Rob Abrazado (flatvurm) wrote,
Rob Abrazado
flatvurm

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Risk management

Because I am not yet prepared for a full-on update, let us break momentarily for a small tale. The setting is a poker tournament for which I was dealing tonight, and for those unfamiliar with the workings of a poker tournament, I have prepared a brief introduction. Everyone else can skip it.

In a regular poker game, you show up with money, change it for chips, play poker as much or as little as you want, finish, and then change the chips back into money. In a tournament, though, you show up with some preset amount of money. Most of this money (the "buy-in") goes into a prize pool. The rest (the "entry fee") is money for the house. You pay the money and you receive some number of tournament chips. They play just like regular poker chips, except that they seldom represent any actual amount of money. You keep playing until you run out of chips, at which point you are out of the tournament. The tournament continues until only one player is left who has, at this point, accumulated all the chips that were in play. The prize pool is then divided up among the top finishers of the tournament, and everybody goes home. How the prize pool is divided depends on who is running the tournament, and is often also based on how many people showed up. If 100 people entered the tournament, perhaps the top nine or ten finishers get paid. The amounts they get paid also vary based on who is running the tournament. Now...it is often the case in poker tournaments that the top finishers will agree to stop playing and "make a deal" or "chop" the remaining prizes. For example, say 100 people entered a tournament and only five players remain. Those five players may agree to split up the remaining prize money among themselves in some fashion other than that intended by whoever is running the tournament. This is all quite normal and happens all the time.

So. I dealt this tournament today, and it got whittled down from an initial 370 or so players down to the final 13 players. The prize structure at the Borgata is pretty top-heavy (in my opinion, anyway) meaning that the top finishers receive a much more significant cut of the prize pool than the lower finishers. Because of this, chopping is very common. It so happened that today there was one runaway chip leader among these 13 remaining players, and the rest of the people still in had a wide variety of chip stacks left. A deal was discussed, and what was finally hashed out was that the current chip leader got a hefty prize (though still less than first place money), and the remainder of the prize pool would be split up equally among the remaining 12 players. The chip leader was to get something like $41K and everyone else was getting close to $10K. (Actual first prize was like $57K. 13th place would get just shy of $2K. Not a bad deal for the short stacks!)

As I said, these kinds of deals are quite common, but at the end of the day, they're still unofficial. From the casino's standpoint, the payouts have to be made as the tournament payout schedule indicates; the state casino commission is pretty hardcore about that. Players can rearrange money as they see fit after they get paid, but the casino still has to assign actual prizes to actual people, so someone has to take 1st place, someone 2nd place, etc. It was decided on this particular occasion that the places would be determined by chip stack size. That is, the chip leader would take 1st place, the second biggest stack would take 2nd place, etc. Again, very common. Everyone agreed to the deal, and everyone started counting out their stacks.

Once the stacks were counted, the person with the second-biggest stack came to the realization that he was getting the short end of the stick on this deal, and he suddenly decided that he no longer wanted to chop the prize, and instead wanted to play on. Now, he was completely within his rights to do this, as far as these things go, but it was pretty much a dick move. It also inconvenienced a couple of players who, thinking the tournament was finished, had actually left the area to get their IDs and such so they could claim their prize money. (It was owing to the tournament staff at the casino, I should mention, that this was merely an inconvenience and not actually putting those players at risk of losing money, which would have happened in a stricter environment.) So this guy, by reneging on the deal, basically made a lot of enemies.

You can probably guess the rest of this story, just based on the fact that I'm telling it at all. The player who reneged on the deal ended up being the next player to bust out of the tournament. He took 13th place and walked out with under $2K of prize money after turning down a deal to get $10K. He left the tournament to thunderous applause (and a bit of needling as well) from the remaining 12 players. Another (nearly identical) deal was reached soon after, and the tournament ended. (The chip leader still got $41K, and everyone else got a little bit more, owing to the $8K or so that 13th place left behind getting split up among everybody else.)

I share this story now because I think it highlights a couple interesting things. First off, there's an element of poetic justice in the outcome. The majority sentiment among the remaining players was that 13th place got what he deserved for being greedy. And that feeling certainly appeals in an Aesop's Fables kind of way. But the fact remains that he didn't really do anything "wrong," aside from back out of the first agreement and piss everyone off, which are wrong things to do in their own way. But what I'm saying is that he didn't break any rules, and he didn't make any unsound decisions. Without actual chip stacks and the payout schedule (not to mention a buttload of math), I don't know exactly what the guy's equity was in the prize pool, but I feel comfortable saying that it would have been more than $10K. ($10K was something like 5th or 6th place money, if I recall.) So from the standpoint of mathematical expectation, he did the right thing by not making a deal. What that means to gamblers is: if he makes that decision the same way every time, then over the long term he will get more money. Part of making gambling decisions, though, is accepting the risk of making the gamble. He ended up losing $8K on a play that "should" have been profitable. Well, things like that happen. But what's interesting to me is how this "right" decision probably doomed itself due to factors that had nothing to do with probability.

First off, reneging on the deal put a bullseye on this guy. Suddenly, everyone wants him out of the tournament. It is not unreasonable to think that people would play differently against this guy now than they would have had he not backed out of the deal. In fact, it's hard to think that he went from 2nd place chip stack to the felt that quickly unless people started gunning for his chips. And while opponents making suboptimal plays is generally something you want to have happen, you don't want it when they're coming after you in particular and it's this late in a tournament when short-term effects have huge consequences. When people start coming after you, you really need luck on your side to make it work in your favor in the short term.

Secondly, in order for this decision to really make sense, it will have to be repeated. (Many times, actually, in order to achieve that sought-after "long-term" effect.) Now, given the consequences of this decision this time (both social and monetary), how easy do you think it's going to be for this guy to make this same decision a second time? Not that easy, I'd imagine. In doing what he did, he pissed off a bunch of people and lost $8K in the process. That's not something I'd be in a hurry to do again. It's possible that in making a positive expectation decision this time around but getting burned, this player will in the future make less positive decisions, thereby ensuring that this particular move will never bear its intended fruit in the future.

Anyway, I just thought this was an interesting thing to look at. The human slant on this involves things like justice and karma and jazz like that. The guy held out for more money, and ended up with less. Makes a great story. But remember that in a lot of other universes where the cards fell a little differently, this guy was able to make good on his equity and cash out above the $10K mark, thereby justifying his decision. People might grumble that he didn't deal, but no one could say that it wasn't the right thing to do. But in this universe, he caught flak, caught the bad cards, and caught a loss on his bottom line, and everyone else involved gets to feel smug about it. It's a crazy ol' world.
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