Do games between top engines typically end within 40 moves? It might be that an optimal player’s occasional win against an almost-optimal player might come from deliberately extending and complicating the game to create chances
According to Braun (2015), computer-vs-computer games from Schach.de (2000-2007, ~4 million games) averaged 64 moves (128 plies), compared to 38 moves for human games. The longer length is because computers don’t make the tactical blunders that abruptly end human games.
Here are the three methods updated for 64-move games:
1. Random vs Optimal (64 moves):
P(Random plays optimally) = (1/35)^64 ≈ 10^(-99)
E_Random ≈ 0.5 × 10^(-99)
ΔR ≈ 39,649
Elo Optimal ≤ 40,126 Elo
2. Sensible vs Optimal (64 moves):
P(Sensible plays optimally) = (1/3)^64 ≈ 10^(-30.5)
E_Sensible ≈ 0.5 × 10^(-30.5)
ΔR ≈ 12,335
Elo Optimal ≤ 15,217 Elo
3. Depth extrapolation (128 plies):
Linear: 2894 + (128-20) × 66.3 ≈ 10,054 Elo
This is a bit annoying because my intuitions are that optimal Elo is ~6500.
This thread made me very curious as to what the elo rating of an optimal player would be when it knows the source code of its opponent.
For flawed deterministic programs an optimal player can steer the game to points where the program makes a fatal mistake. For probabilistic programs an optimal player is intentionally lengthening the game to induce a mistake. For this thought experiment if an optimal player is playing a random player than an optimal player can force the game to last 100s of moves consistently.
Makes me curious to see a game between humans where non-sensible moves are defined in some objective way and forbidden by guardrail AI. Like, not even considered a legal move by the computer UI.
Would this extend the games of humans to around 64 moves on average? What would the experience of playing such a game be for low ELO humans? Confusion about why certain moves were forbidden, probably.
I agree this variation would lengthen the game. The experience would change for sure for all human players.
An objectively losing human player may intentionally play objectively bad moves that lengthen a game and complicate it. It’s a learned skill that some players have honed better than others.
In this variation that skill is neutralized so I imagine elos would be different enough to have different player rankings.
Do games between top engines typically end within 40 moves? It might be that an optimal player’s occasional win against an almost-optimal player might come from deliberately extending and complicating the game to create chances
Great comment.
According to Braun (2015), computer-vs-computer games from Schach.de (2000-2007, ~4 million games) averaged 64 moves (128 plies), compared to 38 moves for human games. The longer length is because computers don’t make the tactical blunders that abruptly end human games.
Here are the three methods updated for 64-move games:
1. Random vs Optimal (64 moves):
P(Random plays optimally) = (1/35)^64 ≈ 10^(-99)
E_Random ≈ 0.5 × 10^(-99)
ΔR ≈ 39,649
Elo Optimal ≤ 40,126 Elo
2. Sensible vs Optimal (64 moves):
P(Sensible plays optimally) = (1/3)^64 ≈ 10^(-30.5)
E_Sensible ≈ 0.5 × 10^(-30.5)
ΔR ≈ 12,335
Elo Optimal ≤ 15,217 Elo
3. Depth extrapolation (128 plies):
Linear: 2894 + (128-20) × 66.3 ≈ 10,054 Elo
This is a bit annoying because my intuitions are that optimal Elo is ~6500.
This thread made me very curious as to what the elo rating of an optimal player would be when it knows the source code of its opponent.
For flawed deterministic programs an optimal player can steer the game to points where the program makes a fatal mistake. For probabilistic programs an optimal player is intentionally lengthening the game to induce a mistake. For this thought experiment if an optimal player is playing a random player than an optimal player can force the game to last 100s of moves consistently.
Makes me curious to see a game between humans where non-sensible moves are defined in some objective way and forbidden by guardrail AI. Like, not even considered a legal move by the computer UI.
Would this extend the games of humans to around 64 moves on average? What would the experience of playing such a game be for low ELO humans? Confusion about why certain moves were forbidden, probably.
I agree this variation would lengthen the game.
The experience would change for sure for all human players.
An objectively losing human player may intentionally play objectively bad moves that lengthen a game and complicate it. It’s a learned skill that some players have honed better than others.
In this variation that skill is neutralized so I imagine elos would be different enough to have different player rankings.