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.)
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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