Math Help - Poker: Am I making profit or just getting lucky?

1. Poker: Am I making profit or just getting lucky?

Hi,

Using normal distribution and/or bayes' theorem I'm trying to work out the probability that I'm making a profit and not just having good luck.

I'm interested in the maths so that I can calculate this for future scenarios.

The example scenario:

The game: SNG. 10 Players, $1 entry. Payout: 1st:$5. 2nd: $3. 3rd:$2.
The sample: 5 games played, net profit: $10. ($5 spent, \$15 won)

What is the probability that the 5-game sample above represents an underlying population of games where I'm on average breaking even or better?

From what I've deduced, there are at least two ways of calculating this, each with different answers?? The book I'm reading, "The mathematics of poker" (I think!!) says that one way would use bayes' theorem and one wouldn't?

Help appreciated!

2. Good question.

First, 5 SNG's is completely useless for real analysis. This type of tournament has very large variance. Once you get a few hundred samples the results will be more accurate, but still not that meaningful. Players who play this type of tournament online usually play many, many tables at once to lessen the variance of the session. I played these for a while, but I got so bored I had to quit.

As for your calculation, you're trying to analyze the ROI - that is the ratio of winnings to entry fees payed. So you are dealing with a proportion, and the answer can be calculated using the appropriate formula from beginning statistics and using distribution tables.

3. Thanks Jameson.

I was just using the 5 games as an example - I would be happy to use 50 or 500 games as an example as well.

I was aware that I needed to use a normal distribution graph etc.

I just wanted to know how to calculate the likelihood that I'm playing profitably... ?