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 contained in Dagon’s reply. Perhaps the gambling market is distorted by regulation, and its failure as a prediction market is entirely due to these regulations. Without such regulations, maybe the gambling business would function much more like an accurate prediction market, which I suppose would make it seem like a much less enticing business to go into.
This would imply that, if you don’t like casinos, you should want regulation on gambling to focus entirely on making sure that casinos don’t use violence to keep other casinos from operating. Then maybe we’d see the casinos compete by bringing their odds closer to reality, which would, of course, make the casinos less profitable, so that they might close down of their own accord.
(Of course, I’m ignoring games that aren’t entirely games of chance.)
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?
This really doesn’t have much to do with the market. While I don’t know the details of gambling laws in all the US states and Indian nations, I would be very surprised if there were regulations on roulette odds. Many casinos have roulette wheels with only one 0 (paid as if 1⁄36, actual odds 1⁄37), and with other casino games, such as blackjack, casinos frequently change the rules as part of a promotion or to try to get better odds.
There is no “gambling market”: casinos are places where people pay for entertainment, not to make money. While casinos do offer promotions and advertise favorable rules and odds, most people go for the entertainment, and no one who’s serious about math and probability goes to make money (with exceptions for card-counting and poker tournaments, as orthonormal notes).
Also see Unnamed’s comment. Essentially, the answer is that a casino is not a market.
Also see Unnamed’s comment. Essentially, the answer is that a casino is not a market.
A single casino is not a market, but don’t all casinos and gamblers together form a market for something? Maybe it’s a market for entertainment instead of prediction ability, but it’s a market for something, isn’t it? Moreover, it seems, at least naïvely, to be a market in which a casino would attract more customers by offering more realistic odds.
Some casinos in Vegas have European roulette with a smaller house edge. I know this from a Vegas guidebook which listed where you could find the best odds at various games suggesting that at least some gamblers seek out the best odds. The Wikipedia link also states:
Today most casino odds are set by law, and they have to be either 34 to 1 or 35 to 1.
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.
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 contained in Dagon’s reply. Perhaps the gambling market is distorted by regulation, and its failure as a prediction market is entirely due to these regulations. Without such regulations, maybe the gambling business would function much more like an accurate prediction market, which I suppose would make it seem like a much less enticing business to go into.
This would imply that, if you don’t like casinos, you should want regulation on gambling to focus entirely on making sure that casinos don’t use violence to keep other casinos from operating. Then maybe we’d see the casinos compete by bringing their odds closer to reality, which would, of course, make the casinos less profitable, so that they might close down of their own accord.
(Of course, I’m ignoring games that aren’t entirely games of chance.)
This really doesn’t have much to do with the market. While I don’t know the details of gambling laws in all the US states and Indian nations, I would be very surprised if there were regulations on roulette odds. Many casinos have roulette wheels with only one 0 (paid as if 1⁄36, actual odds 1⁄37), and with other casino games, such as blackjack, casinos frequently change the rules as part of a promotion or to try to get better odds.
There is no “gambling market”: casinos are places where people pay for entertainment, not to make money. While casinos do offer promotions and advertise favorable rules and odds, most people go for the entertainment, and no one who’s serious about math and probability goes to make money (with exceptions for card-counting and poker tournaments, as orthonormal notes).
Also see Unnamed’s comment. Essentially, the answer is that a casino is not a market.
A single casino is not a market, but don’t all casinos and gamblers together form a market for something? Maybe it’s a market for entertainment instead of prediction ability, but it’s a market for something, isn’t it? Moreover, it seems, at least naïvely, to be a market in which a casino would attract more customers by offering more realistic odds.
Some casinos in Vegas have European roulette with a smaller house edge. I know this from a Vegas guidebook which listed where you could find the best odds at various games suggesting that at least some gamblers seek out the best odds. The Wikipedia link also states: