Hi guys
First of all, wanted to thank Max Cut for such a great work. I’m very grateful for this program, it’s very useful. Also wanted to thank coon74 for his posts, seems to be a very brilliant mathematical mind. Read some parts of this thread and understood a bit better the whole thing.
Wanted to talk about
standard deviation (WARNING: BIG WALL, no summary). Afaik it seems that Max/**** made some crafted approximations, but it’s something still far to be calculated in an easy, fast and precise way. I’ve read you say we want to know standard deviation of luck-adjusted chips won / game. I would rather like to know standard deviation in buy-ins/game or buy-ins/100 games, since gives you an immediate idea of how big variance will be. Also because this is the way to compare it to std dev. in cash games.
I have seen too that there is a “standard deviation” box at Swong Sim visualizer, I guess you have to make a guess here¿? And I’ve also seen in some posts in this thread, that in an old version of the program it was calculated “mean deviation”. Mean deviation it’s ok, but it’s not so useful as standard deviation because it doesn’t get bigger when samples are more spread out, so std dev. would give us a better approximation of what should we expect.
We know that in
cash games (let me know if you need some graphs for explanation of what I want to say), standard deviation responds to a gauss curve in a frequency/winrate graph, whose vertex is our EV. Moreover, we know 1 standard deviation is the maximum difference you will have with your EV during 68% of the time (that means 34% max to either negative/positive side). And 2 std dev is the maximum difference you will have with your EV 95% of the time.
What about
spins? First consideration is that a graph frequency/winrate is not a gauss curve anymore. So first question would be: is regular std dev. useful for measure variance in this case? Maybe we should use a “standard spin deviation” stat. A graph would look as a sloping gauss curve on the left side of the vertex, and it will be a very flat gauss curve on the right side since you can get very big winnings but not very big losses (compared to winnings). Another important point here, is that the vertex of the curve is not our EV anymore, but something a little bit lower. That means our EV point would bet a little right from the vertex; and also that the “most frequent spot” is not getting our EV as it happens in cash, but getting what I would call “Real Spin EV” (RSEV). The bigger the prizes or its frequency are, the bigger the distance between RSEV and EV will be. Also the more games you play, distance gets lower in relative terms, and bigger in absolute terms.
Since the graph is not a symmetric curve anymore, I think regular std dev. is not specific enough (even that it’s going to be necessary to know it if we want to compare it with cash games). I consider it would be better to
calculate 2 kind of std deviations: the “Negative Standard Spin Deviation” (will call it NSSD), and the “Positive Standard Spin Deviation” (will call it PSSD), being of course the last one much more bigger than the first one. Obviously these std dev. will have the RSEV point as a reference, not the EV point. A result example would be something like: “For 3.000 games you have a PSSD of 800 buyins and a NSSD of 260. You have a 30% of getting PSSD and a 38% of getting NSSD from your EV point, and you have a 34% each side from RSEV point. Your RSEV will be 40 buyins lower than your EV”. Ofc I’m inventing buy-ins numbers, but I guess it shows what I mean.
Also, although is not so specific, we could
calculate usual Standard Deviation. Its formula is the result of calculating the square root of: sum of squares of each difference from the sample with the mean divided by the number of samples. Taking into account that the mean is RSEV, not EV. This would give us a good idea of how big variance is compared to cash or other games.
I think it shouldn’t be difficult to implement in Swong Sim these calculations with every sample and get some numbers.
Thank you for reading