Quote:
Originally Posted by silverace
Ah check, that is something else entirely! I used to just use those ters interchangably lol. Now we're on the subject anyways; how much EV variance do you tend to see over in general?
You can use a
poker variance calculator to show how things unfold but it is also possible to calculate it with a little bit of maths.
If we know the win probability p and the loss probability q we can calculate the variance of a game, note q = 1 - p.
Variance per game = ([win payout]^2)*p*q
This model assumes your 'edge' never changes which is not true in practice but this model will work for most things if you use the average win rates.
If you play a $0.5 BI with no juice and on average you win 55% and lose 45% then the variance per game is:
V per game = ([0.5 + 0.5]^2) * 0.55 * 0.45 = 0.2475
as Hero wins 55% the mean win per game is (0.55 x $1.00) - $0.50 = $0.05, so roi is $0.05/$0.50 = 10% roi.
If you play enough games the results become closer and closer to the Normal or Gaussian curve and we can use this to tell what you should expect long term if you play say 5000 games.
The variance of n games = the variance per game x n.
So the variance of 5000 games is:
V per 5k games = 0.2475 * 5000 = 1237.5
Now we have the variance per 5k games we can find the standard dev per 5k = Sqrt(Variance), so
sd per 5k = Sqrt(1237.5) = $35.18
5k games at $0.05 profit per game gives us the mean profit we expect as 5000 * 0.05 = $250
So after 5k game we should expect our results to come from a Gaussian 'bell' curve centred on the mean of $250 and we can also tell what the chances of falling to either side of this mean are.
Roughly 70% of the time we should get a result between +/- 1 standard deviations from the mean and so ~70% of the time we get between $250 +/- $35.18
Roughly 95% of the time we should get +/- 2 sd's so $250 +/- $70.36
Very rarely we should see a result outside of +/- 3 sd's from the mean, this happens 100 - 99.73 = 0.27 of one percentage point, or about 1 in 370 times we are outside this range $250 +/- $106