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Results-Based PR

Posted By: Maik Stiebler
Date: Sunday, 1 February 2015, at 4:35 p.m.

In Response To: Results-Based PR (Bob Koca)

It seems we have to concede that nobody is willing to practically implement something that the VRR crowd would love. But isn't there anything about Rick's suggested PRvrwr that we could like? I think there is.

In a very simplified and idealized scenario - only one-point matches, perfect bot to evaluate luck and skill, neglecting the influence players might have on the number of decisions in a match, and the average number of decisions being consistent with our assumed relation between PR and winning chance - all a player can do to increase their winning chance is minimizing (own_PR - opponent_PR). What does PRvrwr do in this case? It degenerates to PR, when it really should reward players for complicating the game for their opponents, as Bob wrote. That's not very good, but at least not worse than what we currently have. Now let's relax the assumptions and see which ways there are for players to increase their winning chances which are not rewarded by PR.

In a real match, players' decisions influence the expected stake-weighted number of decisions for both opponents in a match. All other things being equal, as they say - here all other things are mainly the two PR's - the stronger opponent can profit from generally increasing the number, the weaker from generally decreasing it. Both players profit from decreasing the number of their own decisions and increasing that of their opponents. PRvrwr handles all of these correctly.

A related point is that to some extent, you can profitably sacrifice some EMG equity in low-stakes situations if you see a balancing skill differential in a higher-stakes situation (think of technically too optimistic takes in situations where you have to be contained, for example). PR is blind to stakes variations, PRvrwr is not.

Real bots are not perfect. In PRvrwr you have no incentive to play what you know the bot would play, if you know that it's nonsense. On the other hand, you are too strongly incentivized not to give your opponent opportunities to outplay the bot, as this hurts you a lot under PRvrwr. As the last sentence sounds a bit esoteric to me (and am not sure I completely understand what I wrote myself), I will still score this paragraph as a point for PRvrwr.

Compared to simply using PR as we usually do now, I think the main drawback of PRvrwr is the additional statistical noise (I don't have data about that, but I confess I am convinced about that without seeing any data). This member of the VRR crowd doesn't care about that very much and says "Play more matches then, for god's sake". I realize that this point of view may not be embraced by a practitioner trying to set up something actually useful for the backgammon community. But even then, in other regards PRvrwr compares favorably enough to PR to give it a try, I think.

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