More about tournament chip distributions

About three weeks ago I did a post about the distribution of chip stacks at arbitrary points in the middle of a poker tournament. I managed to confirm to my satisfaction my previously dataless hunch that the curve would be skewed--steeper on the left, shallower on the right, with the mean chip stack greater than the median.

The Main Event of the World Series of Poker gives me an opportunity to do the same exercise with an even larger field, and to track it over several days. I didn't really expect that I would derive any new conclusions, but I was just curious to see if my theory would hold up, and perhaps be even better demonstrated.

I used the end-of-day chip counts as reported on the PokerNews live blog pages (which are supplied by the WSOP tournament staff). Unfortunately, I can't use the chip counts at the end of Day 1 because two of the four first-day flights went for four two-hour levels, and the other two for five (a discrepancy which was compensated for by reversing the amounts on the two different Day 2s). As a result, the data would be, to use the technical term from the realm of statistical analysis, "really messed up."

Here's how things looked at the start of Day 3, though. (Use the link to the previous post on the subject for a full explanation of how I generated the charts and what things mean.)




The specific numbers at the beginning of Day 3:

Players left: 2028 (counting only the ones with chip counts reported; every day there are a few that don't get reported, for reasons that aren't entirely clear to me)

Total chips: 192,950,180.

Mean chip stack: 95,140

Median chip stack: 80,200

Range: 3,100-610,500


Then here's how things looked at the beginning of Day 4:





Numbers at the start of Day 4:

Players left: 785

Total chips: 192,745,800

Mean chip stack: 245,540

Median chip stack: 208,500

Range: 5,900-1,380,500


And at the beginning of Day 5 (with the numbers now dropping low enough that there's a lot more noise in the data, so the curve isn't as clean):





Numbers at the start of Day 5:

Players left: 404

Total chips: 194,341,800

Mean chip stack: 481,050

Median chip stack: 396,000

Range: 18,300-1,819,000


Finally, here's the start of Day 6 (which is still playing on as I write this):





Numbers at the start of Day 6:

Players left: 185

Total chips: 195,058,500

Mean chip stack: 1,054,400

Median chip stack: 852,000

Range: 109,000-4,872,000


Tomorrow (Tuesday) I'll pick up the chip counts for the beginning of Day 7, give them the same treatment, and add it in an edit here. However, I suspect it will get even uglier, because the numbers are getting too low to look nice (currently at 64 and falling--meaning that 99% of the field has been eliminated).

Conclusions, modest as they are, remain the same as with the last post. This just adds more evidence.


Addendum, July 14, 2009




Start of Day 7 numbers:

Players left: 64

Total chips: 195,714,000

Mean chip stack: 3,058,000

Median chip stack: 2,895,000

Range: 650,000-9,745,000


Addendum, July 15, 2009

It's really kind of ridiculous to expect anything from the data at the beginning of the day of play in which they will go from 27 down to the final nine. But for the sake of completeness of the project....




Beginning of Day 8 numbers:

Players left: 27

Total chips: 195,400,000

Mean chip stack: 7,237,000

Median chip stack: 5,610,000

Range: 1,440,000 - 20,160,000