So haven't posted on twoplustwo in a long time. But this story has caught my attention.
Anyways though, I saw someone else do a regression in R, and I thought I'd add to that work. I'm by no means a pro at this, so if I made a mistake in what I've done, let me know.
I took the google sheet of Postle's results, and did some work with linear regression in R. I'm trusting that the sheet is accurate. I'm also trusting that if the hat field doesn't say 'backwards', it is forward. I segmented variables as follows. The first segment, which is bolded and italicized, is the reference:
1) Hat -
Backwards (or no hat) vs Forwards (HatCat)
2) BB -
$3 vs $5-$10 vs $20+ (BBCat)
3) Phone -
Rail vs Lap
4) Date -
Before vs After the initial cheating accusations on Mar. 13 (I'm guessing he held back a little bit after that point, at least for a while).
Using this, we are trying to predict his hourly BB win rate, and seeing what variables are significant in doing so.
Here's what I got:
How to read this:
(Intercept) is our reference win rate. This would be a non-cheating Mike Postle at the 1/3 game. This is 14.67 BB / Hour, a very strong rate. However, we don't have much confidence in this number (p-value being high demonstrates this). Makes sense because we don't have very much data of non-cheating Mike in the spreadsheet.
From this point, add or subtract BB/Hour in the 'estimate' column for each variable you want to apply.
IMPORTANT POINT: This dataset is not large, so it's important to remember that the numbers are
not 'real' winrates, but rather
estimates confined to this dataset.
Thoughts:
1) Hat forwards postle at $1/$3 (but phone on rail), spikes up to 124 BB/hr predicted win rate. Hat forwards AND Phone in Lap postle at $1/$3 spikes up to over 300 BB/hr predicted win rate. However, the hat is close, but not quite, to the p<.05 value we look for.
If the Hat and the Phone are both significant variables, this changes the model of the cheating. It's possible Mike had both visual information of the hands, AND someone giving him strategy advice on how best to cheat, as crazy as that seems. When one or the other went away, he loses winrate, but he's still at a ridiculously high level.
This could explain why he has some sessions with both looking at his crotch and pulling at his head, but some where he seems to only do one or the other. If these are separate variables which can apply independently of each other, I think this implies there are two accomplices (one supplying info on phone, one supplying info in hat). I can't think of a reason why some sessions he'd only put his hands on his hat, while some sessions he'd only look down at his crotch, while some sessions he would do both.
2) Game Stakes (BBCat) looks to be a significant predictor of performance. Mike performs significantly worse in higher stakes games. Full blown cheating Mike still has an estimated win rate of 200 BB/hr in these games, but without cheating his predicted win rate is deep in the red. This would probably have a better p-value if I had just segmented the games into $3 BB and not $3 BB.
Obviously, Mike doesn't lose 100 BB's an hour at $10 BB poker in his natural form. However, it's certainly possible that when Mike's cheating winrate is 300 BB/hour, that playing against good players can lower the cheating winrate down to 200 BB/hr. It's also possible Mike decided he couldn't make his cheating as obvious at these levels and toned it down a bit.
3) Finally, it's plausible that Mike intentionally toned down the cheating after his first accusation, but it is not proven by this analysis. The adjusted R-squared did slightly improve by adding the variable, however the p value is .162 (which is basically the probability of getting this result by chance). If this is true, he looks to have adjusted about 50 BB/hr downwards to try to deflect attention. I'm sure his opponents appreciated that.
Last edited by cjs55; 10-10-2019 at 03:25 PM.