Bryan Caplan  

Beating the Odds: Why Do People Insist on Even Bets?

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"I'm sure that a Democrat will win in 2008."

"Sure? OK, let's bet at 100:1."

"Umm, no thanks. But I'll do it for even odds."

I've had a bunch of conversations like this. Someone proclaims to know the future with virtual certainty, but when you challenge him to bet on his professed belief, he spurns your offer unless you give him even odds. Of course, if he really believed he was right, 100:1 would still be easy money. What's the explanation for the prevalence of this reluctance?

1. My rational irrationality story. A bet instantly raises the marginal private cost of error, which leads to a sharp increase in rationality. Faced with financial consequences, people suddenly - if temporarily - admit to themselves that they know a lot less than they like to believe - and bet accordingly.

2. The strategic explanation. Why give 100:1 odds if you can bargain for 1:1?

3. Focal points. 1:1 is focal, and the transactions costs of settling on anything else aren't worth the effort.

4. Norms. People think that only 1:1 bets are "fair," so - on principle - they refuse uneven bets that they expect to be profitable.

Explanation #1 is of course my personal favorite.

Explanation #2 may have some merit, but it's far from clear that adamantly insisting on 1:1 is a smart bargaining strategy. In most cases, holding out for 1:1 prevents the bet from happening in the first place. If you really know something with p=.99, you might not want to offer 100:1 odds, but why not offer 5:1 if it's the only way to get the other side to bet?

Explanation #3 works for small bets, but if anything people seem even more reluctant to give odds on big bets. (More evidence for rational irrationality, I say!)

Explanation #4, again, might explain some of the reluctance, but it's not clear that people really think that morality demands 1:1 odds. How many people really think that it's wrong for roulette to pay more to people who win on "lucky number 12" rather than "black"?

Overall, the evidence seems consistent with my view that people like to see themselves as brilliant oracles, but on some level realize that they are anything but. When you raise the cost of this irrational belief, people's residual rationality kicks in to protect them from the consequences of their absurd but gratifying self-image.

Too bad I can't think of a bet to resolve this question...


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COMMENTS (17 to date)
agent00yak writes:

#2 is actually really strong for certain types of bets. There is no reason someone should bet at even 5:1 if they know that other people would be willing to give them odds.

"Bet for 100:1 odds that the democrats are going to win? Are you serious? Why should I give you 100:1 odds when someone is willing to take my bet with odds of only 4:3 on tradesports?"

eric writes:

I think baseball doesn't give more than 25:1 odds, because they can be gamed. I know option market makers, and they quickly back away from low-delta (ie, way out of the money) options because initiators with size tend to have inside information. Sticking to even-up trades keeps you at the more liquid contracts.

jhr writes:

How about:
5. They were lying about being sure.

dWj writes:

I'm with Eric to a significant extent; the odds I set when making a bet aren't the odds I would put ab initio on the event taking place, but are closer to the odds I'd place conditional on the knowledge that someone else is willing to take the opposite side of the bet.

I do think Bryan's onto something, too, though.

Matt Simpson writes:

6. Schelling point. The bettors can either engage in endless bickering over what the odds should be, or choose to pick a unique option. In what way 1 to 1 odds are unique, I'm not sure, outside of fairness, but that doesn't strike me as correct.

See, e.g., http://www.daviddfriedman.com/Academic/Property/Property.html
part I

H. Abraham Cadillac writes:

Gambling is illegal, guys.

chris writes:

Does this strengthen the case for using demand-revealing referenda as suggested by Ed Clarke?:
http://clarke.pair.com/Testpubgoods.html
The point is that talk is cheap. But, as Thomas Sowell pointed out, making people pay is a way of making them think. Doing so can therefore take the bombast and pseudo-certainty out of politics.

conchis writes:

umm, loss aversion?

Cyrus writes:

Morality. Our western moral system disapproves of, although does not really forbid, gambling in general. But a few kinds of traditional wagers are more acceptable than others; these involve small (to the participants) amounts, and equal stakes by all participants. Asking your wagering partner to turn an even-odds bet into an uneven-odds bet raises an additional (small) question of conscience.

As a demonstration, make an even bet with a Chinese colleague, and then offer them favorable odds. They will probably take it.

Cyrus writes:

Also, a friendly bet is no longer friendly if the possible loss by one of the participants exceeds a certain threshold. If you give me 100:1 odds on a $1 bet, I may decline to avoid the (small) possibility of having to take $100 from you.

The office NCAA pool works fine with everyone putting in a small wager that they will probably lose, all of which goes to a single loser. But few will enter a friendly pool in which a single loser has to pay everyone else a small fee, even if they are sure they will not lose, because inflicting the large loss on a friend is not worth the small payoff.

As a grad student, I travelled with a group of professors that almost played this game while eating out on conference trips: the credit card pulled out of the hat by a purportedly neutral grad student paid the entire bill. But to make it more "fair," i.e., spread the pain around, there was an additional rule that the loser of this bet was exempt from future drawings until all other participants' cards had been drawn: over the long run the game merely disarranged who paid what bill, rather than assigning losses to the unlucky loser.

Caliban Darklock writes:

You have failed to apprehend the situation. This is not an economic transaction, but a political transaction. Translate your statement:

"Sure? OK, let's bet at 100 to 1."

This is not a bet on your arguments. This is a bet on the relative value of the parties involved. You think you're asking me to quantify my belief, but what my brain pulls out of this is:

"I believe I am 100 times smarter than you, and I intend to profit from that at your expense."

This statement is offensive. A bet at 1:1 odds is respectful; it recognises the fundamental equivalence of the parties and their arguments. A bet at 100:1 odds is crazy. Would you bet on a horse at 100:1? With odds like that, the horse is probably three-legged and dead. The only time you might make this bet is when you think the person offering the odds is stupid.

I've actually had this bet offered to me before - your theory on odds is hardly new among the sort of folk who attend gaming conventions - and my response was "sure, if you'll bet $50,000."

The same reasoning applies. While you might protest that I don't have five million dollars to make good on the bet, I will respond that it doesn't matter because I am not going to lose.

So you face the same question you tried to ask me. Given an opportunity to win only a small victory (or, in your case, a pyrrhic victory), will you take a significant risk? Your bet assumes that while a $5 bet is meaningless to me, a $500 bet will give me pause - so I won't make it. Mine assumes that while saying "he owes me $500" makes me look like a welcher, saying "he owes me five million dollars" makes you look like a lunatic - so you won't say it.

This is a massive incentive for the bet to end up being merely a "gentleman's bet" where nobody actually collects anything. (I have no intention of actually trying to collect $50,000 from you when I win.) If you really want to bet money, sure, I'll make a token bet of a pittance at 1:1 odds. But the fundamental question is social, not economic.

It's essentially an intellectual game of chicken. It works like this:

"I think this."
"You're retarded."
"No, YOU'RE retarded."
"Wanna go to the mall?"

Okay, maybe it's not so intellectual after all.

sa writes:

#1 isn't always true, millions of people put money in mutual funds trying to beat the index inspite of heaps of evidence that it doesn't work.

Michael Sullivan writes:

There are a lot of differentt things going on here, but one of the more important is that you are mistaking the social meaning of "sure".

Most people will say they are sure of something, when they mean they believe it with somewhere between a 75 and 100% probability.

I could easily toss out in casual conversation that I was "sure" of a democratic victory, when what I mean is that I think there's about a 75% chance of it. By historical standards, that's a very large likelihood.

Consider betting on a major league baseball game. You never see odds going as long as 3-1, so if you really thought that a team was 75% likely to win, that's about as sure a thing as you'd ever get. It would be reasonable to say "I'm sure they'll win" even though you'd never take a bet at 100-1 odds. You certainly would take a bet (to the extent you're willing to gamble at all) at, say 2-1 odds, or IOW, at the odds you might generally expect to see given.

So if I say I'm sure the dems will win, what I mean is that I think they have a much better than 50-50 chance, or much better than prevailing sentiment would indicate, or much better than winning past democratic candidates would have been seen to have had at this stage.

Really long odds in general have a few things going against them. First, when you have very long odds on significant money, the non-linearity of utility often leads *both* sides to want a better bet than linearity would suggest they need. Many people act as if they have a much smaller bankroll than they really do, as if they have a "gambling" bankroll. Given those two assumptions, suppose you bet $100 giving 10:1 odds. That means you're potential payout is 1000. Using log utility and a bankroll of around 20,000, this is an even bet if you are correct around 91.15% of the time, rather than the 90.91% that a linear utility would suggest. If you're gambling bankroll is $1500, then you'd need a 94.5% chance for an even bet.

For a $10 vs. $1000 bet with a $1500 gambling roll, you'd need a 99.45% chance, rather than the 99.0099% chance that linear models would suggest. That corresponds to odds of 165:1. To get to an expected utility profit of even $1.50, you'd need to have 200:1 true odds, for the 100:1 bet to make sense.

Since the combination of transaction costs and welch expectation could easily exceed $1.50, we see that you might not take this bet unless you believed the true odds were more like 500-1. Scaling up the bets, means you have to scale up the gambling bankroll, or else the log utility bites even harder.

So I would argue that people who are not generally gamblers are simply using good intuition about their real utility of money with an artificially low bankroll, and this is one reason why bets almost never go off at super long odds.

We haven't even gotten into people's biases against losses, which argue against taking the sure side of a longshot bet and for taking the longshot side. Why else do people buy scratch tickets with 50-60% EV?

If you hang around with poker or backgammon players, you will find that lots of people make prop bets with odds that are not even. I think there's a social preference for 1:1, and using other odds signals a kind of degeneracy and familiarity with a subculture of dubious respect.

So I think caliban has the primary reason, which is that bets among normal people (as opposed to for profit gamblers, such as securities traders or pro poker players) are much more of a social/political interaction than an economic one.

IMO, this is the biggest source of EV of for-profit gamblers: people who aren't really doing the economic analysis of their bets. A prop-betting huckster is making sure all his bets are +EV, and is very calculating about how to play the social aspects to encourage people to make -EV bets. With gambling games, or zero-sum financial markets, it's the people who are playing "for fun" who become the income source for those who understand the economics.

Erik writes:

While a lot of this talk makes sense, I think 1 thing has been left out- say you are actually 95 percent sure and someone offers you 20:1 odds, why on earth would you take them? Its like betting money on whether you're going to flip heads or tails on a coin, it makes the bet even. Why would you bring accept odds that high for a roughly even calculation on your part, when the other person believes there must be more than a 5 percent chance of them winning - I mean even say its a 7 percent chance, that alone should bring your odds down to 14:1, and more likely they are thinking of it on the order of 10 percent or more. Given the disproportionate utility loss of you losing more money (losing 1 20:1 odds bet hurts more than winning 20 even bets, in my opinion at least) I'd say 3:1 odds are about as high as I would expect them to go in a friendly bet.

Sinclair Davidson writes:

How about ignorance? Many people might not understand how odds are determined.

Ray G writes:

Explanation #1 is correct, and I'd bet someone on it, but you gotta first figure out how to prove it.

#1 is right because it reflects the basic truth of accountability. Why do we choose FedX over the post office when we're really in need? Why do we dread going to the DMV? Why is bureaucracy synonymous with inefficiency?

Because these are examples of us experiencing services that have no effective methods for accountability.

jimi writes:

There is no Soviet Union anymore, but everybody remember those great victories and defeats. We trusted in idea and we made our history through great losses...
www.backinussr.com

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