Roulette odds are actually very close to representing probabilities, although you'd consistently overestimate the probability if you just translated directly. Each $1 bet on a specific number pays out a $35 profit, suggesting p=1/36, but in reality p=1/38. Relative odds get you even closer to accurate probabilities; for instance, 7 & 32 have the same payout, from which we could conclude (correctly, in this case) that they are equally likely. With a little reasoning - 38 possible outcomes with identical payouts - you can find the correct probability of 1/38.
This table shows that every possible roulette bet except for one has the same EV, which means that you'd only be wrong about relative probabilities if you were considering that one particular bet. Other casino games have more variability in EV, but you'd still usually get pretty close to correct probabilities. The biggest errors would probably be for low probability-high payout games like lotteries or raffles.
Roulette odds are actually very close to representing probabilities, although you'd consistently overestimate the probability if you just translated directly. Each $1 bet on a specific number pays out a $35 profit, suggesting p=1/36, but in reality p=1/38.
It's interesting that the market drives the odds so close to reality, but doesn't quite close the gap. Do you know if there are regulations that keep some rogue casino from selling roulette bets as though the odds were 1/37, instead of 1/36?
I'm thinking now that the entire answer to my question is co...
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July Part 1