Expected value and variance can be taken from trackers. Or keep statistics ourselves.
I will show how to apply these formulas using the example of SnGs HU. For example, a person plays a $7 limit and has a win/loss rate of 55% / 45% over the long run.
Then the mathematical expectation and variance will be as follows:
MO = 6.42$ * 0.55  7$ * 0.45 = 0.381$
S.D. = 6.702$ (square root of variance).
Then the confidence interval is calculated using the formula in Excel:
= CONFIDENCE (1A1, A2, A3)
Cell A1 contains the required reliability of the results. We install it ourselves. Usually this number is greater than 0.9.
Cell A2  standard deviation (S.D.)
Cell A3 is the sample size, i.e. the number of SnGs HU games for which we will look at the result. For example, you play 1000 SnGs per month.
= CONFIDENCE (10.9, 6.702, 1000) = 0.3486
Then for the upper and lower profit margins we get:
(0.3810.3486) * 1000 = 32.4 $
(0.381 + 0.3486) * 1000 = $ 874
And for the average profit value: 0.381 * 1000 = $ 381
In order to determine the BRM for a given player, it is necessary to select such a number of games at which there will be a maximum drawdown, i.e. the bottom line of the profit will be the most negative. This number is 211 games. In this case, the lower limit is equal to: 79.73 $.
Because we chose 0.9 confidence, which means that 90% of the time we don't walk out of these limits. In 5% of cases, the result will be better than the upper limit ($ 305.94 for 211 games), and in only 5% of cases it will be below the 11.4 buyins (11.4 * $ 7 = $ 79.8). So, there must be BRM = 12 buyins for this player if he wants to have no more than 5% chance of a crash.
A more conservative BRM can be calculated, for example, for a 2% crash probability. By analogy, you can calculate BRM for cash games, for tournaments. But this requires large statistics for specific games ...
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I am not a cat! I am human! ))
