Utility in Dealmaking

An interesting perspective on the tournment dealmaking process

by Lee H. Jones | Published: Oct 18, 2005

"One man's ceiling … "

As the poker room manager at PokerStars.com, one of my more interesting duties is hosting the final table of our big no-limit hold'em tournament every Sunday afternoon. I chat a little with the players, but for the most part I stay out of the proceedings; I want them to be able to concentrate on the very serious poker at hand. The key job I have there is to facilitate any deals that the players want to make.

Basically, if all the players want to discuss a deal, I pause the tournament. They either come to an agreement or they don't. If they do, I confirm that they're all agreeing to the same deal, and then actually move the money around when the event is over.

Recently at the final table of our monthly $500 buy-in event, we'd gotten down to four players. Because of the number of entrants, there was about $430,000 left in the prize pool, with the prize money distributed $190,000, $112,000, $74,000, and $54,000. The four players had stacks ranging from 1.3 million chips down to about 700,000 chips.

During a break, one of the players suggested that they make a $100,000 save. That is, he proposed that each player take $100,000 from the prize pool, and that the remaining $30,000 be left for whoever actually won the tournament.

Before I go further, let me mention that I never comment on the quality of a deal that the players are discussing. My job is to ensure that the numbers they come up with equal the total prize pool available and that everybody is agreeing to the same deal. Also, PokerStars has instituted a rule that any deal must leave at least $10,000 on the table for the ultimate winner. This ensures that the tournament is played out in good fashion, and I explain that rule to the players if necessary.

Anyway, the other three players quickly accepted the $100,000 save idea, and they went ahead and played for the remaining $30,000.

A friend of mine wrote to me saying that the fellow who had the large chip stack (about 1.3 million) made a terrible deal. "He had almost twice as many chips as the short stack. He gave up a ton of equity! He should have kept pounding on those guys; he probably would have won the whole thing. At the very least, he could have waited until the short stack busted out and then made a deal with the other two."

Well, I disagree. While I don't believe in any kind of "curse" befalling those who refuse to make deals, there are two things that I don't think my friend considered:

1. Because of the "percentage payoff" nature of this (and almost every) tournament, having twice the chips doesn't give you twice the dollar equity. I don't remember the exact chip counts, but let's do an experiment. I assigned the chip leader (call him "Jerry") exactly 1.3 million chips and the short-stack player half that (650,000). I gave the other two players stacks between 1.1 million and 1.2 million chips. Using a chip-count spreadsheet that I have to do tournament chops, I computed the dollar equity that each player had (assuming they left $10,000 on the table for the ultimate winner). Jerry ended up with about $115,000 equity, while the short stack had $85,000 equity. And since Jerry had almost exactly 30 percent of the chips in play, his equity in the remaining $10,000 would have been $3,000. Instead, he got a guaranteed $100,000, plus $9,000 equity in the $30,000 that was left on the table (note that leaving a large piece to play for was advantageous to the big stack). So, he went from $118,000 in equity to $109,000 in equity – about a 7 percent loss. I don't think that's the huge equity hit my friend thought Jerry was taking.

2. This one is perhaps more important. It's about utility. That is, we human beings don't assign equal value to constantly increasing ownership of something of value. For instance, if you are starving, one bag of beans is almost invaluable to you, as it prevents you from dying. The second bag of beans still may be useful to you, but it's not near as useful as that first one. And it's pretty easy to see that the 30th bag of beans is far less valuable than either of the first two. Similarly, if you are broke and somebody gives you $5 million, you are now financially set for life. But if he gives you a second $5 million, you probably won't be quite as appreciative. After all, once you have $5 million, your "needs" are taken care of. Most people (reasonably) believe that the utility of that first $5 million (a lifetime of food, shelter, health care) is more important than the second $5 million (second homes, fancy cars).

Now, how does this all apply to a tournament deal? Well, our chip leader, Jerry, may very well get much greater utility from that first $100,000 than he would from the potential of the $190,000 that winning first place would have gotten him. For instance, let's suppose that Jerry and his wife wanted to purchase their first home, but didn't have any savings for a down payment. The down payment on the house they wanted was $80,000. By making that deal right then, Jerry guaranteed that he and his wife would be buying that house (and would have $20,000 to remodel when they got into it). By refusing the deal, he might have won the whole thing, sure, and had the house plus $110,000 for the remodel ("nice kitchen, Jerry"). But, all it would have taken was a three-outer here and a flush hitting there, and Jerry could have ended up with $54,000 – $26,000 short of his house down payment.

I doubt that's exactly what was going through Jerry's mind when he agreed to the equal $100,000 save; it might have been something like, "Wow – $100,000 is a lot of money, and I'm very tired after playing poker for seven and a half hours. I think I will accept this deal." When enormous sums of money are involved, dollars become very nonlinear in value (to use an engineering term). And that devaluation curve is different for everybody. It's important to respect others' needs to maximize their own utility while you maximize yours.