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Originally Posted by angry_man
I certainly wouldn't dispute a correlation, and I'd expect a strong one. Have you got a large enough sample size to pick out whether the very long term trend shows a steady deviation between the two lines? (I'd not be shocked, but it would be complicated to figure out reasons so I'd rather not try unless there's confirmation one exists in the first place!)
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I haven't seen anything to suggest that the adjusted line is likely to be biased over the long term. I've run it on very big samples of my own SNGs and my adjusted and actual ROIs are very close (re-running atm to get the exact difference...).
I don't think the correlation I mentioned will cause long term bias as over the long run your $EV_luck will just act as a random walk and have no preference for being +ve or -ve (I've tested this on huge samples by taking every 2-way all-in and randomly choosing which side of it a simulated hero should have - over 100's of millions of simulated all-ins the $EV_luck line behaved as a random walk - I did this early on to try to detect bugs in my original code).
The only place where I think bias can creep in is the fact that you are assuming the remaining board cards are uniformly distributed from the unknown cards. The "bunching effect" or it's postflop variant (ie: multiple players seeing a flop and the ones that don't hit folding, etc) could have an effect too.
My best guess though is that the bias (if any) is going to be dwarfed by the sampling bias of the players looking to use the application. It's far more likely that a player who (rightly) feels he is running bad goes to seek out such an application.
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Personally, the reason I care is because I've just started playing a form of the game that's new to me. So far, my adjusted ROI is acceptable (to me), but non-adjusted is definitely not. Most forms of the game I could confidently pass the apparent bad luck off as genuine because of my playing history, but with these I can't. Of course, I'm looking carefully for serious problems with my play but not seeing anything really major but I'd rather not have to play thousands of games only to discover it was just a calculation bias and there really *is* something severely wrong!
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You posted above that you have run it on only 300 SNGs and this is just not enough to get sensible output.
If you are statistically-minded then it's not hard to use the output of my application (possibly HEM's too) to get an idea of the amount of variance the all-in luck is capturing (ie: subtract each cell's value from the one above to get back to the actual data instead of the cumulative data and then work out the standard deviation for both the adjusted and the non-adjusted columns).
From what I've seen so far it appears as though you still need to play 1500-3000 SNGs to get a good idea of your "true" winrate and samples of less than 500 SNGs can often give misleading/strange results. This is still pretty good though, as without luck adjustment you would need 10-20k SNGs to get a good idea of your "true" winrate and often you could get "strange" results for 2k+ SNGs.
(I will post my adjusted and actual ROIs when it finished running on all my hands...)
Juk
Two Plus Two
Linear Mode
