User talk:Slipperymike

Hildebrandt's Equilibrium
in poker theory, the point where player A has equal expectation given a fold or call from player B in a hand where both players A and B currently have the same hand, AND player A is also drawing to a stronger hand. B+P = p(t) [B + P/2] + p(w) [2B + P] left side = amount won by player A after pushing all in and having player B fold. right side = expected value for player A if player B calls an all in bet. where: B = player B's chips P = dead money in pot p(t) = probability of a split pot p(w) = probability of player A winning the whole pot. example: player A holds Ah/7h and player B holds Ks/7s. player A has 22,000 chips and player B has 18,000 chips. there are 4000 chips in the pot. the board is showing 3s/4h/5c/6h. both players are playing a straight but player A can improve his hand to a flush if the river card is a third heart. players A's hand will improve %20 of the time. the pot will be split the other %80 of the time. player A pushes all in. given the money in the pot and probabilities at play in this model, hildebrandt's equilibrium occurs when: B + P = p(t) [B + P/2] + p(w) [2B + P]          =  .8(B + P/2) + .2(2(B)+P) = .8B + .4P + .4B + .2P = 1.2B + .6P .4P = .2B B = 2P when player B's stack is two times the amount in the pot a call or fold by player B represents equal value for player A. in this situation, player B's chip count is more than twice the size of the pot, so player A is hoping for a call from player B.  if player B had fewer than 8000 chips, player A would have been hoping for a fold as the amount in the pot is greater than his expected value if player B calls.

AfD nomination of Hildebrandt's Equilibrium
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