This Is What I Call Being Risk-Averse

Photo: iStockphoto

I found myself in a Las Vegas sports book with good friend and economist John List the other day.  Since we both live in Chicago and have kids who play baseball, we thought it would be fun to bet some money on the Chicago White Sox.  It would give us a reason to root for the White Sox, and give our kids a reason to open up the morning paper to see if the team had won.


We have no special information about the White Sox, no inside information.  It was purely for consumption value.

If the sports book would give us a fair bet, i.e. the equivalent of a 50-50 coin toss, we would be willing to bet a lot because we aren’t very risk averse.  I’d say we would have been willing to bet at least $10,000, probably even more.

But, of course, the sports book doesn’t offer fair bets.  On the particular bet we were looking at — how many games the White Sox would win over the course of the regular season – the sports book charges about an 8 percent vigorish or commission.  We decided that at that price, we were willing to bet $2,500.  Eight percent of $2,500 is $200, so essentially we were willing to pay the sports book $200 in expectation to let us place this bet.

So we strolled up to the betting window and said we wanted $2,500 on the White Sox to win more than 84.5 games this year.

The lady behind the counter said the biggest bet we could make was $300.


We asked her why, and she called over a manager who told us the reason: The casino “didn’t want to take too much risk on this kind of bet.”

This casino is part of Caesars Entertainment, the largest casino company in the world, with annual revenues approaching $10 billion.  And they aren’t willing to let us pay them $200 to flip a coin for $2,500?

The next thing you know, the casino will tell me I can’t lay $2,500 on “Black” at the roulette table.  After all, it is essentially the same gamble as our White Sox bet … a coin toss in which the casino gets better than fair odds.

This seems like a crazy way to run a business.  It is especially surprising because Caesars is one of the few big businesses run by an economist, Gary Loveman, who has brought good economic thinking to many other aspects of the company’s operations.

If I weren’t an economist, running a sports book would be a pretty good job. I wonder if Caesars is accepting resumes?

(For more on sports betting at Caesars and in general, see this column we wrote for The New York Times a few years back.)

VB in NV

Get 8 friends to make $300 bets.

Puneet VOhra

This is their way of eliminating fraud. i.e. they don't want to caught in a situation where you can bet $100K and then bribe a player in the White Sox or other team to deliberately lose, causing a huge loss to the casino.
This is a version of Moral Hazard in economics parlance.
Can I send my CV to you?


They saw you coming, and you're in the Griffin Book...


Roulette wheels are random; baseball outcomes are not. The risk that Ozzy Guillen could bet a large amount on the Sox winning less than 84.5 games and making it so is not a risk the casino is concerned about with roulette wheels.


I am sure that the "risk" they are talking about is that they don't want to lose too much money to people who may have "insider information". This is not a possible risk while playing roulette.


Low limits, I assume, helps ensure that the casino gets equal betting on both sides of the line. A large bet would most likely require them to reassess the over/under for the White Sox to induce more players to take the opposite proposition (i.e. under) and hedge their own losses. A quick test of this theory would be to compare betting limits to the number of participants for a given line. Assuming that gamblers were splitting 50/50 for an individual bet, I would predict that larger max limits would correlate with a larger pool of participants.

Richard B.

Caesar's has much more information on the odds of winning at the roulette table, or at a coin toss, than they do about the White Sox this year. I suspect they are in the sports betting business to support their entertainment business. Taking a risk on a few hundred bucks for the sake of making some customers happy is probably good hospitality business. Taking a position on thousands of dollars on a business over which they have little information and no control is not their business.

Maybe you can find a Cubs fan willing to take the other side of that bet.


It seems much more likely you could have inside information on sports teams than you could on the roulette table. In fact, the house knows with great precision what the true odds are on the roulette table. If you are a particularly sophisticated gambler, you might be able to shop around for the right odds on a sporting event and hope to make money, especially if the betting market is not sufficiently competitive.


Go to the M


Should've gone to the M Resort Spa Casino that is run by Cantor Fitzgerald. They are infamous for taking more exotic bets and at higher stakes than most on-the-strip sportsbooks ( ).


Due to industry consolidation, these casino corporations have become increasingly risk averse in more ways than just the sports book example...there's an apparent market opportunity here for somebody very well capitalized.

Cem Vardar

The reason that they are risk averse in sports betting is that they are open for exploitation. Sportsbooks try their best to offer coin flip bets where half of the people take one side and half the other side and casino makes money in the long run. However, there are many professional gamblers waiting for casinos to make a mistake and take advantage of what is essentially a wrong line estimation on casino's part. Those are the people who place large bets when they have an edge against casino's lines. So when someone comes and makes an unusually large bet there's some (arguably high) probability that casino's line is exploitable. Casinos defend themselves against this by limiting the max bet size. This is not the case for the games where casino is sure to have an edge like roulette, craps and most other pit games.


I agree with Cem and Ryan; I don't think this bet has as much to do with fear of fraud as it has to do with fear of not being able to match the bet with that of another person taking the other side. Maybe the number of people who bet on entire seasons at a time is very small; maybe the amount they're willing to let you bet now is related to the total amount bet so far this season, and if you tried again closer to opening day, they'd let you bet more. Certainly, I suspect that if you tried to bet on a single-game's outcome during the regular season, the limit would be much higher, especially for high-profile games where there are plenty of bettors taking both sides of the money line.

Deepti bhattarai

Wow!! One of the best articles I've ever read. Being an economics major myself, I loved the way you think your point of view is amazing. Would love to read more from you.


I'm stunned. You thought it would be a nice lark to bet over $10,000 on baseball? That's obscene. Then, you were going to train your children to do the same?


There are several factors here, but the main one is a measure of confidence. You presume the odds on that bet are 50/50 minus the vig. And that is what Caesar's is predicting the odds to be... but due to the nature of the bet they may have low confidence or there may be very high variance on the outcomes. As a result, they want to keep the amount of dollars bet per bet low so that they can monitor trends by sharps and try to spot any emergent trends and adjust the lines either direction as needed.

Additionally, as some have mentioned, it becomes a question of volume. A good line will have an equal dollar amount on each side... but does a bet like this actually get enough volume to average out properly? Who wants to place a bet that has a 4 month payout date?


Easy. Their bankroll is not, in fact, the billion dollars in market cap that you quote. Instead, they size their risk to a much smaller virtual bankroll of how much they might lose in a quarter or whatever reporting period they use, because the casino manager is potentially going to get fired or forgo his bonus over bad results. This is true of all of their casino operations, even though their overall risk of ruin is basically zero.

Dan V

The casino wants to minimize variance -- with an expected payoff of a bet of, say, 30 cents for every dollar, it would much rather take one million one-dollar bets than a single one-million-dollar bet. In fact, a lot of casinos DO have maximum bet limits on things like roulette wheels. My friend was recently turned down when he wanted to bet $20,000 on a roulette at a casino.


In additions to the moral hazard arguments below, there is another reason that every game in Vegas has a maximum bet AND MINIMUM bet: the Kelly Criterion.

Recall that even in a fair game (eg a coinf flip), the house eventually gets all of the gambler's money because the house can sustain a longer losing streak than any given gambler. This is the famous "Gamblers Ruin". (definition 2 at's_ruin ).

An economically rational gambler can beat the Gambler's ruin for games with varying (and occasionally positive) expectations by sizing his/her bets using appropriate utility function. The most widely known function amongst gamblers is the Kelly Criterion

However, when the edge is small, the Kelly Criterion requires a large variation in bet size. By imposing both maximum AND minimum size bet for any given game, the house can force the gambler to make sub-optimal bet *sizes* and thereby restore the house's "Gambler's ruin" advantage, even thought the game make offer the gambler repeated instances of positive expectation.

You can see this most clearly at the blackjack tables: while the maximum bet size at a given blackjack table can vary by two orders of magnitude (or supposedly more for "whales"), the ratio of maximum bet to minimum bet at any given table is fairly constant across tables. (or least, it was the last time I walked through the Bellagio many, many years ago).

To summarize: in any game where the (1) the expectation of the bet varies and (2) the player has a reasonable chance of predicting that variation, the house must impose maximum AND minimum betting limits to preclude the optimal sizing of bets. If memory serves, the log is the most commonly used utility function and leads to the Kelley Criterion.



Let me get this straight, just for fun and having odds of 50% you planned to bet at least $10,000

Let me put it this way - you must be pretty rich.