## Saturday, December 27, 2008

### Good Bye Craps

Alternate title: Probability, Why Have You Forsaken Me?

Throughout my adulthood I have been an infrequent patron of casinos. As in, maybe once a year. It made me feel a little dirty, but I found a game that was fun, social, and that I could reliably win, or at least not lose much.

I had many justifications! I had math, for one. I didn't mindlessly feed my quarters into the loud, blinky machines with the terrible house advantage. I didn't sit down at a blackjack table, barely understanding the game, begging the dealer to relieve me of my chips, the sooner the better.

I played probability, not possibility. I played a game that had nothing to do with luck! Every event an independent event! The lowest house advantage in the house! Still more likely to lose my money than not, of course, but the least likely! Barely likely!

For around six years, this worked out fine. Sometimes I would lose a small amount, say less than \$30, but I rationalized that a couple hours of entertainment was a fair trade. More often, I would come away ahead by \$50 or \$70. Soooo smug I was.

Well 2 winters ago, disaster. I walked away from Turning Stone \$200 poorer. That stung. So much that I didn't go back last year.

This year I was feeling confident enough to give it another go...but...pffft. At first I wasn't going to play because the lowest table minimum was \$10. I prefer \$5...at least if you lose money there, you do it slowly. But, since I was there, I felt silly for not playing at all...and 45 minutes later had donated \$112 to the Seneca Nation.

You win, craps. I give up.

I hope they at least support some decent schools with all that profit.

jd2718 said...

In my senior elective, when we go back the week after next, we will analyze roulette. I love this. We've just completed a month on probability, including a few lessons on expected value. They will do the calculations - they're easy.

Then we will either watch video, or play a simulation, and watch how the excitement of one big winner distracts you from all the little losers.

We've been doing this four years now, and they really get it.

Me, I don't mind any of the games in particular, but I walk in with a set amount I plan to lose, and the challenge is to stretch the playing time...plus, I only go in once every other year or so.

Jonathan

Kate said...

Hm...do you have a lesson (formal or informal) that you'd be willing to share? That sounds like fun, but I don't know much about roulette.

jd2718 said...

The course is called "Combinatorics." It's one term. We use Mathematics of Choice (by Ivan Niven, MAA, New Mathematical Library) and cover 6 or so chapters through the end of November, and then December and January we do probability, and then expected value.

I introduce expected value with the PIG game. They played for 2 days, no interruptions, no real directions from me, besides the rules. They were narrowing in, trial and error, on good strategy, I stepped in, showed them how to calculate expected value, and did so for PIG. I defined a fair game, and then gave them some simple games to analyze.

The next day they analyzed some slightly more complicated coin and dice games, including with fancier pay offs, and directions to propose ways to make the games fair.

(Before vacation we had two off days. On one of them I derived the probability of each five card poker hand - they have to memorize 2,598,560 - on the other we do the math of estate division, then I force them to divide a big pile of candy - not relevant to any of this, but fresh in my mind)

When we get back I will hand out roulette boards, hype them about the excitement of the game, teach them the payoffs, then set them to work. I have a worksheet for that, and I will send it to you.

I get pretty revved up about the course. I like the math. I get seniors to work. It really is different from what they've done before.

Jonathan

jd2718 said...

Oh, and for reference for the gambling stuff, I use The Mathematics of Games and Gambling by Edward Packel, MAA (New Mathematical Library).

Unlike the Niven book, I only have one copy of this one - the kids don't have a gambling book.

(I do everything possible to make my kids smarter than gamblers - they write a short paper explaining why people gamble in spite of the odds - it's set up as an anti-gambling assignment, putting them in the position of explaining what's wrong with this. They know that there is a difference between gambling as an occasional diversion (with the expectation of a loss) and gambling as habit or addiction. And they know the casino always wins.

This year I don't think we will have time for "the gambler's ruin" - shame that.

Jonathan

Kate said...

I will check out those books, and thanks for offering your worksheet! That sounds like a fun class for both you and the students.