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Madd
12-24-2004, 09:55 PM
In December I moved up and tried out a new level. As everybody I would like to know if I beat the higher level, however you need quite a lot of tournaments to know if you're a winning player or not. Maybe I get lucky for a few hundred sitngos or Lady Fortune doesn't like me at all. Before I quit my day job although I suck, or I stop playing poker for good although I'm too good to be real, I would like to know if I run hot or cold.

The question is: How to determine if you're running good or bad? The typical situations in which you put a lot of chips at risk although don't know much about the outcome are the coinflips.

So, what I did was: I tracked every all-in and the probability to win the all-in in an Excel-table.
E.g. I pushed with K9, got called by A6 and lost, then the entry reads like this:
K9 A6 41% L,
or somebody pushed HU with J2s on a board of T72 and I called with T4s:
T4s J2s T72 78% W

I only tracked "coinflips" if I voluntarily put money into the pot and another player or me was all-in. That means that I tracked situations in which I had to pay the big blind of 400, had 402 in my stack and voluntarily put the final 2 chips into the pot. I did not track situations in which I only had 398 chips and the big blind put me all-in.
I also didn't track all-ins after the river card because there was no luck involved in the outcome.
These statistics obviously don't take into account the tournament situation or how many chips you win/lose, but you can't have it all.

Adding up all win percentages gives the expected number of won all-ins. This number divided by the number of all-ins gives the average win percentage. Based on these figures and the number of won and lost (and split) coinflips, one can calculate the probabilities to end up better or worse.
(Assuming the all-ins are binomial distributed with p = average win percentage which should approximately give the correct result. Alternatively, you can calculate the standard deviation and use the normal distribution.)

At the new level I played 100 tournaments and reached a whopping ROI of - 4,8%. However, the all-in gods didn't serve me well as I tracked 254 all-ins with an average win probability of 51,1% (so I was supposed to win 130 of them), but I only won 108, split the pot 11 times and lost 135. The probability of having a better result is 97,9%, having a worse result 2,1%.

Questions, comments, suggestions? Did anybody work on some similar approach before? If yes, is my average win probability too low? or too high (not showing enough aggression at the later stages)? How much better would my ROI approximately be if I would have won the "right" amount of all-ins?

Happy Xmas