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Is it more cost effective (as far as payout of bux per chip gambled) to gamble infrequently with a bet of many chips, or to gamble frequently one chip at a time?

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Both options will be the same in the long term, because payouts scale linearly with number of chips bet, and odds are not dependent on the bet.

Betting 1 chip at a time will cause your earnings to regress to the mean more rapidly than betting as many as possible, assuming the same total number of chips, but it will not give you either more or fewer Bux on the whole.

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