Does a Larger Bankroll Increase Your Chances of Winning in Roulette?

Question

If Carlos bets $1 at a time in roulette with a starting bankroll of $100 trillion, does he have a better chance of winning $100 compared to Alice who starts with $10,000?

Answer 1

Despite the massive difference in their bankrolls, Carlos and Alice have nearly the same chance of winning $100 by betting $1 at a time, which is extremely low at 0.00265%. The difference in odds is so minuscule that it's almost negligible.

Comments

My students often come up with questions how to win in casinos....
When I'm done with them,  I have quite a number of shocked and disillusioned students that just learned how bad it is to be bad at math :-)


PS: it I was carlos, I would buy the casino....

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Carlos is a good buddy of mine, we hang out on his yacht all the time.

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I once heard a story of a guy who played the casino trying to walk away with $10. He would bet $10 and lose, then $20, etc. up to $510 or something, just to come out ahead by $10. Would this strategy work given you have a large money supply compared to the amount you are trying to earn?

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I knew Carlos had a bigger chance, I just knew it