I do not post in this forum often, but I am looking for opinions on this question.

Firstly, I do not play Holdem for a living, only for entertainment, but I still play 2 – 3 hours a day on average. I usually play the $2 Jackpot Poker at Black Chip Poker. I am not sure it is a game that gives as much as it gets, but I enjoy the fast pace, and perhaps the opportunity of a large payout (highest table I have been on though is $40, and that only once, in about 850 games). I would say I was a below average player, but not completely dead money.

Now to the question: I have been keeping track of heads-up All-in Pre-flop results in a spread sheet. I started out of curiosity just to see how my reality compared with statistical probability. I used the percentages from the “Hand Details” in PT4, throwing out those in the 46% to 54%, because I felt they were pretty much a toss-up (the numbers below did not change when they were included).

After 703 qualifying hands,

267 had a win probability from 0% to 45%, average and median of 32.5%
436 had a win probability from 55% to 100%, average and median of 66.7%

As I interpret these numbers, over a large number of hands, I should have won about 32.5% of time I go into showdown with a hand below 45% probability, and won 66.7% of the better than 55% probability hands. Am I correct in this assumption?

In fact for the “bad” hands I won 34.1% of the time, but for the “good” hands I won only 60.1%. Since I play many more good than bad hands, that means the discrepancy in the winning percentage for the good hands has had much more impact overall than the slightly better than expected winning percentage in the bad hands.

I intend to keep on tracking this number, in the hopes that it will tend toward the statistical probabilities before I run out of money.

Welcome to the Forum! You ask a good question and have taken a reasonable approach at looking at your poker successes.

Generally speaking it is never a good idea to "sub-sample" a sample to look for anomalies. If you dig deep enough in any sample, even the most "random" sample, you can find anomalies.

So it is generally best to look at your entire database of All In Pre-Flop situations. Define Pi to be the probability of your winning the ith situation. (Ignore pot size for the moment.)

Then the following results hold:

(1) The expected number of all-ins you should win is the Sum{Pi};

(2) The standard deviation of the number of all-ins you should win is the Sqrt[Sum{(Pi)*(1-Pi)}].

From this you can determine how many standard deviations your actual number of all-in wins is below the expected number.

Why?

Thanks for your explanation. I hope I have interpreted you correctly, but if not let me know.

Assuming you calculated correctly, your number of wins is 1.23 standard deviations below the mean. This will theoretically occur about 11% of the time so while you were a bit unlucky, it is far from an outlandish or suspicious result.

By subsample, I’m sure whosnext was meaning you looked at certain ranges within your sample to find anomalies, rather than analyzing the whole sample. He correctly advised that generally that is not a good practice.