Author: Robert Hyatt
Date: 13:45:59 09/10/99
Go up one level in this thread
On September 10, 1999 at 16:21:48, Alessandro Damiani wrote: >On September 10, 1999 at 15:58:45, Ed Schröder wrote: > >>On September 10, 1999 at 13:17:57, Robert Hyatt wrote: >> >>>On September 10, 1999 at 11:29:04, Alessandro Damiani wrote: >>> >>>>On September 10, 1999 at 09:36:51, Robert Hyatt wrote: >>>> >>>>>On September 10, 1999 at 08:01:35, Alessandro Damiani wrote: >>>>> >>>>>>On September 10, 1999 at 07:48:44, Ed Schröder wrote: >>>>>> >>>>>>>On September 10, 1999 at 00:19:37, Robert Hyatt wrote: >>>>>>> >>>>>>>>Here is an interesting position given to me by Steffen Jakob: >>>>>>>> >>>>>>>> /p/P5p/7p/7P/4kpK/// w >>>>>>>> >>>>>>>> +---+---+---+---+---+---+---+---+ >>>>>>>> 8 | | | | | | | | | >>>>>>>> +---+---+---+---+---+---+---+---+ >>>>>>>> 7 | *P| | | | | | | | >>>>>>>> +---+---+---+---+---+---+---+---+ >>>>>>>> 6 | P | | | | | | *P| | >>>>>>>> +---+---+---+---+---+---+---+---+ >>>>>>>> 5 | | | | | | | | *P| >>>>>>>> +---+---+---+---+---+---+---+---+ >>>>>>>> 4 | | | | | | | | P | >>>>>>>> +---+---+---+---+---+---+---+---+ >>>>>>>> 3 | | | | | *K| *P| K | | >>>>>>>> +---+---+---+---+---+---+---+---+ >>>>>>>> 2 | | | | | | | | | >>>>>>>> +---+---+---+---+---+---+---+---+ >>>>>>>> 1 | | | | | | | | | >>>>>>>> +---+---+---+---+---+---+---+---+ >>>>>>>> a b c d e f g h >>>>>>>> >>>>>>>> >>>>>>>>Obviously black is getting crushed. He has one move, Kh3, which leads to a >>>>>>>>mate in 6. Steffen asked me to try this and Crafty found a mate in 4, which >>>>>>>>doesn't exist. I spent the entire day debugging this thing and here is what >>>>>>>>I found: >>>>>>>> >>>>>>>>If you recall the discussion here a couple of weeks ago, I reported that I store >>>>>>>>absolute mate scores (EXACT scores) in the hash table, and that I adjust them >>>>>>>>so that they are always stored as "mate in N from the current position". This >>>>>>>>has always worked flawlessly for me, and still does. >>>>>>>> >>>>>>>>For bounds, I once tried adjusting the bounds as well, but found quirks, and >>>>>>>>left them alone. Wrong answer. To fix this mate in 4 problem, I decided to >>>>>>>>adjust the bounds as well, but I now set any bound value that is larger than >>>>>>>>MATE-300, by reducing it to exactly MATE-300, but still using the "LOWER" >>>>>>>>flag to say that this is the lowest value this position could have. For bound >>>>>>>>values < -MATE+300, I set them to exactly -MATE+300 and leave the flag as is. >>>>>>>> >>>>>>>>This position is cute. Because not only is it a mate in 6, but there are >>>>>>>>transpositions that lead to mate in 7, mate in 8, and there are shorter (but >>>>>>>>non-forced) mates in 4 and 5. And there are stalemates, and positions with >>>>>>>>1 legal move, and so forth. >>>>>>>> >>>>>>>>You ought to find the following variation as one mate in 6: >>>>>>>> >>>>>>>>Kh3, f2, Kg2, Ke2, Kg3, f1=Q, Kh2, g5, hg, Kf3, g6, Qg2# >>>>>>>> >>>>>>>>If you find a shorter mate, it is wrong. If you find a longer mate, you >>>>>>>>are probably just extending like mad on checks (crafty finds a mate in 8 at >>>>>>>>shallow depths (9 plies, 2 secs on my PII/300 notebook), and doesn't find the >>>>>>>>mate in 6 until depth 10, 3 seconds. >>>>>>>> >>>>>>>>It is a good test as the transpositions are real cute with white's king caught >>>>>>>>in a tiny box, but with several different moves that triangulate and transpose >>>>>>>>into other variations... >>>>>>>> >>>>>>>>If you get it right, you have either handled the bounds right, or else you are >>>>>>>>very lucky. IE Crafty 16.17 gets this dead right. But if I disable the eval, >>>>>>>>it goes bananas, yet the eval is not important when mate is possible. >>>>>>>> >>>>>>>>Have fun... >>>>>>>> >>>>>>>>I did... :) >>>>>>> >>>>>>>A simple solution: do not store a position in the hash table if there is >>>>>>>no best-move. It solves the mate-cases and also repetition cases. Also >>>>>>>there is no speed loss of the search. >>>>>>> >>>>>>>Ed >>>>>> >>>>>>Do you mean by "no best-move" >>>>>> bestmove == 0 >>>>>>or >>>>>> best<=alpha, after having searched all moves (best: minimax score)? >>>>>> >>>>>>What I do: >>>>>> if bestmove == 0 then don't store anything, just return the score (mate or >>>>>> stalemate). >>>>>> >>>>>>Alessandro >>>>> >>>>> >>>>>that doesn't make sense to me. If _every_ move at one node in the tree returns >>>>>alpha for the score, which is the best move? And since you don't have one, you >>>>>don't store anything? That hurts performance, because the next time you >>>>>encounter this position, you get to search it again, while I discover that the >>>>>last time I searched it I returned alpha, so I can just do that now and not >>>>>search anything... >>>> >>>>No, no. My answer was misleading. What I mean is explained by the following code >>>>(the code is simpilied!). I have marked the important things by an "****". It is >>>>assumed that >>>> - when the king is removed from board its position is -1 ( < 0) >>>> - alpha, beta < INF >>>> >>>>Alessandro >>>> >>>>int AlphaBeta (int alpha, int beta, int depth) { >>>> >>>>//************************************** >>>>// legality check: >>>> >>>> if (myKingSquare<0) return -INF; >>>> >>>>//************************************** >>>> >>>> if (depth==0) return Quiescence(alpha,beta); >>>> >>>> // here use info from the transposition table >>>> >>>> best= -INF; bestmove= 0; startalpha= alpha; >>>> i= 0; n= GenMoves(); >>>> while (i!=n && best<beta) { >>>> // m[i] is the current move >>>> >>>> make(m[i]); >>>> value= -AlphaBeta(-beta,-alpha,depth-1); >>>> unmake(m[i]); >>>> >>>> if (value>best) { >>>> best= value; bestmove= m[i]; >>>> if (best>alpha) alpha= best; >>>> }; >>>> i++; >>>> }; >>>> >>>>//********************************************** >>>>// no best move => mate or stalemate >>>> >>>> if (bestmove==0) { >>>> if InCheck(Me) return -MATE+ply; >>>> return STALEMATE; >>>> }; >>>> >>>>//********************************************** >>>> >>>> // here update the transposition table >>>> >>>> return best; >>>>} >>> >>> >>>Same question as before. The above simply doesn't work as you think it >>>does. Here is why. >>> >>>at ply=N you set best to -inf, and then step thru each move and do a search >>>after making it. And you pass that search a value for alpha and beta that is >>>used to terminate the search when it can prove that the score below that move >>>is >= beta (which at our ply=N node means the move we tried is <= alpha.) >>> >>>So lets assume that after we search the first move, we get a score back that >>>is obviously > -infinity, but < alpha. You remember that move as "best". But >>>the problem here is that the 'proof' search stopped as soon as it found a score >>>> beta. It didn't try _all_ moves to get the largest score > beta, just the >>>first score > beta... which is why we refer to the search as returning a bound. >>>At least as low, but maybe even lower. >>> >>>So you end up with a bunch of random bounds that are all <= alpha, and you take >>>the largest one and assume that is the best move and store that move in the hash >>>table? I will run some tests as this is easy to do, but when I tried this a few >>>years ago, my tree got _bigger_. And when I looked into why, I found myself >>>searching nonsense moves from the hash table _before_ I got to the winning >>>captures (the first of which was a move that would refute the move at the >>>previous ply.) >>> >>>Easy to test. I'll supply some data in a bit, just for fun... >> >>For one moment forget about alpha and beta, you are on the wrong track as >>alpha and beta are not a part at all of the code. You need an extra stack >>that is set to -INF at each ply. Then before you do A/B you do the bestmove >>calculation for that ply. Involved variables: SCORE and STACK, no alpha beta. >> >>Ed > >I think the best way to explain is to write a small piece of code in pseudo C, >else we talk around the point. > >Alessandro OK... here is what I did: Normal alpha/beta first: int Search(int alpha, int beta, etc...) { best=-infinity; bestmove=0; foreach (move in movelist) { MakeMove(); value=-Search(-beta,-alpha,etc.) if (value > best) { best=value; bestmove=current.move; } if (value > alpha) { if (value >= beta) { return(value); } alpha=value; } } HashStore(bestmove,alpha, etc...) } So what I did was to simply take the score for each search made after trying one of the moves at this ply, and remember the 'best' score and associated move. All I am saying is "this does not work". It is a characteristic of the alpha/ beta search. It isn't a "it might work if ..." it simply won't work. Because the searches below this node (again, assuming this is a fail-low node where _no_ move produces a score > alpha, which is the case where I claim there is never a best move to try here) return a bound on the value for that move. And I have no idea how to choose between a move with a bound <=200 and another move with a bound <= 150. Because the first could have a score well below 200. I simply don't know as I told the search below this node to stop whenever you find a score > X, where X is my negated alpha bound. Now, we have code. Did I misunderstand what you are saying? If not, then I can certainly explain further why that 'best' and 'bestmove' above are no good in this context. You can think of "best" as a random number that is <= alpha, nothing more. Which means "bestmove" is a random move chosen from the moves searched at this ply. And that is _not_ the move we want to try first when we get back to this position and it is suddenly not a fail-low position where all moves have to be tried, but rather it is a fail high position where the best move will let us cut off quickly...
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