Author: rasjid chan
Date: 08:38:43 04/30/04
Go up one level in this thread
On April 30, 2004 at 10:43:52, Robert Hyatt wrote: >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... You should not have replied ! I may not be discouraged from the fact that there is so much more in chess progamming; others (Uri) may give up. I don't yet fully understand, but still good, I will keep this in mind as when needed. I think this reply of yours may benefit the higher chess programmers. Thanks Rasjid > > > > > > >> >>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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