Saturday, June 02, 2007

Tournament Strategy and the Prisoner's Dilemma

Bob Ciaffone's article in the May 23 CardPlayer magazine got me thinking.

Briefly, Ciaffone relates a letter from a player who had five big blinds left in a home-game tourney and was debating whether or not to call an all-in raise with JJ. He offers a lot of analysis of the situation, much of it wrongheaded, but he makes it clear that in this tournament everyone is playing very tightly—five big blinds is an average stack.

Ciaffone of course said, shove your chips in, you rate to be a huge favorite, we should all hope and pray we get something as good as pocket Jacks when we're in the big blind and short on chips. And, for the most part, I agree.

However, this game is not normal. These players clearly read the beginner-level books, and they've divined that you should play tightly. And obviously, they're all playing tightly. What that means is that playing tightly is not wrong in this game. In his analysis, the writer figured he was racing, and he didn't like the idea of a race for his tournament life. In this game that line of thought is valid.

I want to emphasize that I would not play like this, even in this game. Somebody who was playing even slightly aggressively would run this game over in about five minutes. Obviously, the players in this game don't know this, and they effectively have an unwritten agreement that they won't play aggressively. When I realized this, I was reminded of the prisoner's dilemma.

Buried in the dense article I linked to, heavy on game theory, is the following "classic" presentation of the prisoner's dilemma:

Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both stay silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a two-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make. So this dilemma poses the question: How should the prisoners act?

If you're a game-theory wonk (and I'm not), you can easily show that it's in each suspect's best interest to betray the other. I was reminded of the prisoner's dilemma because of this: Everybody playing tightly in this game, is akin to everybody keeping silent in a multiway prisoner's dilemma. They have their nice poker game, which never gets to "real" short-stack, late-tourney strategy, and that's the equivalent of everybody getting a light sentence in the prisoner's dilemma. However, if one person decides to get aggressive (betray), he is rewarded and everyone else is punished. At that point, the only way to reach equilibrium again is for everybody to start playing aggressively (betraying), at which point they'll have something like a real poker game. And, somehow, that's like a two year sentence. Or something.


They sprung something on us at the end of last week, right before the holiday weekend: We were given a 28-page application for gaming licenses from the Pokagon Band of Pottawatomi Indians. It was mainly a very detailed job application, but there were three things that caused a lot of people problems, including me. First, we had to our entire criminal history (anything misdemeanor or higher we've been charged with). Second, we had to furnish our entire financial record, with detailed information on all our assets and debts. Third, we had to provide copies of our last three tax returns.

Now, I understand the reason for all of this: The tribe wants to know how much of a risk we'll be to steal from the casino. Some of the people in class don't seem to get that; they were bitching and moaning about why do they need to provide all of that information. I'm not complaining about that.

I am complaining a bit about having this sprung on me. We got the forms last Friday and had to return them by this Friday, and we lost a day due to the holiday. And, okay, I knew, or should have known, that something like this was coming, yet, but I was still caught having to scramble to get all of my information together. Even so, a lot of my tax information is estimated.

For the first seven (or is it eight?) weeks of craps class, stickman was the easy job. He had to keep an eye on the dice, and call the rolls. But now, finally, we're learning the bets in the center of the table, the last real thing we have to learn before it's all just practice. I wasn't anticipating that this would be a problem: The center bets seemed pretty obvious to me. But if a player bets several of them at once, and a roll goes by, he may win some and lose some, and you have to compute a total payout. If any of his bets are odd-sized, that can take a while. The game stops while you stand there and think, "Okay, he has a $30 'yo' bet, so he gets $450 for that, but he also had a $45 crap check and a $15 high/low, so to keep his bets up I need to subtract $60. Pay this man $390, please."

One of the pit bosses that they hired is kind of an asshole. He came around the table and asked who was ready for his audition; nobody jumped on the chance. But I observed the craps table at a live game at Blue Chip casino last weekend, and I think I was 80–90% of the way to being able to tap out one of the base dealers. Now, that said, part of the reason was that people weren't betting anything crazy; the biggest place bets I saw were $24 and the biggest bets overall were $10 come bets with $100 odds. I thought of saying that, when that pit boss was at our table, but I wasn't sure it was wise. I have no independent verification that I'm really 80%ndash;90% of the way there; I wish I'd asked my instructor today. (The instructors have been switching up. We had a different instructor this week, so when I see my usual instructor on Monday he won't have seen me for over a week.)

Whether or not I am 80–90% there on base, I'm (now) only about 30–40% of the way there at stick. I know what I need to do, but putting it all together and being smooth about it is a whole different thing.


You would think they would have this screening before training begins?

It's quite standard to provide criminal history and credit information for a "bondable" position - bank teller, wells fargo, etc. (aka anyone handling a lot of cash). If their money is insured, there is a minimum standard the insurance company requires.

However, they should be able to get all of your debt info from a credit report, so all they really need is a SSN.

I always thought employers could only ask if you've been convicted of a felony (or a crime).

If the casino (employer) is on sovereign land, basically they can ask for any info they want, standard employment legalities may not apply there.

Good luck with the new gig.
In my opinion, you're right. They should have this screening before training begins. In their defense, I think they only just got their act half-together when they asked us to submit everything. This is the tribe, remember, not Michigan, so they had to set up their own deal.

People who've been through this before, at other casinos, say that this is more info than other gaming commissions have asked for.

A lot of the application itself reads like badly-localized boilerplate from an Indian gaming trade group of some sort.

In any case, this is all submitted. My tax situation is the only likely sticking point; even though I don't owe the IRS much if anything, I'm not exactly current. If this becomes a sticking point, I'll just get the info I need (might take a while) and get the last three years taken care of. I might owe for 2006, but I am almost certainly owed for 2004 and 2005.

And, yes, the casino is on sovereign land. I don't ever expect a problem with that, but if I were to have one, I'd have to sue the tribe in their own court, as successful as that's likely to be.
Replying to the 06/30 post

Glad to see you're officially hired on. Good luck with your new job.

- Sam

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