Is an EV Calculation Really Appropriate For Tourneys?

[Lexander]

A common argument I hear stated for the benefits of playing tournament Poker is that a good player has a higher EV for tournaments than for a regular ring game. I can accept easily that a truly great player might find such tournaments a windfall, but is this really a solid argument for a average or merely good player?

Relying on your EV makes a great deal of sense for a single decision in a ring game. The Law of Large Numbers pretty much assures that you would have to be pretty unlucky for your actual BB/hr to be terribly different than your theoretical BB/hr. Even better, the actual BB/hr converges fairly quickly for such nicely behaved situations.

There is a danger in relying on EV that I believe is often ignored by players who want to do well by playing large tournaments. The EV calculation works on the assumption that your actual BB/hr will converge to the theoretical BB/hr in some reasonable period of time. But is this a fair assumption in such a situation?

Means and Variances are nice measures when you are dealing with a normally distributed model. But one basic problem with these measures is these values are heavily affected by extreme results. A few extremes can produce means that do not accurately reflect the results a player can really expect to see in practice. Over the very longterm this would not be an issue, but how many players are going to be able to ever really reach a useful longterm?

The tournament payout structure is hardly distributed normally. The top few places get the vast majority of the payout, producing a highly skewed distribution. This situation is a disaster when trying to make use of the mean. After all, if 99 people make $1 a day and one guy makes $9901, saying that the average pay is $100 a person may be accurate but hardly representative.

This can lead to some very dangerous conclusions. For example, you can expect that your EV would go up the larger the tournament. After all, more players means more dead money and that increases your EV. Unfortunately, the increase in EV isn’t the really thing you should be worried about when playing in tournaments.

A tournament player generally lacks an infinite bankroll and certainly lacks an infinite capacity for playing tournaments. Both of these are required for the EV calculation to be completely accurate. In practice a tournament player is stuck with the problem that his chance of winning the real money gets smaller and smaller with more players.

And therein lies the real rub. Those precious few times you hit the jackpot you will make a lot of money. But when hitting that jackpot requires you to increase your odds from 1 in 10 to 1 in 100 you are putting your bankroll at considerable risk. And what truly makes the whole thing scary is that the longer you play the more likely you are to hit a truly long bad stretch.

So a tourney player might in fact have a higher EV. But that higher EV comes at a high price. With such highly skewed payouts (with correspondingly lower odds for winning as those payouts increase) you might have a positive EV but you are forcing yourself to carry a much higher bankroll, suffer much higher variance, and therefore go through long stretches where your actual results can be expected to be negative for long periods of time.

In my mind, this suggests that talking about tournaments in terms of EV calculations is misleading, and dangerous for a regular player. I would argue that we need to find another more useful measure for tournaments that would provide a regular player with a better sense of what can really be expected when playing these larger tournaments.