[blahblah3]

hey murbard is the answer to this 1-goldenratio? (.618...)

to get this I computed the function f(x,y) which is my expected value if I reroll if roll <= x and my opponent re-rerolls if roll <= y. let p be the optimal value. by symmetry f(p,p) = 0.5 so there must be a local minimum around that point. solving by taking a one sided derivative gives me (sqrt(5)-1)/2

[murbard2]

Indeed it is, isn't it a nice result? :)

(to be thorough, you also need to show that re-rolling based on a single threshold dominates other strategies, but it's fairly intuitive and not too hard to prove)