I have a question about prediction markets. I expect that it has a standard answer.
It seems like the existence of casinos presents a kind of problem for prediction markets. Casinos are a sort of prediction market where people go to try to cash out on their ability to predict which card will be drawn, or where the ball will land on a roulette wheel. They are enticed to bet when the casino sets the odds at certain levels. But casinos reliably make money, so people are reliably wrong when they try to make these predictions.
Casinos don’t invalidate prediction markets, but casinos do seem to show that prediction markets will be predictably inefficient in some way. How is this fact dealt with in futarchy proposals?
One way to think of it is that decisions to gamble are based on both information and an error term which reflects things like irrationality or just the fact that people enjoy gambling. Prediction markets are designed to get rid of the error and have prices reflect the information: errors cancel out as people who err in opposite directions bet on opposite sides, and errors in one direction create +EV opportunities which attract savvy, informed gamblers to bet on the other side. But casinos are designed to drive gambling based solely on the error term—people are betting on events that are inherently unpredictable (so they have little or no useful information) against the house at fixed prices, not against each other (so the errors don’t cancel out), and the prices are set so that bets are -EV for everyone regardless of how many errors other people make (so there aren’t incentives for savvy informed people to come wager).
Sports gambling is structured more similarly to prediction markets—people can bet on both sides, and it’s possible for a smart gambler to have relevant information and to profit from it, if the lines aren’t set properly—and sports betting lines tend to be pretty accurate.
I have also heard of at least one professional gambler who makes his living by identifying and confronting other peoples’ superstitious gambling strategies. For example, if someone claims that 30 hasn’t come up in a while, and thus is ‘due,’ he would make a separate bet with them (to which the house is not a party), claiming simply that they’re wrong.
Often, this is an even-money bet which he has upwards of a 97% chance of winning; when he loses, the relatively small payoff to the other party is supplemented by both the warm fuzzies associated with rampant confirmation bias, and the status kick from defeating a professional gambler in single combat.
The money brought in by stupid gamblers creates additional incentive for smart players to clear it out with correct predictions. The crazier the prediction market, the more reason for rational players to make it rational.
The money brought in by stupid gamblers creates additional incentive for smart players to clear it out with correct predictions. The crazier the prediction market, the more reason for rational players to make it rational.
Right. Maybe I shouldn’t have said that a prediction market would be “predictably inefficient”. I can see that rational players can swoop in and profit from irrational players.
But that’s not what I was trying to get at with “predictably inefficient”. What I meant was this:
Suppose that you know next to nothing about the construction of roulette wheels. You have no “expert knowledge” about whether a particular roulette ball will land in a particular spot. However, for some reason, you want to make an accurate prediction. So you decide to treat the casino (or, better, all casinos taken together) as a prediction market, and to use the odds at which people buy roulette bets to determine your prediction about whether the ball will land in that spot.
Won’t you be consistently wrong if you try that strategy? If so, how Is this consistent wrongness accounted for in futarchy theory?
I understand that, in a casino, players are making bets with the house, not with each other. But no casino has a monopoly on roulette. Players can go to the casino that they think is offering the best odds. Wouldn’t this make the gambling market enough like a prediction market for the issue I raise to be a problem?
I may just have a very basic misunderstanding of how futarchy would work. I figured that it worked like this: The market settles on a certain probability that something will happen by settling on an equilibrium for the odds at which people are willing to buy bets. Then policy makers look at the market’s settled probability and craft their policy accordingly.
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.
In the stock market, as in a prediction market, the smart money is what actually sets the price, taking others’ irrationalities as their profit margin. There’s no such mechanism in casinos, since the “smart money” doesn’t gamble in casinos for profit (excepting card-counting, cheating, and poker tournaments hosted by casinos, etc).
The most obvious thing: customers are only allowed to take one side of a bet, whose terms are dictated by the house.
If you had a general-topic prediction market with one agent who chose the odds for everything, and only allowed people to bet in one chosen direction on each topic, that agent (if they were at all clever) could make a lot of money, but the odds wouldn’t be any “smarter” than that agent (and in fact would be dumber so as to make a profit margin).
The most obvious thing: customers are only allowed to take one side of a bet, whose terms are dictated by the house.
But no casino has a monopoly on roulette. Yet the market doesn’t seem to drive the odds to their correct values. Dagon notes above that regulations make it hard to enter the market as a casino. Maybe that explains why my naive expectations don’t happen.
Actually this raises another question for me. If I start a casino in Vegas, am I required to sell roulette bets as though the odds were p = 1⁄36, instead of, say, p = 1⁄37 ?
Casinos have an assymetry: creation of new casinos is heavily regulated, so there’s no way for people with good information to bet on their beliefs, and no mechanism for the true odds to be reached as the market price for a wager.
I have a question about prediction markets. I expect that it has a standard answer.
It seems like the existence of casinos presents a kind of problem for prediction markets. Casinos are a sort of prediction market where people go to try to cash out on their ability to predict which card will be drawn, or where the ball will land on a roulette wheel. They are enticed to bet when the casino sets the odds at certain levels. But casinos reliably make money, so people are reliably wrong when they try to make these predictions.
Casinos don’t invalidate prediction markets, but casinos do seem to show that prediction markets will be predictably inefficient in some way. How is this fact dealt with in futarchy proposals?
One way to think of it is that decisions to gamble are based on both information and an error term which reflects things like irrationality or just the fact that people enjoy gambling. Prediction markets are designed to get rid of the error and have prices reflect the information: errors cancel out as people who err in opposite directions bet on opposite sides, and errors in one direction create +EV opportunities which attract savvy, informed gamblers to bet on the other side. But casinos are designed to drive gambling based solely on the error term—people are betting on events that are inherently unpredictable (so they have little or no useful information) against the house at fixed prices, not against each other (so the errors don’t cancel out), and the prices are set so that bets are -EV for everyone regardless of how many errors other people make (so there aren’t incentives for savvy informed people to come wager).
Sports gambling is structured more similarly to prediction markets—people can bet on both sides, and it’s possible for a smart gambler to have relevant information and to profit from it, if the lines aren’t set properly—and sports betting lines tend to be pretty accurate.
I have also heard of at least one professional gambler who makes his living by identifying and confronting other peoples’ superstitious gambling strategies. For example, if someone claims that 30 hasn’t come up in a while, and thus is ‘due,’ he would make a separate bet with them (to which the house is not a party), claiming simply that they’re wrong.
Often, this is an even-money bet which he has upwards of a 97% chance of winning; when he loses, the relatively small payoff to the other party is supplemented by both the warm fuzzies associated with rampant confirmation bias, and the status kick from defeating a professional gambler in single combat.
The money brought in by stupid gamblers creates additional incentive for smart players to clear it out with correct predictions. The crazier the prediction market, the more reason for rational players to make it rational.
Right. Maybe I shouldn’t have said that a prediction market would be “predictably inefficient”. I can see that rational players can swoop in and profit from irrational players.
But that’s not what I was trying to get at with “predictably inefficient”. What I meant was this:
Suppose that you know next to nothing about the construction of roulette wheels. You have no “expert knowledge” about whether a particular roulette ball will land in a particular spot. However, for some reason, you want to make an accurate prediction. So you decide to treat the casino (or, better, all casinos taken together) as a prediction market, and to use the odds at which people buy roulette bets to determine your prediction about whether the ball will land in that spot.
Won’t you be consistently wrong if you try that strategy? If so, how Is this consistent wrongness accounted for in futarchy theory?
I understand that, in a casino, players are making bets with the house, not with each other. But no casino has a monopoly on roulette. Players can go to the casino that they think is offering the best odds. Wouldn’t this make the gambling market enough like a prediction market for the issue I raise to be a problem?
I may just have a very basic misunderstanding of how futarchy would work. I figured that it worked like this: The market settles on a certain probability that something will happen by settling on an equilibrium for the odds at which people are willing to buy bets. Then policy makers look at the market’s settled probability and craft their policy accordingly.
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:
In the stock market, as in a prediction market, the smart money is what actually sets the price, taking others’ irrationalities as their profit margin. There’s no such mechanism in casinos, since the “smart money” doesn’t gamble in casinos for profit (excepting card-counting, cheating, and poker tournaments hosted by casinos, etc).
The most obvious thing: customers are only allowed to take one side of a bet, whose terms are dictated by the house.
If you had a general-topic prediction market with one agent who chose the odds for everything, and only allowed people to bet in one chosen direction on each topic, that agent (if they were at all clever) could make a lot of money, but the odds wouldn’t be any “smarter” than that agent (and in fact would be dumber so as to make a profit margin).
But no casino has a monopoly on roulette. Yet the market doesn’t seem to drive the odds to their correct values. Dagon notes above that regulations make it hard to enter the market as a casino. Maybe that explains why my naive expectations don’t happen.
Actually this raises another question for me. If I start a casino in Vegas, am I required to sell roulette bets as though the odds were p = 1⁄36, instead of, say, p = 1⁄37 ?
[Edited for lack of clarity.]
Casinos have an assymetry: creation of new casinos is heavily regulated, so there’s no way for people with good information to bet on their beliefs, and no mechanism for the true odds to be reached as the market price for a wager.
Normally I wouldn’t comment on a typo, but I can’t read “assymetry” without chuckling.