If a gambler and the casino keep going forever, how come the casino is always the winner?
In: Mathematics
If the odds of winning are 50%, and the prize for winning is to double your bet, then the more games that are played, the more the average earnings for the house and the players are going to break even.
Therefore, if the house wants to win, all they need to do is to either lower the chance of player victory or lower the payout. A 45% chance to win 1.9 times your bet doesn’t sound like much of a change, but when you run the numbers, it means that, instead of breaking even and earning a net $0 per game, every single game under the new odds gives the house an average of about 15% of the original bet. It doesn’t matter if more people win than expected for a while, the results will always trend towards the average which means that the house will slowly be building up money over time.
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