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Match analyzing paradox

Posted By: Bob Koca
Date: Wednesday, 6 July 2011, at 5:33 p.m.

Suppose that you have analyzed a match on 2 ply with bot one and will then analyze with a bot two also on 2 ply. In general the bots are equally strong. Suppose you know that the first bot rated play A as being an amount x above play B. Without knowing the particulars of what the position is or what the particular bots are then it should be the case that the second bot’s opinion of how much better A is than B should be random but with mean x. Going through the entire match there will be plays that you got “right” (according to bot 1) and those you got “wrong” again according to bot 1. Using bot 2 some of those designations may change. If a play is correct for both bots then there is no change in your total error. A play that is changed from right to wrong increases your total error and a play changed from wrong to right lowers it. Consider a play that bot one evaluates as wrong by an amount z. The cases where the second bot changes the relative ranking lowers your total error but only by z. But if it thinks it is even worse than bot 1 the change in the error is not bounded. For example suppose bot one says play is wrong by .02. Bot 2 is as likely to say it is wrong by .015 as it is wrong by .025. That on average keeps the error the same. It is also as likely to say though that play is correct by .01 (helping your error rating by only .02) as it is to say it is wrong by .05 (hurting it by .03). Thus looking at plays you got wrong will on average increase your total error going from bot 1 to bot 2.

Now consider a play that bot one says is right by an amount z. If the change going to bot 2 is less than z than there is no change in error rate (they both say you got it correct). But if the change is greater than z then you may get stuck with an error. Thus on average looking at plays you got correct will on average increase your total error going from bot 1 to bot 2. So it seems that bot 2 will give a higher error rate. But what if you had used bot 2 first? Then bot 1 would give the higher error rate. Something is not right!

What is going on? I will give my thoughts on Friday.

Messages In This Thread

• Match analyzing paradox
  Bob Koca -- Wednesday, 6 July 2011, at 5:33 p.m.
  • Match analyzing paradox
    Daniel Murphy -- Wednesday, 6 July 2011, at 6:11 p.m.
    • Match analyzing paradox
      Sam Pottle -- Thursday, 7 July 2011, at 2:34 a.m.
  • Match analyzing paradox
    Stein Kulseth -- Wednesday, 6 July 2011, at 7:23 p.m.
    • Match analyzing paradox
      Bob Koca -- Saturday, 9 July 2011, at 5:50 a.m.
  • Match analyzing paradox
    Rich Munitz -- Wednesday, 6 July 2011, at 8:10 p.m.