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May 3[edit]

Casino bet: how long could your chips last?[edit]

If you play roulette with, say, 25 chips and set on either red or black. Win doubles, loss=100% loss. Chances are slightly less than 50%, but we can take it as 50%.

What are your chances of playing 400 times before you lose everything?--Hofhof (talk) 09:02, 3 May 2018 (UTC)[reply]

What is the strategy here ? Do you bet 25 chips each time ? In that case your winnings can be modeled as a 1-dimensional random walk. Or do you bet all winnings each time ? In that case to survive 400 plays you need 400 wins, with a probability of 1 in 2⁴⁰⁰ ? Gandalf61 (talk) 13:52, 3 May 2018 (UTC)[reply]

Looking at your earlier comment that got clobbered, I'm assuming you're starting with 25 chips, you bet 1 chip each time, and your probability of winning is 18/37 (for European roulette). I'm also assuming you stop when you've run out of money or when you make 400 bets, whichever happens first. In that case, the expected number of chips that you finish with is approximately 15.868, and you'll finish with more than 0 chips about 68% of the time. –Deacon Vorbis (carbon • videos) 13:58, 3 May 2018 (UTC)[reply]

Just for fun, if your chance of winning is 18/38 instead (with a double 0), then your expected number of chips is about 9.087 with about a 43% of finishing with some chips. –Deacon Vorbis (carbon • videos) 14:14, 3 May 2018 (UTC)[reply]