I am currently trying to evaluate my expected value in HU SNG. One part of this is using a binomial distribution to understand P to win exactly or fewer tournaments out of some amount.

So, I have a function of k, n, p, where k - an amount of the tournaments I won, n - total amount, p - a probability of winning a tournament.

By doing all of this, I stumbled upon one question: could I get a probability out of ROI %?

If I assume I play with 10% ROI against the limit (which is very decent), how could I transform this assumption into probability?

I thought that way. Let's assume I played 1k tournaments. ROI = (Gain from Investment - Cost of Investment) / Cost of Investment. Then, if I get 10% ROI playing 15's HU SNG, I could calculate the proportion of the tournaments I won. 10% - ROI, x - total of return, 15000 = buy-in total for 1k tournaments.

1.1 = x / 15000

x = 15000 * 1.1

x = 16500

So, 16500 - an amount of money I get after playing 1k tournaments with 10% ROI and BI = 15.

Then, I could get a sum of tournaments I won by dividing a sum by 28.78 (which is a sum minus rake). I get 16500 / 28.78 = 573,314802 ~ 573 tournaments.

So, my probability of winning a tournament is 0,57 in distance.

I would like to know does my thoughts and calculations make any sense or I'm far away from finding out the answer?

P.S. I know I could make a confidential interval for my sample proportion and understand if I have a significant edge against players on the limit, but I'm mostly just curious about the question above.

1 Answer 1


Not following where you are getting 28.78

Make it $100 buy-in and no rake so you get $0 or $200

profit = num x (200 x winRate - 100)
profit = num x 100 x .10
num x (200 x winRate - 100) = num x 100 x .10
200 x winRate - 100 = 10
winrate = 110 / 200 = 55%

  • 28.78 is how much I get after winning excluded rake. Apr 30, 2018 at 14:31
  • Still not clear to me. You should explicitly state the rake. It is not clear if 1k is the number of tournaments or the buy-in.
    – paparazzo
    Apr 30, 2018 at 14:33

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