# Will games be perfect, and most likely a draw, if both players get infinite time?

I have played a lot of chess games. The thing that always bothered me was that bloody clock. It looks as if the game is a game about who can think the fastest and it makes one nervous. Now, I know it's part of the game and this gives it charm too. But what if there was no pressure of time? Could a player win? Of course the opponent can do this too. Would this give the best games?

Suppose that both players have all the time they need and all means at their proposal, even the best chess computer in the world). Will some perfect play evolve? Would both players make the same moves (if in each others shoes)? Or is there always some guessing involved?

• Comments are not for extended discussion; this conversation has been moved to chat. Aug 8, 2021 at 14:05

Computers don't need infinite time to play perfectly. Nearly but not quite. They need exponential time according to Fraenkel and Licthenstein (Journal of combinational theory).

Humans could theoretically achieve a similar result if they checked all positions and committed no errors in their calculations. Potentially having an extremely large number of boards where they could check the moves. However calculating a single move would take many generations of humans playing a single game.

On a practical level, if you are bothered about clocks and would like to go deeper in your calculations you should probably play correspondence chess. Most sites e.g. chess.com and lichess.org allow you to play in a format that allows you to think for a move for several days.

• Comments are not for extended discussion; this conversation has been moved to chat. Aug 8, 2021 at 14:05

No, time is not everything. Memory is also important, for a brute force approach one has to memorise all the branchings and lines already read out.

Note also that solving chess is a problem of finite size, albeit the size is really huge. So you can do it in some finite time using some finite amount of memory, at least in theory. Solving chess is probably impossible in the real physical universe, good judgement in pruning the game tree becomes another requirement. Without good judgement, even infinite time will not help.

For a game between human players, limits can be lifted in several ways, correspondence chess does not only allow rather long time limits but also allows the use of any resource available to the player, including access to a library of chess books (extending memory in some way, as you can lookup opening lines) and computers (with their faster "thinking" they increase the time effectively, and they also provide additional memory).

• Thats interesting. Two different approaches. I mean this one and the other answer. Especially the judement seems important indeed. Aug 7, 2021 at 18:40
• Good judgement would imply heuristics and not perfect play. That would simply be probabilistically good play. What computers today do. Aug 7, 2021 at 22:02