Thursday, August 09, 2012

"Average" tournament chips

A few years ago I wrote about my observation that having an "average" stack in a poker tournament puts one ahead of more than half of the field, which, on first blush, is a counterintuitive proposition. See here and here for the full explanation, along with examples taken from chip counts at the World Series of Poker to illustrate the point.

I have continued to notice this phenomenon while playing online poker ever since writing those two posts. The tournament lobbies make it trivially easy to see where one stands relative to the current average and, at the same time, figure out where one's chip stack ranks relative to all of the other players.

Every time I have checked, without a single exception, has confirmed the rule that I discovered long ago: The mean chip stack size is always greater than the median chip stack size. If you have an average (mean) stack, you are ahead of more people than you are behind. If you are at the median (i.e., there are just as many players with bigger stacks than yours as there are players with smaller stacks than yours; this is usually impossible to know in a live tournament, but easy online), then you have a below-average stack.

Here are two recent examples that demonstrate the point:

In the shot above, you can see that I exactly define the median; 50 players have more chips than I do, and 50 have fewer. But my stack, at 3535 chips, is significantly below the average, shown as 3979.

Conversely, in this shot you can see that I have a chip stack that is almost exactly at the current tournament average, but I am ahead of more than half of the field. (The difference is small because it's such a small field.)

The point is this: When you see that you have a stack that is at or near the current average for the tournament, it doesn't imply what you would tend to think. It means that you are ahead of most of the field.


DavidCF said...

I have been saying for years that the stat should be given as the median chip stack, instead of the mean. I think that'd be much more useful.

ASG said...

Unless you are looking at where you're at for cashing purposes, mean is more important than median, IMO. those guys at the bottom are likely going to be knocked out soon. If you look at median stack, it will jump in large numbers as those people get knocked out. You're trying to win/make the final table, not finish in the top 25% but out of the money.