ITM %

Newt_Buggs · #1 06-05-2007, 09:24 PM

If on average you place ITM 45% of the time in a tournament, what would be the probability of averaging a 50% ITM over 100 tournaments? What if your true average ITM % was only 40%, how often then would you run at 50% over 100?

AaronBrown · #2 06-05-2007, 09:39 PM

Let's start with coin flips. If a coin has 45% chance of coming up heads, the chance of getting exactly 50 heads out of 100 flips is 4.82% and the chance of getting 50 or more heads out of 100 flips is 18.27%. If the coin has a 40% chance of coming up heads, the numbers are 1.03% and 2.71% respectively.

The poker tournaments may be different. For example, you might play half the time in tournaments in which you have a 90% chance of being in the money and the other half in tournaments in which you have a 0% chance of being in the money. Your average chance is still 45%, but the chance of finishing in the money 50 out of 100 times is different. Or your results from one tournament might influence your results in another, perhaps due to your confidence, or you might try harder tournaments after winning.

But if the winning probability is constant and the tournaments are independent, it's just like flipping coins.

Newt_Buggs · #3 06-06-2007, 02:43 AM

Yes I am assuming that it is a constant probability, and even thought of phrasing it in terms other than poker when I originally posted it.

I'm just curious on how you calculated this, if you don't mind explaining? I should have been able to do this on my own but it had been so long since I last did it that I can't remember.

jogsxyz · #4 06-06-2007, 07:44 PM

Hope you mean SnGs or STT and not MTT. Most MTTs pay a little over 10% of the field. If your ITM were over 40%, you would be the most successful player in history.

AaronBrown · #5 06-11-2007, 04:33 PM

The easiest way to compute it is in Excel:

Binomdist(K,N,p,False)

gives you the probability of placing in exactly K tournaments out of N, if the probability of each is p. The mathematical formula is:

C(N,K) * p^K * (1 - p)^(N - K)

where C(N,K) is N choose K, or N!/[K! * (N - K)!].

If you put "True" instead of "False" in the Excel formula, you get the probability of K or fewer successes.