Confidence intervals.

This article will attempt to explain why 40% winners on your
PokerTracker summary tab doesn't mean that 40% of poker
players win.

You have all heard of variance. There's also variance of the
variance. This means the variance can vary greater from table
to table. This is especially true in no limit. In fixed limit
the variance within any limit is small enough to be disregarded.

Your database is the sample of your play. From this sample the
expected winrate can be calculated. Now what you weren't taught
in Stat 2. The reliability of this expected winrate is determined
by the size of the sample and the variance of your play.

Let's return to why there aren't 40% longterm winners. In the
online 2/4 fixed full limit games the average player is losing
2bb/100. His standard deviation is about 16bb/100. Statisticians
normally use 2 s.d for confidence intervals. But I'm lazy and
will use only 1 s.d. After 100 hands average player winrate is
-2bb/100 + 16bb/100 or

-18bb/100 < average player < 14bb/100.

Assume no player is any better than any other player. Each
player loses at the rate of the rake expense. Then just under
50% will be winners.

Now increase the number of hands to 400. The square root of
the s.d. is a function of time. 16bb/100 becomes 8bb/400.

-10bb/400 < average player < 6bb/400

Those doing one quarter of a s.d. better than average will win.
That's about 40%.

Now increase the number of hands to 10,000. 16bb/100
becomes 1.6/10K

-3.6bb/10K < average player < -0.4bb/10K

That's 1.25 s.d. better to win. That's about 10.5%.

For those of you with millions of hands in your database. Only
include the players with over 10K hands. That group should show
10% or fewer winners.
................

We have all heard the truly outstanding player should be able
to win at the rate of 4bb/100. Is this really possible online?
Those who have succeeded played before 2003. The game has
tightened up since then.
Nowadays it's very unlikely that more than one in a thousand
players is truly 4bb/100 better than the average 2/4 player.
Knowing the math isn't sufficient. To maintain such a high
winrate one must play the player. Online one never can get
sufficient data on that many opponents. Most decisions are
made from small data histories. Identify opponent and leap
to sweeping conclusions which may or may not be right.
.............

Any player capable of beating the 5/10 for a net of 2bb/100
will build a decent bankroll fairly quickly. Do the math.
5K hands a week. That's only 25 hours a week of two tabling.
It works out to $1000 per week. In six weeks there should
be sufficient bankroll to play 10/20 with comfort.
This is the reason I tend to be suspicious of players claiming
to be beating the 5/10 for 2bb/100 over 30K hands. That's $6K
additional bankroll. Why is he still in the 5/10?
Players boardcast to others their winrate while winning. The
true winrate is the rate after the losing and the winning.
It's the average of the good and bad times. Maintaining 2bb/100
is a lot tougher when one includes the losing.