I Who would win a perfect game of chess?

[PeroK]

A question related to this. If I had a chess book thta contained every possible game of chess(10^100 pages or 10^1000 pages). And if i could with infinite speed find any page I needed, could I beat a grandmaster if I were a beginning player?

If you are a beginner and want to beat a grandmaster all you need is a computer!

 

[mfb]

Could you explain why you think this is the case? I find it to be a dubious claim.

Consider it from the point of a losing position: All moves must go to a winning position for the opponent. With about equal material this is a really rare condition. There are not many losing positions. If it's your move and you want to keep your advantage you must move to one of these. If you can find any of these you have a winning position - they are common.
If the game is a draw then you still need to find a position where the other player cannot move to a winning position (for them).

Sure, in the late game these conditions are easy to find. You can move around your king forever or until the 50 move rule applies. If one side has a big material advantage it's also easy to find - but that shouldn't happen in this case (unless white can force a win and the amateur makes very poor choices in their losing position, knowing they can't force a draw).

and count how many moves result in an evaluation between, say, -0.8 and +0.8 (in my experience, this is usually the boundary between winning/drawing)

It's the boundary with current computers or players. There is a good chance a perfect player could force a win from most of these situations if they are not too late in the game.

 

[Infrared]

If the game is a draw then you still need to find a position where the other player cannot move to a winning position (for them).

Kind of... for a side to make progress, there is usually not a single move that does the trick. You generally have to follow a plan for several consecutive moves to gradually improve your position. Randomly choosing a move that preserves the evaluation at each juncture won't do this. You'll choose plenty of suboptimal moves that don't help/might worsen your position and throw away any progress you've "accidentally" made, but aren't bad enough to actually change the evaluation. I can give some examples if you'd like.

It's the boundary with current computers or players. There is a good chance a perfect player could force a win from most of these situations if they are not too late in the game.

Current computers aren't perfect, but they're as close as we have. And they indicate the drawing margin in chess is rather large. I'm not sure why you think there is a "good chance" things are much different in a perfect game.

 

[mfb]

Current computers aren't perfect, but they're as close as we have.

You know that means nothing.

And they indicate the drawing margin in chess is rather large.

I expect perfect players to draw, but I also expect that nearly all games by humans don't follow such a strategy. Replace a human with a perfect player after a few moves and I expect them to win with white most of the time, and maybe even with black (if you replace both, then whoever is moving next is more likely to have a winning position).

Do you Nim? It's a nice game for game theory. It can't end in a draw but it shows nicely how the winning/losing moves work together. If you have a losing position you can have something like 10-20 possible moves. If you have a winning position there is often exactly one move you have to follow, otherwise the opponent can force a win.

 

[PeroK]

You know that means nothing.I expect perfect players to draw, but I also expect that nearly all games by humans don't follow such a strategy. Replace a human with a perfect player after a few moves and I expect them to win with white most of the time, and maybe even with black (if you replace both, then whoever is moving next is more likely to have a winning position).

The top engines would beat a human opponent, even the world champion, almost every time with white or black. Just look at Stockfish's ELO rating. Humans eventually crack under the relentless pressure of the computer's relatively flawless play.

 

[Infrared]

You know that means nothing.

I disagree- my personal view is that the top computers play close enough to perfect chess that we can make inferences like this. But aside from this, the higher the calibre of play, the more draws we see. I don't see any reason why this trend would suddenly reverse, and that the path should be so razor thin.

.I expect perfect players to draw, but I also expect that nearly all games by humans don't follow such a strategy.

Neither does a player who randomly chooses among the moves that preserve the evaluation! I don't see what's wrong with my previous argument.

Randomly choosing a move that preserves the evaluation at each juncture won't do this. You'll choose plenty of suboptimal moves that don't help/might worsen your position and throw away any progress you've "accidentally" made, but aren't bad enough to actually change the evaluation.

Do you Nim? It's a nice game for game theory. It can't end in a draw but it shows nicely how the winning/losing moves work together. If you have a losing position you can have something like 10-20 possible moves. If you have a winning position there is often exactly one move you have to follow, otherwise the opponent can force a win.

I'm aware of Nim, but I don't think it's similar to chess at all. I think a better comparison would be with checkers, which has been solved to a draw, and my understanding is that it is very "drawish" in the sense that there are usually many paths to a draw.

May I ask if you've studied chess at all? Your views certainly aren't standard in the chess community.

 

[mfb]

The top engines would beat a human opponent, even the world champion, almost every time with white or black. Just look at Stockfish's ELO rating. Humans eventually crack under the relentless pressure of the computer's relatively flawless play.

Indeed. And future programs will beat current programs easily.
It's a common mistake to look at the current situation and to say "that's the best we can possibly get. How could it possibly get better?"

Your views certainly aren't standard in the chess community.

Which view exactly? That the starting situation is probably a draw is the general expectation. That a particularly bad move can ruin the game should be fairly uncontroversial. That computers outplay humans from nearly any position in the early game is clear as well - demonstrating that they can win where a human doesn't figure out how. A perfect player would outplay the computers quite significantly, too.

 

[PAllen]

Anyone can explore the question of draw breadth and similar questions in chess assuming perfect play for the test case of 7 or fewer pieces (instead of just arguing). My guess is the general nature of positions with more pieces shouldn’t be that different from 7 pieces. Just go to:

https://lichess.org/editor

set up a position and select analysis board. If the position involves 7 or fewer pieces, you will get perfect information, including distance to mate for winning moves (using tablebases).

 

[PAllen]

Anyone can explore the question of draw breadth and similar questions in chess assuming perfect play for the test case of 7 or fewer pieces (instead of just arguing). My guess is the general nature of positions with more pieces shouldn’t be that different from 7 pieces. Just go to:

https://lichess.org/editor

set up a position and select analysis board. If the position involves 7 or fewer pieces, you will get perfect information, including distance to mate for winning moves (using tablebases).

Here is what I see:

1) For materially balanced or even unbalanced by one pawn, most are drawn, and in most cases many moves draw (only a few lose).

2) If a balanced position is a win, there are usually only one or a few moves to win.

3) For a substantially unbalanced position that is a win, many, and sometimes all moves win. However, most of them are nonsensical, in that they do nothing to bring the win closer, they just don't give away the win. If they were all scored with 'forced win', and you randomly select from them, you could imagine a won game that never ends yet is always 'won'. Of course, with Nalimov tables you can always choose the shortest win. The link I gave uses syzygy tablebases, which have less information, but you can still always make progress from the given information.

I believe most chess GMs would say these characteristics are true of chess positions in general, not just with those with 7 or fewer pieces.

 

[PeroK]

Here is what I see:

1) For materially balanced or even unbalanced by one pawn, most are drawn, and in most cases many moves draw (only a few lose).

Material is the biggest single factor in a positional evaluation, but one side can have a material deficit and anything from a winning edge to a crushing position. Pawn and exchange sacrifices for short-term tactical or long-term positional advantage are common. Especially at grandmaster level.

Moreover, many games have material equality long after one side has a winning advantage.

In my experience, positions a clear pawn up are more often winning that drawn.

 

[Infrared]

Indeed. And future programs will beat current programs easily.
It's a common mistake to look at the current situation and to say "that's the best we can possibly get. How could it possibly get better?

I'm not sure. Alphazero was generally regarded as a massive improvement over stockfish (the previous best chess engine). Still, in their match, 839/1000 games were drawn. When a new best engine comes along, with an entirely structure (reinforcement learning from zero knowledge vs traditionally programmed with human heuristics), and still the large majority of games are drawn, I take this as evidence that computers are converging on perfect play.

Which view exactly?

This:

Typically you expect a game situation to have just one, maybe two moves that preserve your current status unless you are in a losing situation or it's in the late game approaching a draw.

In balanced position, this is rarely the case unless there is a very specific tactical reason. If you are in a position where you have only one or two moves, it's probably you're worse because you're opponent previously played strong moves that put you under pressure- this is unlikely to happen if they just played moves randomly that do not change the evaluation. There can be lots of moves that don't objectively lose, but still aren't good.

 

[PAllen]

Material is the biggest single factor in a positional evaluation, but one side can have a material deficit and anything from a winning edge to a crushing position. Pawn and exchange sacrifices for short-term tactical or long-term positional advantage are common. Especially at grandmaster level.

common in the sense of a reasonable fraction of games have them. Uncommon in the sense that most positions during a game do not have a valid sacrifice available.

Moreover, many games have material equality long after one side has a winning advantage.

again, you are talking games and I was talking positions.

In my experience, positions a clear pawn up are more often winning that drawn.

It so depends. If only kings and pawns, yes. On the other hand, if each side has a minor piece, not so much. Even if GMs fail, perfect play on both sides most often ends in king and piece versus king, which is drawn. Perfect play has more cases of turning “practical winning chances” into draws than cases of “practical drawing chances“ becoming losses.

 

[Infrared]

It so depends. If only kings and pawns, yes. On the other hand, if each side has a minor piece, not so much. Even if GMs fail, perfect play on both sides most often ends in king and piece versus king, which is drawn.

I don't think this is true- the stronger side is not obligated to allow so many pawn trades. If all else is equal, a pawn up in a minor piece ending is often objectively winning (there are some important classes of exceptions of course, like opposite color bishops, or if all pawns are on the same side of the board)

 

[PAllen]

I'm not sure this is true. If all else is equal, a pawn up in a minor piece ending is often objectively winning (there are some important classes of exceptions of course, like opposite color bishops, or if all pawns are on the same side of the board)

No, you don’t need those cases. You just need to be able to reach most any position of two kings, two pieces, and one pawn. Then one piece sacrifices for a pawn, leading to draw. Looking at perfect play using tablebases, this is achieved far more often than human GMs can achieve it.

For example, this is a random position that many GMs might have trouble holding as black, but is a draw with perfect play

https://lichess.org/analysis/8/8/3kn3/2p5/8/1P1KP3/3B4/8_w_-_-_0_1

 

[Infrared]

I've looked at plenty of pawn-up endings with engine analysis in my chess study- it's very often winning. The side a pawn down can't in general force enough pawn trades to reach those drawn positions. To make progress, the stronger side can try to create a passed pawn to win more material, or to distract the opponent's king.

For what it's worth, my FIDE is around 2100 and my blitz rating on chess.com is a little over 2400.

 

[PAllen]

I've looked at plenty of pawn-up endings with engine analysis in my chess study- it's very often winning. The side a pawn down can't in general force enough pawn trades to reach those drawn positions. To make progress, the stronger side can try to create a passed pawn to win more material, or to distract the opponent's king.

For what it's worth, my FIDE is around 2100 and my blitz rating on chess.com is a little over 2400.

You are rated higher than me, for sure, but I think our disagreement probably boils down to how to count positions, and what is a random position. In my last post, by random, I literally mean that. I placed the material without any thought.

 

[Infrared]

Sure, but one key feature is how many pawns are left. The weaker side wants fewer because then the position is closer to being drawn, as you noted. In your example, it's 2 vs 1, so it's not so surprising that the weaker side can hold. In a similar ending with, say, 6 pawns vs 5, I'd expect the stronger side to be winning much more often. Of course, this can't be tested with a tablebase...

 

[mfb]

I took a random game, Carlsen vs. Ding, blitz game from last year, up to here:
1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 54. Ba4 Nf6 5. O-O Be7 6. d3 b5 7. Bb3 d6 8. c3 Na5 9. Bc2 c5 10. d4
and put that into https://lichess.org/analysis
Stockfish says +0.3
Then I made some random nonsense moves:
Ra7 -> +1.3
Rb8 -> +1.3
Rg8 -> +2
h6 -> +1.2
c4 -> +1.4
b4 -> +1.3
Nb7 -> +1.9
Nb3 -> +5.3
Nc4 -> +1.5
Most of them are "doing nothing". One of them sacrifices the knight. They all give white a big advantage. All larger than 0.8, the threshold where Infrared expects a win for white.
Then I looked for non-random moves:
cxd4 and exd4 preserve the +0.3.
Qc7 leads to +0.4
I didn't find anything else that is reasonable.

There are three moves that don't ruin your position completely.

------

I went a bit deeper into the same game:
1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 54. Ba4 Nf6 5. O-O Be7 6. d3 b5 7. Bb3 d6 8. c3 Na5 9. Bc2 c5 10. d4 cxd4 11. cxd4 O-O 12. h3 Re8 N 13. d5 Bd7 14. Nc3 Qb8 15. Bd3 Rc8

Now Stockfish says +0.1.

"Doing nothing" is harder in this position, so I picked random moves:
Rb1 -> -0.4
a3 -> 0
h4 -> -1.2
g3 -> -2.3
Nxe5 -> -3.6
Ng5 -> -0.2
Nb1 -> -0.5
Bg5 -> -0.3
Kh1 -> -0.3
Qd2 -> -0.3
The actual move done in the game was Ne2 (+0).
Here the situation is very different, there are many moves that don't immediately ruin the evaluation.

I let Stockfish evaluate all the positions up to then. Most of the time white had +0.2 to +0.4. The biggest change was Bd6 of white in the move before, which changed the evaluation from +0.5 to 0. Stockfish suggests doing Ne2 in this move already, leading to a +0.4 evaluation. I did that and then followed its advice every time.
After 14. Nc3 Qb8 15. Ne2 Nb7 16. Be3 Nc5 17. Ng3 Rc8 18. Nd2 Na4 19. Rb1 Qc7 20. Bd3 Nc5 21. Be2 Na4 it evaluated the position as +0.7 and suggested Nb3, which lowered the evaluation to +0.3. A bit weird.
Similarly, after
22. Nb3 Qc2 23. Qe1 h5 24. Na1 Qc7 25. Bxh5 Nxh5 26. Nxh5 Bh4 27. Qb4 a5 28. Qd2 Qd8 29. Qe2 f5 30. exf5 Bxf5 31. Rbc1 Qe8 32. Ng3 Bxg3 33. fxg3 Be4 34. Kh2 Bxd5 35. b3
the evaluation was +0.3 but then white improved it to +0.8 by moving b3.
Stockfish later ended up in a circle of the white queen setting chess from two different places.
35. b3 Nc5 36. Bxc5 Rxc5 37. Rxc5 dxc5 38. Rf5 Qc6 39. Nc2 Be4 40. Rxe5 Re8 41. Rxe8+ Qxe8 42. Ne3 Bc6 43. Qd2 Qe5 44. Qd8+ Kh7 45. Qd3+ Kg8 46. h4 Kh8 47. Qd8+ Kh7 48. Qd3+

Looks like both cases can happen. There are situations where just a small set of moves is reasonable*, and there are situations where a single move is unlikely to ruin your situation (unless it's obviously stupid).

*and this is not including things like an exchange where it is obvious

 

[Infrared]

They all give white a big advantage. All larger than 0.8, the threshold where Infrared expects a win for white.
Then I looked for non-random moves:
cxd4 and exd4 preserve the +0.3.
Qc7 leads to +0.4
I didn't find anything else that is reasonable.

There are three moves that don't ruin your position completely.
...

Looks like both cases can happen. There are situations where just a small set of moves is reasonable*, and there are situations where a single move is unlikely to ruin your situation (unless it's obviously stupid).

*and this is not including things like an exchange where it is obvious

The position you gave after 10. d4 does fall into the category "things like an exchange where it is obvious". White is threatening to win a pawn on e5. The three moves you gave are the most reasonable ways to not lose the pawn. The only other two ways I see to save the pawn are 10...Nd7 and 10... Nc6. The move 10...Nd7 definitely looks unnatural but it still only gives white an advantage of +0.4 according to lichess' version of stockfish [Edit: running for a bit longer, more like +0.6]. Only 10... Nc6 is on the verge of losing because black loses a lot of time on the queenside. So if we restrict to moves that don't obviously lose the e5 pawn, 4/5 seem to be in the acceptable range and the fifth is borderline.

Edit: I noticed a 6th move that doesn't lose a pawn immediately: 10...Bb7, counterattacking on e4. The engine does indicate this is bad (again around +0.8) because the bishop is blocked out after 11. d5. Still, I don't think this changes the statistics much.

Edit 2: Just to clarify, I'm not saying that there are never balanced positions that only allow very few moves. Sharp positions do of course exist, but they're usually the critical moments of the game, and and more often there is a range of better and worse options. Also, these sharp positions usually come about from both players playing very purposefully, and I still doubt that you'd get many such positions playing randomly.

 

[Biflittle]

"the player who goes first will always win " doesn`t work in all games, but the idea is rather interesting!

 

[PAllen]

"the player who goes first will always win " doesn`t work in all games, but the idea is rather interesting!

It is trivial to construct games where the player who goes first must lose with mutual perfect play. For example, sprouts with 1 initial dot (in this case, the first player loses in all game trees; there are only 3 nodes in the complete game tree).

 

[PAllen]

The question is when if ever will we exhaust all the number of moves possible in chess?

A complete game tree for chess? Never. Even a 32 piece tablebase which would allow perfect play I once calculated would require a number of bits comparable to the number of atoms in the moon.

 

[Infrared]

It's easy to come up with examples even in chess. A typical "mutual zugzwang" is: white has a pawn on e4 and king on d5, and black has a pawn on e5 and king on f4. Whoever goes first loses.

 

[Biflittle]

perfect play I once calculated
How did you manage to do that?

 

[jbriggs444]

perfect play I once calculated
How did you manage to do that?

He calculated the size of the tablebase. Which is roughly the same as calculating the number of chess positions. Which is just a matter of putting a reasonable upper bound on that number. The moon has somewhere in the neighborhood of 10^44 atoms, give or take a few powers of ten. So you just have to come up with something that imposes a similar bound on the number of chess positions.

One upper bound is 13^64 -- 13 possible pieces at each position and 64 positions. Though you have to add a few bits for whose turn it is and how many turns have elapsed without a pawn advance or a capture. Tighter bounds are possible.

 

[PAllen]

perfect play I once calculated
How did you manage to do that?

Look up the storage density of Syzigy tablebase average bits per position. Enlarge it due to earlier positions needing more information. Look up estimates of total distinct positions in chess (or calculate it - this is not hard). Modern tablebase use very good compression.

[edit: best modern estimate for number of possible legal chess positions I could find is about 10⁴⁶. I got more like 10⁴⁸ atoms in the moon, so the estimate still looks about right.]

 

[zinq]

Based on statistics, White wins more often than Black. I'd be willing to bet that if there exists a guaranteed winning strategy for one player or the other, it would be White. But it's possible that no matter how either player plays, the other one can always force a draw with careful play from Move 1.

And although chess players often speak of the "best move" in any given position, it's not clear that this concept is really well-defined. If one player is in a position to win, then as long as they maintain the possibility of winning, who's to say one move is better than another?

Which move wins most quickly, you say? What if many different moves can all result in the same quickest win (regardless of the other player's moves)?

 

[PeroK]

Based on statistics, White wins more often than Black. I'd be willing to bet that if there exists a guaranteed winning strategy for one player or the other, it would be White. But it's possible that no matter how either player plays, the other one can always force a draw with careful play from Move 1.

And although chess players often speak of the "best move" in any given position, it's not clear that this concept is really well-defined. If one player is in a position to win, then as long as they maintain the possibility of winning, who's to say one move is better than another?

Which move wins most quickly, you say? What if many different moves can all result in the same quickest win (regardless of the other player's moves)?

The question is to what extent, if at all, you consider the ability to assess a position. Ultimately, you might say, chess is not solved until every possibility has been looked at. But, it's difficult to believe that current analysis counts for nothing. You can judge the best moves by how big an advantage they give one side. That, more than anything, is why a forced win for black is unlikely. It would mean that there is something fundamentally missing in our understanding that no human or computer has even guessed at.

Chess is very much a finite game, so it's difficult to believe there is an opening strategy for black that gains an advantage.

If we assume the game is ultimately drawn with "best play", then there may be no obvious end to the game other than the 50-move rule. Then it may be difficult to judge "best play", as anything that leaves the game drawn would count.

If, however, there is a forced win for white with checkmate in at most 560 moves, say, then the assessment of a position could simply be how many moves until checkmate. White may have several moves at each turn that do not increase this; and black may have several moves that do not reduce this. All of that would count as best play.

That said, I doubt very much that a move that is currently considered a poor move for white would actually be the only winning move. I would guess that the win, if it is there, would follow well understood ideas, but avoid the subtle inaccuracies that might lead to a draw.

 

[zinq]

How do you define "best play" ... and what it means for chess to be "solved"?

 

[PeroK]

How do you define "best play" ... and what it means for chess to be "solved"?

https://en.wikipedia.org/wiki/Solving_chess

 

[SSequence]

And although chess players often speak of the "best move" in any given position, it's not clear that this concept is really well-defined. If one player is in a position to win, then as long as they maintain the possibility of winning, who's to say one move is better than another?

Which move wins most quickly, you say? What if many different moves can all result in the same quickest win (regardless of the other player's moves)?

I agree. Yes, if one player is in a "guaranteed winning position" [with perfect play from that point, regardless of the other player], then as long as the player keeps its guarantee of winning as such it isn't necessary at all there has to be a single best move from each game state.

An analogy would be having different ways to obtain the same high-score in a (single-player) score based game [game with ending, not endless].

P.S.
I haven't thought about this topic in detail for quite some time. Though I have wrote about it in length before. But naturally, most of it I expect it to be well-understood (and somewhat obvious) ... though there might be a few novel points. I do like the "hate to lost" point that I made since it isn't immediately obvious unless one thinks about it a little bit.

I am hesitant to link to my own post, but there seems to be fair amount of interest in this topic (more so than I expected). Here is the link. Maybe it would be useful or interesting for some, though there isn't anything specific to chess in my post.

I didn't mention in the post directly (due to length considerations), but for chess [or other multi-player games] a reasonable idealized view would be to see it from the perspective of a single player such as white/black (as a non-deterministic single-player game). But there can be some issues in such over-simplification [for example, consider a game where the actions of other player(s) could lead to endless play], which would need to be looked/described in more detail. The possibilities do seem to increase quite a bit with addition of "other" players. That's why I didn't add it in the post.

In the post, I assumed [for simplicity and focus on illustrating the basic-point] that there is a path to win/lose states from each game-state, but clearly that needs to be changed if there are draw possibilities [also increasing the "classifications" of game-states]. Actually, I tried to make the assumptions specific enough that there would be no (somewhat-natural) $L$ state either.

 

[PeroK]

I agree. Yes, if one player is in a "guaranteed winning position" [with perfect play from that point, regardless of the other player], then as long as the player keeps its guarantee of winning as such it isn't necessary at all there has to be a single best move from each game state.

In any game/algorithm, a solution in fewest steps can always be preferred and described as "best". That's part of the definition of "best" in algorithmic computations.

 

[SSequence]

I don't disagree, but the point was that there doesn't "necessarily" need to be a single best move from some game-state.

 

[PeroK]

I don't disagree, but the point was that there doesn't necessarily need to be a single best move from some game-state.

Let's take a simple example of King + Queen against King. This can be solved from any position and the minimum moves to checkmate calculated. There will typically be many different ways to deliver checkmate in this number of moves.

These solutions are still "better" than a solution where the pieces wander round the board for nearly 50 moves before delivering checkmate.

So, yes there may be more than one "best" move in a position. But this set of moves can still be preferred to others that are also "winning" moves.

 

[SSequence]

I haven't thought about the specific context (directly analogous to chess) that much [since it is somewhat different from context(s) which I thought about in more detail], but I would tend to agree.

===============

Yes, if our criterion is based on "minimum" no. of moves to win for example (with the assumption of a guarantee to win), then we would typically expect to cut-out a lot of sub-par solutions (ways of playing).

In fact, it doesn't seem a priori impossible that there might actually be a unique path leading to win in a minimum number of moves. I suppose this would be analogous to a single (unique) path giving the highest possible score in a single-player non-endless game.

 

[sysprog]

Let's take a simple example of King + Queen against King. This can be solved from any position and the minimum moves to checkmate calculated. There will typically be many different ways to deliver checkmate in this number of moves.

King + Queen against King can always be won in fewer than 11 moves. I don't care if I use all 10 moves, or even maybe a few more, if I have enough time. If I see a clear path to a win I don't care to try to find a shorter one.

In any game/algorithm, a solution in fewest steps can always be preferred and described as "best". That's part of the definition of "best" in algorithmic computations.

As you are doubtless well aware, algorithmic steps at the level of decision of which move to make don't have a 1-to-1 correspondence to chess moves, so winning the game in the fewest moves is not always preferable to winning with the most easily arrived at certainty, even if the latter winning sequence has a greater number of moves; the player must also consider the time on his clock.

In an actual game if I can see a mate in 4 easily, but would have to think longer to find a more elegant mate in 3, the 'best' move, in my view, is the one leading to the more easily found win.

Also, sometimes in chess one move is exactly as good as another; e.g when you have a 1-move back-rank mate by promotion of a pawn and a rook is as good as a queen for the purpose.

 

[PeroK]

K+Q vs K can always be done in fewer than 11 moves. I don't care if I use all 10 moves, or even maybe a few more, if I have enough time. If I see a clear path to a win I don't care to try to find a shorter one.

As you are doubtless well aware, algorithmic steps at the level of decision of which move to make don't have a 1-to-1 correspondence to chess moves, so winning the game in the fewest moves is not always preferable to winning with the most easily arrived at certainty, even if the latter winning sequence has a greater number of moves; the player must also consider the time on his clock.

In an actual game if I can see a mate in 4 easily, but would have to think longer to find a more elegant mate in 3, the 'best' move, in my view, is the one leading to the more easily found win.

We're talking about solving chess, not practical over-the-board play!

 

[sysprog]

We're talking about solving chess, not practical over-the-board play!

I get that. I think, as most players and programmers do, that neither side has a winning advantage at the outset. I was replying regarding the notion of 'best' move -- I think that for the 'solving chess' question, any path that leads from an arrived-at position to a certainty of winning is as good as any other; it doesn't matter how many moves it takes to win; how you win doesn't matter -- only whether you win matters.

 

[PeroK]

I get that. I think, as most players and programmers do, that neither side has a winning advantage at the outset. I was replying regarding the notion of 'best' move -- I think that for the 'solving chess' question, any path that leads from an arrived-at position to a certainty of winning is as good as any other; it doesn't matter how many moves it takes to win; how you win doesn't matter -- only whether you win matters.

That's your definition of "best": any move that retains a winning position. An alternative definition of "best" is any move that wins by the least number of moves.

Your definition is rather odd in that if there is a checkmate in one move, that is not the best move. It's just as good - by your definition - not to deliver checkmate. It only becomes the best move when you near the 50-move draw rule. If you remove that rule then with "best play" (your definition) you might never win. You could play indefinitely with K + Q against K, claiming every move is "best" but never delivering checkmate. Only the 50-move rule provides you with the impetus to finish the game!

In any case, describing not delivering mate when you have the chance as "best play" is stretching a point.

 

[sysprog]

That's your definition of "best": any move that retains a winning position. An alternative definition of "best" is any move that wins by the least number of moves.

Your definition is rather odd in that if there is a checkmate in one move, that is not the best move. It's just as good - by your definition - not to deliver checkmate. It only becomes the best move when you near the 50-move draw rule. If you remove that rule then with "best play" (your definition) you might never win. You could play indefinitely with K + Q against K, claiming every move is "best" but never delivering checkmate. Only the 50-move rule provides you with the impetus to finish the game!

In any case, describing not delivering mate when you have the chance as "best play" is stretching a point.

I don't claim that sub-optimal moves can ever be legitimately called 'best' -- I think that 'not incorrect' would be a better name for any move that preserves a certainty of winning in finite time, including the optimal move; for purposes of the 'solving chess' problem optimal moves are not 'best' and are not definitively better than sub-optimal moves that are equally certain to produce a win.

For a working solution to 'solving chess', every winning line is as good as the optimal one, so there isn't, in my view, a 'best' move in every situation -- when there is only 1 move that leads to victory, I would call that move 'correct' rather than 'best'; however, I mostly don't strongly disagree with your point. It's true that chess problem solutions require that the fewest moves be made in accomplishing the goal.

This is just humor, but when I was kid, sometimes when someone would refuse to resign a very obviously lost position, just so he could inflict on me the drudgery and tedium of proving my position was a winning one, I would deliberately delay checkmate; I would proceed to confine his king to 2 squares, then capture every one of his pieces and pawns, then promote all of my remaining pawns, then place my pieces in some tidy arrangement, and only then deliver checkmate -- punishment for trying punish me instead of resigning and playing again or not.

 

[jbriggs444]

You could play indefinitely with K + Q against K, claiming every move is "best" but never delivering checkmate.

An interesting point. A strategy which is clearly not best in which each individual move is "best". However, any loop prevention heuristic could succeed at avoiding this. The "fastest mate is preferred" heuristic is just one possibility. Though a very convenient one.

 

[SSequence]

The notion of an "optimal move" on a given game-state should still be quite well-defined though [optimal in the sense that it retains an already winning position].

A lot of terminology would remain constant within games that have finite number of states. Very briefly, I think something similar to this would be enough (number of other ways would be possible I guess). We might define a strategy as a 1-1 correspondence between game-states and action/move of the player at that game-state. So, for a two-player deterministic games, if a given state is a winning state for some player, then we can define any "action/move" as "optimal" if it is part of "some" winning strategy [starting from the given/chosen state].

So, a strategy that is simply based on selecting "optimal moves" from each game-state may not be an optimal strategy. That would merely be a necessary condition.

Making the notions in above paragraph precise shouldn't be difficult. It isn't much different from post#182 [except that the context of a single-player non-deterministic has some differences from two-player deterministic (different classifications of states), which one needs to account for properly].

 

[PAllen]

There is a real problem defining best play in the context of chess assuming the starting position is drawn. Minimizing moves to mate objectively chooses one or more best moves in a winning position. But if it is drawn, there is no such simple criterion for favoring one or a few moves out of all those that preserve the draw. For a minimal definition of perfect play, you don’t need to distinguish, but to achieve wins against an imperfect player, randomly choosing a move that preserves the draw will be very poor at achieving a win. The truly optimal approach to play against an imperfect player would be to have a model of that player’s “error profile”, and would be different against different players.

 

[SSequence]

There is a real problem defining best play in the context of chess assuming the starting position is drawn.

Agreed.

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From a practical perspective, assuming that start-state for some board-game (not chess) isn't a draw, I think there would also be some difference between storage of optimal strategy and execution of it under real time-constraints? It doesn't seem implausible that the former might be possible practically but the latter might not be? It seems worth mentioning as an aside explicitly, but this is an entirely different topic though.

 

[user30]

While chess hasn't been solved yet, other games have. For example, I know that in in some games, like connect four, if both players play perfectly, the player who goes first will always win. On the other hand, some games, like tic tac toe, a perfect game will result in a draw; in fact, I recently found out that this is true for checkers as well. What I'm wondering though, is if it's possible to predict which scenario a perfect game of chess would lead to even without having fully solved it yet, and if it is possible, what the answer is.

I'm a chessplayer and the general consensus is that the game is a theoretical draw. The game is fairly sensitive to what we call "tempos" (how many moves have I moved "forward" compared to my opponent) but it's likely not enough to force a win.

While it is true that chess is incredibly complex, a lot of lines are garbage. A super sophisticated future super computer might very well solve it with perfect pruning (excluding irrelevant lines).

But not in our lifetime.

 

[Halc]

Perfect chess is likely a draw, but if there is a win, it will be white.
Other games like go and reversi probably do not end in a draw, and especially in the reversi case, it is unclear if it is an advantage to go first.

I haven't read the entire thread, so all this has probably been brought up.