### Las Vegas says the odds of Murphy topping Callahan...

Are 1-in-20.

What does this mean? Many people have the impression that there are a bunch of sports experts in Las Vegas who know the likelihood of different outcomes of a contest, and use their expertise to "set" odds that somehow reflect an objective fact about the world. But what really happens is this:

"By adjusting the odds in their favour or by having a point spread, bookmakers will aim to guarantee a profit by achieving a 'balanced book', either by getting an equal number of bets for each outcome or (when they are offering odds) by getting the amounts wagered on each outcome to reflect the odds."

If the bookmaker can equalize the dollar amount to be paid out when Murphy wins and when Callahan wins, and then can take a commission or vigorish from that, the business is guaranteed to make money, no matter the outcome of the event.

So picture a contest between some hypothetical Callahan and some imaginary Murphy for "Lightweight intellectual champion of the world." It just so happens that for every dollar bet on Murphy, 19 are bet on Callahan. Let's say there were only 20 \$1 bets, to make our math simple. The bookmaker has \$20 in his pocket. He wants some of that left there when the contest is over. So he sets the odds 19 to 1 in favor of Callahan. If Callahan wins, he pays out something like \$1.04 for every one dollar bet, and is left with a quarter in his pocket. If Murphy wins, he pays out \$19.75 to the single Murphy better, and is left with a quarter in his pocket. The bookmaker wins either way!

So the bookmaker has no interest at all in anything that might be called the "real" odds in the contest. His odds are simply the odds that balance his book, and guarantee he will make money whoever wins. If he personally believes that Murphy is being seriously underrated in this contest, he may make a bet himself on Murphy. But then, of course, he is acting as a bettor, and not a bookmaker.

1. Good but two things:

(1) Surely they use experts when setting the initial odds or spread, and then move away from that based on wagers.

(2) A Chicago economist would say the best measure of "expert opinion" is indeed how the market wages money.

1. 1) I bet (hee-hee) they do, but really don't know. How do we find out? And how does that expert set his odds?

2) Granted. I just wanted to correct a misperception based on the way this is usually reported... one I myself shared before I became aware of how one makes book.

2. And I wonder if the initial-odds-setting expert is more concerned about his take on the game, or his take on how betting will go?

3. What does this mean? That, by transitivity, Callahan-Krugman is 20-in-1,000,000

4. Oh, Ken, you are a funny fellow!

2. I don't think you're right. At least from what I've read about odds setting (and from the one odds setter I've met) they really are interested in the probability.

Let's say, for example, my bookmaking company offer odds on Liverpool vs Man Utd that are significantly different to the probabilities. In that case, the customers who are looking to bet in one direction will be offered a bad deal. Rather than take it they'll go to another bookmaker and they may stay with that company. So, it's bad for customer loyalty for a start. The customers want to bet the other way will get a much better deal. If this is spotted by professionals then a lot of money could be put on in that direction in a short space of time. That space of time could be too short to change the odds in to balance the two sides of my book. To avoid large risk, that could mean that I have to lay off by making bets with other bookmakers myself. The other bookmakers may not give me a good price on that.

1. "In that case, the customers who are looking to bet in one direction will be offered a bad deal. Rather than take it they'll go to another bookmaker and they may stay with that company."

Right, which will unbalance your book, which will lead you to change your odds. If you can't change those fast enough to balance your book, why should you think you can change them fast enough to reflect the "real probability," whatever that is: I'd say there isn't even any such thing TO match!

I think the real point here is that a bookie doesn't want to let his odds drift too far from OTHER BOOKMAKERS odds, or people can make Dutch books against the bookmakers as a whole.

And note I didn't just make what I wrote here up: that quote is from Wikipedia.

2. "If you can't change those fast enough to balance your book, why should you think you can change them fast enough to reflect the 'real probability.'"

Do you think that the probability of, Man City winning against Arsenal, for example, changes quickly? I doubt that. Certainly if there's an injury, for example. But, the flows of money through a bookmaker can change very quickly. Not all bookmakers are electronic, in the city I live there are dozens of the old fashioned shop based one with the paper tickets.

If you don't like my language here, I'll put it like this. For a large set of bets where the bookmaker has given 3:1 odds (for example), the average outcome distribution will closely match the odds with a narrow standard deviation. Does that feel more scientific?

"I think the real point here is that a bookie doesn't want to let his odds drift too far from OTHER BOOKMAKERS odds"

No. If the bookmakers as a whole are wrong then the professional gamblers will take them to the cleaners. I don't understand what you mean about Dutch books.

The quote may be from Wikipedia but it's still a simplistic theory of how bookmaking works.

3. "Do you think that the probability of, Man City winning against Arsenal, for example, changes quickly?"
No, what I actually think is there is NO SUCH THING as the probability of Man City winning against Arsenal. There are the odds people need to see to make a bet on Man City, but these are just a matter of their beliefs, not some real thing floating out in the world somewhere.

4. "For a large set of bets where the bookmaker has given 3:1 odds (for example), the average outcome distribution will closely match the odds with a narrow standard deviation."

OK, but that just means that when you even your book, time after time, the actual outcomes reflect the betting odds: the crowd, as a whole, bets well.

Let us say you are getting bets 10-1 for Arsenal. But YOU, the bookie, think the "real" odds are 5-1. What do you do?

5. And I am really curious about these questions, current: what I know about bookmaking comes from reading some general stuff like the Wikipedia article, and my friends experiences going around making Dutch books against London bookies.

3. "No, what I actually think is there is NO SUCH THING as the probability of Man City winning against Arsenal."
Well, yes. You can argue that any abstraction doesn't exist.

Putting it differently, the money that flows into the offices of a bookmakers can change fast. Bookmakers have to deal with that well and that means that the odds they give at the start must make some sense.

"OK, but that just means that when you even your book, time after time, the actual outcomes reflect the betting odds: the crowd, as a whole, bets well."

It could mean that if bookies were setting odds in the way you describe. But, studies of this have shown that gamblers don't bet in line with probabilities over the long run.

Odds are set to maximize the bookmakers profits, but not in such a simple way. In practice books aren't balanced.

http://pricetheory.uchicago.edu/levitt/Papers/LevittWhyAreGamblingMarkets2004.pdf