Posted by Dr Fro 8:46 AM
One of my first posts was called "there is no transitive property in poker" on Sept 23.

John's post below deals with a situation where his overall strategy is superior to Al's overall passive strategy. However, when involved in the same pot, Al's strategy tends to foil John's. This may be somewhat due to luck, but it is also an example of what I am talking about.

It is funny that just last Friday, Boyd was complaining that he can't beat Todd, Todd said he can't beat me, I said I can't beat Juan, Juan said he can't beat Matt, and Matt lost to Boyd. (actually, I don't remember who foiled whom, but that was the gist of it). This shouldnt be terribly surprising because often in game theory (and certainly in poker game theory), rarely does one strategy dominate all strategies. Even optimal stratgey (we'll call it Strategy A), which fares the best against most strategies most of the time, will consistently lose to an alternative strategy (we'll call it Strategy X). The reason that one does not switch to Strategy X is that it only fares well against Strategy A - it loses against stategies B throught Y, making it an overall horrible strategy.

So when you get beat by a bad player know that "luck" may be the reason why, but another possible explanation is that their style of play can expect to consistently beat you. However, these losses are just a cost of doing a profitable strategy.

[Consider a business like retail that makes a lot of money by spreading their clothes out for customers to peruse unescorted. This is the optimal (and most common) strategy for retailers ("Strategy A"). However, the strategy of shoplifting (if done well) consistently foils the wide open market ("Strategy X"). The retailers view this as a cost of business. They do not retreat to a business strategy of selling only from a catalogue just to avoid the losses to shoplifters. They view it as a cost of business. And, btw, I think the Walton family makes more money than the most succuessful shoplifters.]

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