Author: Dann Corbit
Date: 00:09:11 05/18/00
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On May 17, 2000 at 22:17:19, Michael Fuhrmann wrote: [snip] R.H.: >>doubling the cpu speed is generally said to produce 50-60 rating points. >>Since the typical effective branching factor is around 3.0, every time the >>speed is tripled, we get another ply, and using the 60 point figure above, >>a ply would be about 90 rating points, roughly. But there is nothing that >>says that as we go deeper this doesn't taper off. Nor is there anything that >>says that as we go deeper, the gain doesn't actually get larger... >> >Do you have a hunch which is true? Robert Hyatt and Ernst Heinz did "Go Deep" experiments for the ICCA. In those experiments, each new ply still gave additional benefit. However, if we extrapolate forward, at *some* point forward you will arrive at "win/lose/draw." It takes no intelligence to realize that there is no value in additional plies against optimal play. However, it may be that you will have to have 50+ plies or some absurd depth at an arbitrary point in the game. A bit of simple reasoning shows why additional plies always will have value [up to the exact point where the game is firmly decided]. Pertend you have an opponent who can see exactly two plies. You can see exactly 3. With this information, you can easily see that you will win more games. The same is true for 3 plies against 4, 5 against 6, etc. You will see the dangers that the opponent will miss. Suppose the game is 50 moves. Each player has 50 opportunities to make a mistake based on not seeing quite as far. Once in a great while (just because you did not see further still) it will turn out that the less deep move was actually better. But more often than not, the deeper analysis will be superior. If you can see one ply deeper, you have a one half move advantage. As you go deeper and deeper, the really stupid moves get thrown out. But even when you go deeply forward, odds are good that there are two or three good candidates of which one is better than the others. It is actually rather strange that additional plies don't make incredibly better moves. Each ply contains a multiple of the information in the previous ply. If (for instance) your branching factor is about 3, then an additional ply contains about 3 times more data. Doesn't it seem funny that you see 3 times as many possibilities and yet your chances of improvement are only about 15%? Seems odd to me. But then, you rapidly weed out the stupid stuff as you go deeper, until finally only the moves that are pretty good are left as possible answers.
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