Diminishing Marginal Value

Diminishing Marginal Value of Money

Years ago I got my MBA. In the process, I took several economics courses. Somewhere in one of them, I was exposed to the theory of marginal utility. Basically, the marginal utility of something is the value of one more unit of that thing. For example, if you are without water and are extremely thirsty, one bottle of water has a high marginal utility. The second bottle of water would have less value. By the time you get the 100th bottle, it is more of an annoyance than a benefit. The same logic applies to money. It has a diminishing marginal utility. If you are broke, $10,000 means an awful lot. If you have $100,000, it means something. If you are Bill Gates, it is effectively meaningless or lacking in marginal utility.



The concept of the diminishing marginal utility of money becomes important in major poker tournaments. Players with large bankrolls want to win or at least capture one of the huge prizes. Since a small addition to their bankroll is essentially meaningless, they are willing to risk finishing completely out of the money if it increases their chances of winning. Players with small bankrolls, often those who have won their entry through a satellite, want to make sure they get a payday. They are very reluctant to finish out of the money. They are often willing to give up some equity in order to ensure cashing. Making the money has a great deal of marginal utility to them.



This affects your strategy in two ways. First, you should know your own goals. If making the money is really important to you, adopt a more conservative strategy as you near the bubble. If not, look for good opportunities to gamble when close to the bubble. Second, try to figure out the goals of the other players at your table. You will have a high degree of success bluffing a slightly smaller stack who is desperately trying to get into the money. This won't work nearly as well against an aggressive pro, who has come there to win the event. One way to figure this out is to strike up casual conversations with unknown players. Someone who tells you he is a college kid, playing in his first big tournament after winning a seat online with a $22 buy-in, is likely to really want to cash. Someone who tells you he is a very successful commodities trader from Chicago, and bought in on a whim, is much more likely to be shooting for a win or at least a final table.



Diminishing Marginal Value of Chips

In normal tournaments, another factor comes into play, as well. Chips also have a declining marginal value that exceeds the declining marginal value of money. If you start a ninehanded cash game in which everyone begins with $1,500 and you win all of the money, you will have $13,500. Even if we take into account the declining marginal value of money, that $13,500 is worth very close to its face value. If you start a ninehanded sit-and-go under the same conditions, first place usually gets around 50 percent of the prize pool. Thus, ending up with 13,500 in chips in a tournament means that you receive only $6,750 in cash. Thus, chips started off being worth their face value (you paid $1,500 for 1,500 in chips), but ended up being worth only half of their face value (you got only $6,750 for 13,500 in chips).



This also makes a big difference in your tournament strategy. Take the example of a sit-and-go with a payout structure of 50 percent for first, 30 percent for second, and 20 percent for third, and four players are left. If three of them have 4,499 in chips and the fourth has 3, it is a complete disaster for any of the big stacks to get eliminated. Rational behavior suggests that they avoid any big confrontations until the short stack has been eliminated. This type of situation should be obvious to all of the big stacks, but if it is not, it is extremely unethical (well, OK, cheating) to point it out in the middle of the tournament. It is perfectly acceptable for all of the big stacks to behave in a way that increases their equity, but it is wrong for them to overtly collude to do so.



The example above is pretty obvious. The diminishing value of tournament chips should influence your strategic decisions in a number of more subtle situations. To try to solve these situations requires some type of mathematical modeling. The most popular model right now is the independent chip model, or ICM. It has many flaws. It assumes that the players are equally skilled, and it doesn't take into account the position of the blinds or big stacks. Given these limitations, it does produce some interesting conclusions, which can be modified as you like. In general, if you think you are more skillful than the other players, you should be more conservative than the model suggests. Of course, since virtually all players think they are more skillful than their opponents, they will all be playing too conservatively, so you can loosen up and take advantage of them.



I am going to conclude this column by recommending two books. They are Kill Phil by Blair Rodman and Lee Nelson, and Kill Everyone by Lee Nelson, Tysen Streib, and Kim Lee. The first is aimed at beginning tournament players, and the second at more advanced players. But there is enough in them that everyone will get something out of both. The reason I am recommending them here is that Kill Everyone gives the best discussion I have seen of the ICM and how it matters to your strategy. In one of my future columns, I will talk about these books and some of the topics they cover in greater detail, but for now, anyone wanting to learn more about the ICM should start reading Kill Everyone.



Steve "Zee" Zolotow, aka The Bald Eagle, is a successful games player. He currently devotes most of his time to poker. He can be found at many major tournaments and playing on Full Tilt, as one of its pros. When escaping from poker, he hangs out in his New York City bars near Houston on Avenue A – Nice Guy Eddie's, The Library, and Julep. Almost every Friday, he ends up at Doc Holliday's on Avenue A and 9th St. He plans to be in New York City from mid-April to late May, when he will head back to Vegas for the World Series of Poker. He has been known to buy a drink for any Card Player reader who is capable of talking about poker without mentioning bad beats.