Three people play a money game with (perhaps differing) initial stakes in the range [$1, $255]. On each turn they flip a fair coin to determine an odd-man-out. (If there are three heads or three tails they flip again.) The poorer of the remaining players then "doubles up" at the expense of the richer player. For example: If the initial stakes are ($15, $70, $150) then depending on which player sits out, the stakes at the end of the turn would be ($30, $55, $150), ( $30, $70, $135) or ($15, $140, $80).

The game ends when the two active players in any round have exactly the same stake.

For each set of initial stakes there is a minimum number of turns that must be played. In the above example, clearly two rounds must be played (more than two, actually.) Starting with ($1, $4, $6,) at least three turns must be played.

Your task is to improve on that. Find initial stakes for which the game cannot end before N turns have been played, where N is the greatest number you can find. If you can beat N=3, post your solution and let others take a shot at beating it. Gold star will be awarded if the best possible N is found.

(This was adapted from a puzzle in a well-known puzzle site, which I will attribute when the best solution is found.)

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## bonanova 85

Three people play a money game with (perhaps differing) initial stakes in the range [$1, $255]. On each turn they flip a fair coin to determine an odd-man-out. (If there are three heads or three tails they flip again.) The poorer of the remaining players then "doubles up" at the expense of the richer player. For example: If the initial stakes are ($15, $70, $150) then depending on which player sits out, the stakes at the end of the turn would be ($30, $55, $150), ( $30, $70, $135) or ($15, $140, $80).

The game ends when the two active players in any round have exactly the same stake.For each set of initial stakes there is a minimum number of turns that must be played. In the above example, clearly two rounds must be played (more than two, actually.) Starting with ($1, $4, $6,) at least three turns

mustbe played.Your task is to improve on that. Find initial stakes for which the game

cannotend beforeturns have been played, whereNis the greatest number you can find. If you can beatN=3, post your solution and let others take a shot at beating it. Gold star will be awarded if the best possibleNis found.N(This was adapted from a puzzle in a well-known puzzle site, which I will attribute when the best solution is found.)

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