Recently I have wondered if it is possible to calculate the probability of winning a poker tournament based on which strategy you use and how your all in moves are distributed. During the process of collecting data to solve this problem I have run into some interesting observations which I would like to share with you (warning: math content ahead). First a little teaser….my findings indicate that it is possible to make good mathematical estimations on how many hours it will take before the final table in a tournament is reached based on the number of players registered for the tournament:

In the table below you will get a feel for how many hours you will have to play to reach the final table based on the number of players registered.

In the following table you will get a feel for the size of tournament you should choose given the time you have available.

Here’s a recollection of how I calculated the numbers above:

My tournament statistics project is based on online poker tournaments at Fulltilt poker and more precisely freezeout tournaments (i.e no rebuys and add ons). First of all, I came to realize that I would need to be able to estimate the number of players in an MTT given the time it takes for the tournament to finish. For example if a tournament lasts 3 hours, how many players were registered to play in it from the beginning?

What I did was to note down the following information for 25 online poker freezeout tournament on Fulltilt poker:

• The time the tournament had been running
• The number of players registered
• The number of players remaining

From this data set I was able to calculate the exit percentages, that is the relative number in percent of player exits, and plot them against the time the tournaments had been running. For example, in one tournament running for 3 hours and 28 minutes, 611 players registered and of them 25 remained yielding an exit percentage 95,9%.

Player exit percentage raw data

I was quite surprised to see the raw data plot shown above because it indicates an exponential mathematical relationship between the exit percentage and the time an online freezeout tournament has been running for. This relationship seems to be independent of the buyin of the tournament and the number of players entering.

I transferred the raw data to Origin and did a peak fit analysis to determine the mathematical relationship between the exit percentage (EP) and the hours played (x). Based on my original data set I imposed the following boundary conditions:

• EP(x=0)=0% : No players exit the tournament before it starts
• EP(x=6 hours) = 100% : All the freezeout tournaments I sampled had ended within 6 hours

Player exit percentage fitted data

Turned out the relationship was exponential as expected:

• EP(x) = A(1-exp(-Bx)), in this case A was 99,5 and B was 0,96

Now here comes Now here comes the interesting part. Given the equation above, relating the exit percentage with the number of hours played, it is now possible to estimate both the hours it takes a tournament to finish and the inverse, namely the number of players entering into a tournament given the hours it takes to finish.

Since I’m not able to paste Excel formulas into Wordpress blog posts, I have made some tables with some sample data just to give you an idea of how you can use the formula.

In the table below you will get a feel for how many hours you will have to play to reach the final table based on the number of players registered.

In the following table you will get a feel for the size of tournament you should choose given the time you have available.

Hope you found the information in this article useful. If you have any comments or want a copy of the Excel spreadsheet I used to calculate the data in the tables, please let me know.

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