soon enough.

With the impending release of the Space Wolves codex, a new piece of wargear has come out: Wolf Claws. After looking through a preview copy of the codex, I've confirmed the rumors on the internet. Wolf Claws are lightning claws, except that you can choose to re-roll the to hit instead of the the to wound roll, but this choice must be made at the beginning of each close combat.

Mathhammerwise, my initial thought was that you should always reroll the roll with the worst chances. I.e., if you were fighting an Avatar and needed a 5+ to hit and a 6+ to wound, you should go with rerolling the 6+. But if you were fighting a squad of aspect warriors, and you needed a 4+ to hit and a 3+ to wound, you should reroll the 4+. I wasn't sure of that, though, so I ran the numbers. And that initial intuition was wrong.

Below are the actual numbers. In the first column, you'll see the target numbers. In the second column, you'll see the chance to succeed. Third column, the chance to succeed with a reroll. And the fourth column is the important one: it's the _increase_ in likelihood with a reroll.

2+  0.83  0.97   0.14
3+  0.67  0.89   0.22
4+  0.5   0.75   0.25
5+  0.33  0.56   0.22
6+  0.17  0.31   0.14

Thus, when picking what you want to reroll, always reroll the number that's closest to 4+. If you're fighting an Avatar, reroll the 5+ to hit instead of the 6+ to wound. If you're fighting an Aspect Warrior, reroll the 4+ to hit instead of the 3+ to wound. But if you're fighting a Blood Claw (3+ to hit, 4+ to wound,) reroll the to wound instead of the to hit. Got it? Good. Because that 11% difference between a 4+ reroll and a 2+ reroll isn't insignificant over the long run.