With the main event of the world series of poker wrapping up tonight, I thought I’d throw a wet blanket on the dreams of aspiring poker players by looking at the risk-adjusted payoff of entering this tournament. The results are worse than I expected.
The entry fee to the main event is $10,000. However, the prize payouts average only $9400 per player. Without any risk adjustment the average player is losing $600 by entering the tournament. To an insurance company with billions in assets, this analysis makes sense. But to people of more modest means, a reasonable amount of risk aversion makes the loss much higher.
A sensible level of risk-aversion involves treating gains and losses geometrically. This means that doubling your net worth from $100,000 to $200,000 is as good as it is bad to have it cut in half to $50,000. Based on this model of the utility of money, a person with a $100,000 net worth expects to lose $5918 playing in the main event if his tournament result is just random (equally likely to be first, second, or at any other position). This is a lot worse that just giving away $600.
Here are the results for other levels of net worth:
$1,000,000,000: loss of $610
$100,000,000: loss of $699
$10,000,000: loss of $1360
$1,000,000: loss of $3356
$100,000: loss of $5918
$20,000: loss of $8183
This isn’t the worst of it, though. Most people have higher levels of risk aversion than I used in this model of the utility of money. If we use what is called a “harmonic” model the results look even worse:
$1,000,000,000: loss of $620
$100,000,000: loss of $796
$10,000,000: loss of $1932
$1,000,000: loss of $4405
$100,000: loss of $7038
$20,000: loss of $9144
The lesson here is that you have to be a well above average poker player to have an expectation of coming out ahead playing in the world series main event. Of course, many poker players can convince themselves that they are good enough to win. Only a minority of them can be justified in their confidence.