Author: Robert Hyatt
Date: 07:43:52 04/30/04
Go up one level in this thread
On April 30, 2004 at 01:26:15, rasjid chan wrote: >On April 29, 2004 at 11:25:47, Robert Hyatt wrote: > >>On April 29, 2004 at 03:13:07, Tony Werten wrote: >> >>>Hi all, >>> >>>a while ago we had some discussions about diminishing returns in search for >>>chess. >>> >>>My opinion was that you can't prove that with programs searching d vs d+1 ply >>>depth because the advantage of the d+1 program gets smaller. ie at d=1 it has a >>>100% depth advantage, at d=2 it's 50% etc. >>> >>>Some people claimed that you can't compare it that way because bla bla >>>exponential something bla :) >>> >>>Well, I found an easier way to explain it. >>> >>>A few assumption: >>> >>>The easiest way to win is when you see a trick, your opponent doesn't see. >>> >>>The depth that needs to be searched to see a trick is equally divided. ie there >>>are as many tricks hidden 1 ply away as there are tricks at 2 ply ( it doesn't >>>really matter but it's easier to visualize ) >>> >>>w is player d+1 >>>b is player d >>> >>>d=1: b sees tricks 1 ply away, w sees ply 1 and 2 => w sees 2.0x as many tricks >>>d=2: b:1,2 w:1,2,3 => w: 1.5x >>>d=3: b:1,2,3 w:1,2,3,4 => w: 1.3x >>>... >>>d=10: b: 1..10 w: 1..11 => w:1.1 x >>> >>> >>> >>>Conclusion: There may or may not be diminishing returns in chess, but d vs d+1 >>>are not going to prove it, because those matches by itself are a clear example >>>of diminishing returns regardless what game is played. >> >>That is all well and good. But the fact remains that D+1 is _always_ better >>than D. How much better really doesn't matter, IMHO. Just the fact that it is >>better makes it worthwhile... > >I have a question which I'm not sure relates to diminishing returns. > >You posted in the past that Crafty don't evaluate pins and you >mentioned something about depths... nowadays .. reaching 12/14 plys... >I think your reasoning was invalid. My reasoning is based on probability theory. I am _certain_ to play the first move in a PV my search returns. My opponent is not forced to play the second move, however. And I am not forced to play the third. Etc. IE the more moves there are in the PV, the lower the probability that the move will actually be played in the real game. Or, to put it another way, the farther out in the PV some tactical trick happens, the more likely it is that I can vary earlier in the sequence and avoid the trick completely... > >Searching deeper clears 1 pin but then there is the next.. and the next. >So even if we search till 24 plys, if eval pins is beneficial, it will >be beneficial at whatever plys we reached even with super hardware. While your idea is basically correct, probability is that the farther out the pin is pushed, the less likely it is to actually influence the real game... Just play a game with any program and for each move, write down the PV and then compute how many times the second move is actually played, then the third. You'll see the probability drops steadily and quickly... > >Hope not triple dumb move! > >Rasjid > >> >> >> >> >>> >>>disclamer: I know chess isn't only about tricks, but it is an advantage to see >>>more of them then your opponent. Clearly the win percentage is depending on >>>other (random) stuff as well. BUT When you see less more, the advantage becomes >>>less. >>> >>>Tony
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