mpotd
so the math problem of the day comes to us from war hammer quest. what? it's a game. with miniatures. and a random dungeon to be bashed. it's fun for timmers. anywho. i play the dwarf. normally, damage is 1d6 plus strength. dwarf strength is 3. i said normally. the dwarf has a special axe. roll two dice instead of one for damage. pick the larger. unless they're doubles. then add them together. unless they're double ones. then trip over your beard. the swing misses completely. and you spend the rest of the round getting up. now. monsters have toughness. which stops that amount of damage. damage in excess of toughness is recorded as wounds. so the warm up question is... figure out average wounds per hit as a function of toughness. okay that was easy. now it gets complicated. the dwarf is level two. so he gets two attacks per round. and he has the mighty blow skill which allows him to give up one attack for an extra 1d6 of damage. clearly at toughness 0, it's better to make two attacks. and at toughness 15, it's better to make a single mighty blow attack and hope for big doubles. cause they're the only thing that gets through. so .. at what toughness is it better to make one mighty blow attack than to make two normal attacks?