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I've been playing around with a Roulette Simulator investigating how different stake sizes and strategies can affect outcomes.

The strategy I was using was doubling your stake every time you lose this covering your losses and doubling your initial stake whenever you win.

Some results:

Playing 1000 games, initial stake \$10, starting pot \$20,000, target end pot: \$40,000

American: (0 and 00): Won 183 out of 1000

European: (only 0): Won 271 out of 1000

Never going to happen (no 0 or 00): Won 475 out of 1000

I was surprised that even if the house took nothing (i.e. no 0 or 00 slot) you can still only double your money every other time.

I was surprised by this. To lose your pot you need to get a long line of odd numbers. surely the chance of getting odd many times in a row is much less than 1 out of 2?

Can someone explain how the probability works here?

Thanks.

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If the game is fair (the no 0 or 00 case), your expected fortune stays constant. Thus if the only possible final outcomes are to lose your initial stake or double it, those will occur with equal probabilities.

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