One good idea for analyzing probability deviations is to consider them strictly as evidence. For instance, if you are playing poker with your buddies whom you know fairly well, especially their abilities at the poker table, and you believe you are a better player than most or all of them, and you are consistently losing to them over a significant period of time, then this deviation might be telling you that one of your buddies is moonlighting as a poker cheat!
The best way to do this sort of analysis is to use a sample grouping, say the number of hands played over a long period of time, say 20 to 40 sessions at the poker table. Remember that the smaller the sample group, the more the influence of luck, usually bad luck. If your sample group is too small, you most likely are looking at a run of bad luck where your amateur poker buddies are just getting lucky...or maybe they're just better players than you had thought. What you should do is use probability to figure what your win rate per hour should be, and then if there is more than a 30% negative deviation from that over a period of 10 sessions, you should begin to look into the possibility of cheating going on. I would say that deviations of 10 to 20% should not set off any alarm bells unless they go on and on and on. The long-term negative deviation difference between 10% and 30% or more might also be reflected by the ability of the poker cheats in question to cheat.
Remember one thing that is very important when you are trying to determine if somebody in your home game might be cheating: the cheating poker player has nothing to fear legally from his attempts to cheat in home games. True, he might risk getting the shit kicked out of him if exposed, but that is a helluva lot better than going thru the legal system and possibly ending up in prison, which are the results of getting caught cheating in public cardrooms.
BTW...how accurate is my assessment of home games poker cheating?...100%
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