How many times has a game of chess been played?

[wazz]

In the UK there is a text service called Any Questions Answered. Ask them any reasonable question and they should give a justifiable, near-factual, reply within half an hour.

I asked them:

I have just finished playing a game of chess with my friend. On average, how many times has this exact game been played throughout history?

Their reply:

'There are millions of chess moves which can be made in 1 game, although many are dead-ends. Your exact game has been played more than 10 dozen times.'

I can't say I'm entirely satisfied with their reply as they gave no real logic, even though they took the full half hour to reply. Would anyone here like to take a stab at working out an approximate answer?

As an aside, I also asked them what was the size of the largest single recorded pot won in a game of poker. Their answer was $1.43M, won by Lee Nelson of NZ. Could anyone verify that?

[MidGe]

[ QUOTE ]
Their reply:

'There are millions of chess moves which can be made in 1 game, although many are dead-ends. Your exact game has been played more than 10 dozen times.'

[/ QUOTE ]

My reply:

It could have never been played, played once before, or more!

[wazz]

No-one fancy giving it a shot?

[MidGe]

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No-one fancy giving it a shot?

[/ QUOTE ]

I did.

By the way, There are more than at least 10 followed by 134 zeroes variants within a typical 50 moves chess game.

What else is there to add. The millions or billions possible variants is a very underestimated number of variants.

Chess games: number of variants

[wazz]

Yeah but like they said a good proportion of those moves are dead-ends and not widely used. When you figure that the average chess-player is not of that high a skill level only a smaller range of moves is usually used. Factor in that chess games have been played for so long and by so many people and I'd stab that it's more likely than not that any game of chess that I play has been played before by someone else.

[atrifix]

Depends on the game.

If the moves were 1. e4 c5 2. Nf3 d6 3. d4 cxd4 1/2-1/2, then your game would have been played millions of times before. If you tend to make gross blunders as many amateurs do, or you open with the relatively unpopular 1. h4, then the chances that your game has been played before go down considerably.

If you are talking about a 50-move game, the odds are close to 0.

[atrifix]

Forgot to mention:

[ QUOTE ]
When you figure that the average chess-player is not of that high a skill level only a smaller range of moves is usually used.

[/ QUOTE ]

This is incorrect. As skill increases, the range of moves will decrease dramatically.

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Factor in that chess games have been played for so long and by so many people and I'd stab that it's more likely than not that any game of chess that I play has been played before by someone else.

[/ QUOTE ]

There are more chess positions than there are atoms in the known universe, so it's much more likely than not that a game of around 40 moves has not been played before.

[FortunaMaximus]

So a dozen games would just be standard deviation from the mean?

[Thythe]

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There are more chess positions than there are atoms in the known universe, so it's much more likely than not that a game of around 40 moves has not been played before.

[/ QUOTE ]

I think you are incorrect.

[atrifix]

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So a dozen games would just be standard deviation from the mean?

[/ QUOTE ]

The odds that your average 40-move game has been played even once before are pretty close to 0. I don't think that you can say that it is simple statistical variance because obviously the results are not independent. The sequence

1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 a6 6. Bg5 e6 7. f4 Qb6 8. Qd2 Qxb2 9. Rb1 Qa3 10. f5 Nc6 11. fxe6 fxe6 12. Nxc6 bxc6 13. e5 dxe5 14. Bxf6 gxf6 15. Ne4 Be7 16. Be2 h5 17. Rb3 Qa4 18. Nxf6+ Bxf6 19. c4 Ra7 20. 0-0 Rf7 21. Qd6 Be7 22. Qxe5 Rxf1+ 23. Kxf1 0-0+ 24. Kg1 h4 25. Qh5 Qxa2 26. Qg6+ 1/2-1/2

is much more likely to have occurred multiple times than some random 26 move sequence.

Bottom line: without seeing OP's game, my guess is that the odds that it had occurred even once before are effectively 0.