What is perfect play?

What exactly is perfect play? Can there can be multiple perfect plays, which sounds quite contradictory? If perfect play is known for all openings then why would a player play anything other than that? Such a thing would make all high level games futile because then players would intentionally divert from perfect play in order to just create a show or something similar.

• In the vast majority of positions, perfect play isn't known. Commented Jun 25, 2020 at 11:55
• There can definitely be different "perfect plays". If you have a winning position, every move that leaves you with a still winning position is theoretically "perfect play" Commented Jun 25, 2020 at 12:34
• @David That is not the usual definition of perfect play. For instance If you had forced mate in 3 and afterwards you have only a forced mate in 5, this would (usually) not be considered perfect play. Commented Jun 25, 2020 at 14:51
• @user1583209 why wouldn't it that be so? I don't see why forcing a mate in 5 is any worse than forcing it in 3. If you managed to play like this you'd still win every single game. The "objective funcion" in chess is maximized by winning, not winning as fast as possible. Commented Jun 28, 2020 at 16:55
• Of course mate in 5 is not worse than mate in 3 in most contexts, particularly in most games. I was specifically thinking of the more theoretical discussion of say endgame tablebases, where you could see statements like: "this position is mate in 13 with perfect play". Commented Jul 5, 2020 at 19:56

In the context of game theory, perfect play involves playing truly optimal moves. Specifically, if the game state is a (theoretical) win for the player to move, perfect play would be a move that both preserves that state (eg keeps the game a winning state) and minimizes the number of moves remaining until victory. If the game state is a draw, perfect play preserves the draw. If the game state is a loss, perfect play cannot improve the theoretical outcome, but instead maximizes the number of moves until defeat.

Perfect play is, by definition, known for solved games like Tic-Tac-Toe. Chess is not yet solved, so in most board positions, perfect play is not known. For some situations, for example positions with 7 or fewer total pieces on the board, we have endgame tablebases which have perfect play recorded. Also, for positions with forced checkmate in sufficiently few moves, engines can calculate perfect play on-the-fly by simply looking at all possible moves and responses and choosing one that gives checkmate the fastest. Perfect play is not (yet) known for chess openings. If chess were solved and perfect play were widely known, then it is possible competitive chess may die.

There can be multiple perfect moves for a given board position. For example, if there are two different moves that immediately checkmate the opponent, both are perfect. Playing around with endgame tablebases, it is fairly common to find positions where multiple moves lead to checkmate in (say) 18 moves. If the game is a theoretical draw, often many moves preserve the draw. All of these moves are perfect from a game-theory perspective, though some may give better practical chances than others.

• +1 Excellent answer. Though in a losing position people might reasonably differ on choice of definition of perfect play, since there is no way to win in perfect play anyway, so maximizing moves to loss is not necessary in some definitions. This differs from winning positions, because it is possible that from a winning position there is a move that leads to another winning position but if you do not minimize the number of moves then it is possible that you will never win and hence it cannot be considered perfect play. Commented Jun 25, 2020 at 4:51
• " If chess were solved and perfect play were widely known, then it is possible competitive chess may die." that was the confirmation i needed. Seems like chess tournaments are just for a show then , which i enjoy BTW. thanx Commented Jun 27, 2020 at 15:35
• What do you call "game state", knowing that a position is a win or draw only when game is over (ie no more move is allowed) ? I can guess answers but would prefer a clear explanation. Do you have serious references for the terms you use, and assertions you make, because wikipedia is not really helpful ? I am quite surprised, annoyed, after searching a little, at the lack of rigor, the poor logic, displayed by people who are supposed to have rigorous minds -the editors of wiki for instance.
– plm
Commented Sep 6, 2023 at 16:14

Technically, perfect play would consist of making moves that do not adversely affect the result of the game. In endgame theory books, only mistakes can change the result, and they are flagged as such. Strictly, in a winning position, you might require that perfect play reaches the win the the smallest number of moves, or conversely postpones the defeat for as long as possible in a losing position.

On either of those definitions, there may be several equally good moves in a position. A chess engine announcing a mate in 5 (or 15!) may see multiple different routes of the same length to checkmate.

That's the game theory answer - John Nunn takes that approach in his endgame books, for example.

However, there are the twin facts that chess is not yet solved (so we do not know the perfect play) and you may be facing a human opponent who is both fallible and has particular strengths and preferences. I would argue that best play in this case would choose the moves that are most likely to lead to a win today against this particular opponent - which might not be (game-theoretic) perfect play. Playing moves which are not theoretically best in order to maximise winning chances in a real game introduces an element of risk.

Finally, sometimes in a tournament or a match, a draw is as good as a win. In those circumstances, the change in the relative value of the outcomes would lead to a different optimising solution for the practical approach even though the game-theoretic solution (if it were known) would be unchanged.

• So the winning player chould prefer a complicated line that leads to mate in 40 moves against the most stubborn defense, to a simple foolproof line that takes 41 moves? And the losing player should prefer the latter? In real life I'd be more interested in maximizing my winning chances or minimizing my losing chances than in shortening the game or dragging it out.
– bof
Commented Jun 25, 2020 at 1:23
• @bof: If the winning player can see the mate-in-40 in its entirety, choosing that does not at all increase losing chances, by definition. In real life, you cannot see a complicated mate-in-40, so obviously you cannot prefer it since you don't even know it exists. Commented Jun 25, 2020 at 4:13
• @wotnotv: For that same reason, your answer is incorrect. Perfect play is never risky. Trying to achieve perfect play without having the capability to do so may be risky, but that has nothing to do with perfect play and merely arises from lack of ability. Commented Jun 25, 2020 at 4:17
• You can, however, fix your answer by carefully distinguishing between perfect play and fallible play. If each player makes mistakes (i.e. deviating from perfect play) according to some probability distribution (which may depend on the position), then the best move is the one that maximizes your expected outcome, which indeed may not be perfect play. But that is fine, because you are taking into account your likelihood of making mistakes as well as the likelihood of your opponent making mistakes (in each line). Commented Jun 25, 2020 at 4:20
• Hmm, your answer was still incorrect, because "perfect play" is a technical term and you cannot just consider it to mean what you like. I hope you don't mind me editing it to fix the errors but retain the content. Commented Jun 25, 2020 at 9:53

1. What exactly is perfect play?

Firstly, the definition of perfect play is very subjective. One may say that a 4-move checkmate is a perfect play for me! Or, the best possible move that you could have done regardless of the situation you are in, "Oh! that was a perfect play because you could not have played any other move any better!".

According to me, a perfect play is when the entire game is always in your control. In the sense that, with every move you make, you force your opponent to make a move of your choice rather than his own choice. This is not possible in the game of chess. You can predict the probability of a move, but cannot force an opponent to play moves in every given scenario unless you are some intelligent silicon-based life form that can simulate every possible scenario. Therefore, according to my definition of "perfect play", it simply cannot exist.

2. Can there be multiple perfect plays?

Maybe according to some other definition of a perfect play.

3. If perfect play is known for all openings then why would a player play anything other than that? Such a thing would make all high level games futile because then players would intentionally divert from perfect play in order to just create a show or something similar.

Well, if perfect play did exist, then no one would willingly play anything other play than that, unless given good enough motivation (e.g. bribery) during competitions. That is the only logical answer here.

• "unless you are some intelligent silicon-based life form" - There's probably not enough silicone in the universe.
– D M
Commented Jun 24, 2020 at 20:54
• We have only explored about 4% of the universe to this date! So, determining a probability based on 4% experience is like saying that in a football match of kids team v/s a national Barcelona team, kids would win with pure skill! Commented Jun 25, 2020 at 5:25

I am not sure whether there is a single definition of "perfect play".

The answers so far considered perfect play separately for the winning or losing player. In this sense it is often used in the negative sens: white's position is lost, even with perfect play

However, "perfect play" can also refer to the combined play of both players. As such it is what you get if the winning player is minimizing DTM (depth to mate) while the losing player is maximizing DTM. So basically what a minimax engine does.