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Old 10-24-2005, 11:38 AM
AaronBrown AaronBrown is offline
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Join Date: May 2005
Location: New York
Posts: 505
Default Re: Utility Function for Chips

I think you are making two different points.

First is that the individual preferences of a player might overwhelm calculations based the mathematics of the tournament. While that could be true in principle, I don't think it's very important in practice. Whether you love or hate risk, in precisely what flavor, will determine whether you enter the tournament, but once you're in, it almost always makes sense to try to win as much money as possible. One guy might care only about the dollars won, another might be willing to take a lower expected value for a better chance to win first place, another might take a lower expected value to reduce the chance of being eliminated early. But only in extreme cases would these considerations make the marginal utility of chips increasing.

There are two strong reasons that the marginal utility of tournament chips decreases. First is that some of the prize money is given to people who do not finish first. That means some of the value of your second chip is wasted, and more of each subsequent chip, because it decreases your chance of winning some of the lesser prizes by increasing the chance of winning first prize.

The second relative advantage of a shortstack is that you may win a pot when a hand that could beat you folds after you are all-in.

I think your second point is that different playing styles favor different stacks. One guy might play at his best when shortstacked, another might be best at exploiting the advantage of a large stack. Again, that is true in principle, but I can't believe it is important enough to change the overall declining marginal utility of chips.
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