Question about variance
Posted by HaAbDe
Posted by
HaAbDe
posted in
Low Stakes
Question about variance
I played almost 71k hands at NL2 and my winrate is 18.94bb. I put in Primedope variance calculator for real winrate 10.15bb and for observed winrate my current winrate at nl2. Primedope says that the probability that my winrtate in 71k hands is at or above 18.94bb is almost 1%. So this means that if we somehow knew that my real winrate was 10.15bb, 99 out of 100 times I would be below 18.94bb winrate in 71k hands. Since I am not below that winrate this means that we can say with 99% accuracy that my real winrate is above 10.15bb.
Is this a correct way to think about my winrate? We can't obviously know the real winrate unless we play 1 million hands(or as much hands as it's required anyway). However, I think this way of thinking is good to know where at the worst case scenario my real winrate is going to be.
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Have you identified the true standard deviation from your tracker?
With the given stats your assumptions (true WR being > 10.15 with 99% certainty) are correct.
You can as well see it in the confidence interval. With 70% certainty the winrate is between 6.39 and 13.91% (which is quite narrow, hence the low certainty) and with 95% certainty it's between 2.64 and 17.66 bb/100. As your above that, you're in the 5% interval - which spans below and above (meaning 2.5% certainty that actual WR is below 2.64 and 2.5% that it's above 17.66). So, yes, with actual winnings of almost 19bb it's very, very likely that your true winrate is higher than 10.15.
Ah - and congratulations for that. :)
BigFiszh ,Thank you! :)
I play 6max and my standard deviation is 96.27. However, I see it to change easily after each session I play and so I put in variance calculator 100 in order to be sure not to get wrong results.
When will my standard deviation is going to stop increasing or decreasing so easily? I don't check it often but sometimes when I do, I see that if I play 500 hands and I check it afterwards, it might increase from 96 to 96.4 for example. When will I know what's my true standard deviation? Does this take sth like 1 million hands just like the true winrate?
SD is the square root of variance. Variance is the median of squared results of chunks.
Sounds a bit complicated, right? :) OK, let's get real. You got 75k hands on your clock. Now, we separate these in chunks of 100 hands each. That makes 750 chunks. Let's imagine these were "mini-sessions". Now, we look at all those 750 sessions and note the deviation from your average winrate for each. Say, it were +300bb (=300bb/100), -200, +50, -80, +450 and so on. Now we square those and calculate the median:
M = [(300^2) + (-200^2) + (50^2) + (-80^2) + ... )] / 750
Say, we got a median of 9.025. That is your variance! Now, we take the square root - which is root(9.025) = 95 - and that is your standard deviation. It's a measure for the spread of actual results around the overall median (which is your current overall winrate).
In other words, a standard deviation of 95 means that on average (!) you ended each chunk within a margin of 95bb above or 95bb below your average winrate, meaning your chunks ended in a range of [-76bb;114bb].
Now, if you wanna get a feeling on how future sessions might impact your SD, just grab excel and try the following:
Cell A1 = Enter your current number of hands (75k)
Cell A2 = Enter your current SD (95).
Cell A3 = Enter your current winrate (19).
Cell A4 = Enter a formula that calculates the number of 100-chunks (=A1/100).
Cell A5 = Enter a "ficticous swingy" amount of bb won or lost over the next 100 hands (i.e.400).
Cell A6 = Enter the following formula (substitute x by the asterisk, can't do it here):
=SQRT(((A4-1)xA2^2+(A5-A3)^2)/A4)
Now, you can play around with the number of hands in A1 - to see at what amount the swingy session of +400 (or -400, doesn't matter due to squaring) does not show any "significant" impact on SD anymore.
Got clear?
I understand this better now. Thanks for the detailed explanation.
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