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.