Probability and the NCAA Tourney

You lost me on that one. If the two sports books just give each other a piece of the action, it doesn’t change your expectation one bit.

What you are probably thinking of is having the books actually move the lines away from each other. Before the technology allowed all the sports books to communicate efficienty, this used to be a common way for professional gamblers to make money. Syndicates of pros would have spotters and runners at all the sports books, calling in line changes. If the lines in two places were significantly different, you could bet the ‘middle’, and guarantee yourself a profit. Or you could use the middle as a hedge, anyway.

It’s very rare now that you’ll find sports books who will differ by all that much, simply because there are pros now who have every book’s line on his computer screen, and if a ‘middle’ opportunity comes up it’s guaranteed that people will bet it. So the books have to be very careful. And, they can communicate with each other easily.

If you want to make money betting sports, one way is to find co-workers and friends who want to bet with you (assuming this isn’t an ethical problem for you). Most casual bettors won’t demand anything like the real odds. You can often find people willing to bet their favorite team even-money against yours, even if the book in Vegas has your team as a 2-1 favorite or even more. Take the bet from the aquaintence, place an offsetting bet against the money line, and you’re guaranteed to break even if your team loses, or make money if it wins. Or if the bookie’s vig is set by a goal line or puck line, you can middle it that way. Say your friend bets you tomorrow that Anaheim will beat Colorado. The Vegas line is Anaheim +1.5 goals. Place an offsetting bet of the same amount on Anaheim to win at +1.5. If Colorado wins the game by more than 1.5, you win from your friend and pay the sports book. If Anaheim wins, you pay your friend and collect from the sports-book. BUT, if Colorado wins by less than two goals you collect from your friend AND the casino. If the game ties, you push with your friend but win your bet at the casino.

The one catch here is that the casino usually requires you to lay 1.10 to win 1.00, or 1.20 to win 1.00. So in the case where the casino side wins and you lose to your friend, you show an overall loss of 9 cents on every dollar wagered. If the goal spread is big enough to cover that expected loss, you have a positive expectation bet. If it’s not, you’d lose in the long run. For instance, if you try and middle two casinos, each of which is charging you a 1.10 to 1 vig, you’ll need a bigger goal spread that you’d normally find in order to make the wager.

Here’s a couple of examples of some pure mathematics plays I’ve seen in the past:

A few years ago the ‘Sports Select’ lottery screwed up big-time. In one of them, they didn’t account for time-zone differences in European Soccer games, and were actually letting players place bets after the game was over, or at least after it had been going on for some time. They got killed on this.

Another Sports-select error cropped up in their parlay system. On a sports-select ticket you can parlay your bets (i.e bet team A in one game, and team B in another game, and if they both come in you’d get paid 3-1 instead of even money). The parlays were very popular, and the lottery commission started adding more events to them. Unfortunately, not being good at math they didn’t realize that for the parlay odds to be correct the events have to be independent. So they’d offer bets like which team will be ahead at the half, and which team will win, and let you parlay them. Well, obviously the team ahead at the half is much more likely to be the team that wins. By betting both, you gained a big edge over the house.

Another error is highlighted in one of David Sklansky’s books (“Gambling for Living”). A few years ago, the Stardust offered a parlay card with 10 teams on it. There were 1024 different ways you could bet those two teams. David did the math, and found out that if you filled out 1024 $1 cards, one for each possibility, you’d get back $1660. Guaranteed. And you could bet more than that. They did the math wrong. He found a backer who had more ready cash than he did, came up with a decent system that maximized the expectation (by adding a little risk), and he made tens of thousands of dollars in one afternoon.

These opportunities pop up in casinos from time to time, and pro gamblers are always on the alert for them. A casino will introduce a new game and get the math wrong, and it actually favors the player. It lasts a week or two before the casino realizes they are getting killed, and gets pulled. Or a Casino will make what they think is an insignificant rule change which actually changes the expectation in the game enough to show a profit for the player. Or they’ll do something stupid like let the customers spin the big six wheel themselves, not realizing how easy it is to get the wheel to stop in a reasonably large zone with just a couple of spins for practice. The list of these ‘coups’ by professional gamblers is very long.

I wasn’t very clear. Let’s say you are a bookie in Dallas, based on what you said, you are going off some nationally published line. But being in Dallas you get far more action on the Cowboys than you want. So that weekend the Cowboys are playing the Bears, and the bookies up there have more action on the Bears than they want.

My understanding is that these bookies some how lay their excess action off on each other so that their risk is minimized. I think this would work by having the Dallas bookie, bet on the Cowboys with the Chicago bookie.

I think this happens on an organized basis in Las Vegas, but I was wondering to what extent the illegal bookies did this, and if there was any cross pollination between the two markets.

I think the use of widely published spreads would force this to happen. If a local bookie has to give more points to the away team in order to lower his risk level, then the smart bettor you described above would be able to do similar hedging by betting with the local bookie at one spread, and with the Vegas casino at the national spread.

Thanks for the great info Sam.

If bookies do it with each other, they aren’t going to charge the vig. If YOU do it with them, you pay the vig.

They can share each other’s action even if the lines are identical. In this case, it’s just a case of trading paper. Pass over some wagers to me, I’ll pass offsetting ones to you. There. We balanced our action, and didn’t have to move our lines.

This goes on even among small-time bookies, or perhaps especially with them. In the case of the small sports book or ‘entrepreneur’ bookie, their lines are never balanced, simply because they don’t get enough bets to form a statistical curve. Some bookies may only take one or two bets in a day, and if both are on the same team, their risk is high. So, they enter into some gentlemen’s agreements with other small-timers who have bets going the other way, and split the action to cut their risk.

If they didn’t do that, then if they wanted to balance the action they WOULD have to move the lines in opposite directions, and the pros would step in and middle them to death. By trading action, they keep the lines identical and minimize risk.