Craps, Odds, and Expected Returns

I’ll be in Vegas this weekend and have been brushing up on some gambling strategies. One great resource that I like to use is the Wizard of Odds. It gives you the best play on all the basic casino games and allows you to play some of them for free.

But one strategy that has always struck me as intuitively wrong deals with taking the fullest odds allowed in craps. The wizard's craps guide, like other strategies I’ve seen, suggest taking the fullest odds possible after a pass line bet. The basic idea is that the house has an 1.41% on the pass line bet while there is no house edge on the odds bet. So every extra dollar on the odds bet reduces the average house edge:

House Edge – Pass Line Bet With Odds

Odds	Edge
1X	.848%
2X	.606%
3X	.471%
5X	.326%
10X	.184%
20X	.099%
100X	.021%

As the table shows this strategy seems to make sense. You can reduce the house edge all the way to .021% with 100X odds! But hold on. What’s the expected return on each of these bets? I’ll use a pass line bet of $100 (I wish!) to demonstrate:

Expected Return – Pass Line Bet With Odds

Odds	Expected Return
1X	-$1.41
2X	-$1.41
3X	-$1.41
5X	-$1.41
10X	-$1.41
20X	-$1.41
100X	-$1.41

As you can see, even though the house edge is reduced, the expected return remains unchanged. However, you now have a lot more cash on the table.

You can look at it another way to see the logic doesn’t hold. What if they weren’t "even money" odds? What if the odds bet actually had a .50% house edge. Well, again, every extra dollar bet on the odds would reduce the overall house edge. But every extra dollar is still a losing proposition and I don’t think many people would suggest betting 100X odds.

To make one more illustrative point, let’s take a car company that loses $5 dollars for every car they make. Because of this loss, they decide to make trucks that only lose $1 per vehicle. Now they can reduce the average loss per vehicle to $3! Does this sound like a good plan? Of course not. What should drive the investment decision is the marginal profit/loss not the average profit and loss.

Now of course the odds bet is still among the best you will find in the casino and anyone who gambles will want to take advantage of it. But the decision of how much to put down on the odds bet is completely independent of the house edge on the pass line bet. The pass line bet is a sunk cost and there is nothing you can do to change it. The marginal return of each bet should be the only factor in the decision making process, and of course the marginal return on the odds bet is zero.

So if your not a high roller don’t worry about only taking 1X or 2X odds on the pass line bet. There is not a valid economic reason to bet more. You will have the same expected return of the bettor who puts down 3x odds or 10x odds.

Thank Your Lucky Stars

Great seasons in college basketball are only validated by a trip to the final four. So it's easy to understand the jubilation shown by Illini fans after the remarkable comeback Saturday night. It was not only the joy of winning, but the relief of not watching another Illinois team fall short of expectations.

With four minutes left I had already started pondering how this team will be remembered. Overachievers? Chokers? A team that peaked too soon? But those questions will never have to be answered after a 4 minute run that remains too good to be true.

But for some reason, I can’t seem to fully share in the unbridled joy being displayed by players, coaches, fans and sportswriters. There is just something unsatisfying about how this game was won.

First, I need to say that this was not one of the "greatest college basketball games ever played", a statement made by more than one sportswriter in the past few days. Come on, was it really that great watching the Illini get their asses handed to them for most of the second half? I’ll give you that it was one of the greatest comebacks in tourney history. But game? I would never want to sit through the first 36 minutes again, that’s for sure.

Second, Illinois got beat in this game in every way except on the scoreboard. They were outplayed, outsmarted, and outcoached. A huge reason they are advancing to the final four is sheer luck. I know every team needs a few breaks to advance in the tourney. But if someone had scripted this ending for a movie the audience would walk out saying “bullshit”.

This is not to say that Illinois didn’t play great the last four minutes or show a lot of heart. Indeed they did, and they should be proud. My only point is that they could have played great and showed a lot of heart and still lost by 8.

I would rather Illinois win their games in the fashion of the 1985 Bears - not the 2001 Bears. I want them to beat their opponents not luck out at the end.

Of course, they wouldn’t be the first team to receive a few fortunate bounces on the way to a championship. But if they lose to Louisville on Saturday, I can’t help but think how I will remember the 2005 Illini: a team that was lucky to make it to the final four.

Friday Notes

My last post was premature as Mark Buehrle did not suffer a broken bone in his foot and is scheduled to start opening day.

The bad news of the week is that they brought Chloe back on 24. Is there a more annoying character on TV right now? I thought I had seen the last of her on 24 when she appeared on Fox's "The Sketch Show". I guess 24 decided to extend this year's torture theme beyond the storyline and to its viewers.

Speaking of 24, it's been very hard to take the President seriously in this year. The actor used play the father in the Married With Children take-off, Unhappily Ever After. I keep waiting for him to speak to Mr. Floppy.

But on the bright side of TV land, Mikalah Gordon was voted off American Idol. She was just plain awful (not to mention weird).

Buerhle Out

The Sox got their first bad break of the season as it looks like Mark Buerhle may be out up to six weeks with a fractured bone in his foot. Thankfully, Brandon McCarthy has been pitching great in spring training and looks like he will be a capable fill-in for a couple of starts before Buerhle comes back the end of April/early May. But even with McCarthy pitching well, the loss of Buehrle comes at a horrible time for the Sox as they start the season with a slate full of AL Central opponents.

On a personal note, I plan on blogging more after taking a couple of months off. There has been limited blogging for two reasons: first I was finishing up my MBA and my final two courses happened to be quite challenging; second, I don't follow the baseball offseason that closely.

Now that the season is approaching I plan on blogging more, although there will be a short interruption as I plan to celebrate finishing the MBA program by going out to Vegas for the final four and opening day.