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> You’re dramatically overstating the advantage Carlsen had in Game 12. It was not decisive or obvious in any way and afterwards various engines played out the

> You’re dramatically overstating the advantage Carlsen had in Game 12. It was not decisive or obvious in any way and afterwards various engines played out the position to a draw. You're misstating the results of the Game 12 replays (see: https://www.chess.com/computer-chess-championship https://www.chess.com/computer-chess-championship, which is pitting numerous engines against each other in the position at Game 12's resignation). It's currently +3-18=14. That's 3 wins for Caruana's position, 18 wins for Carlsen's, and 14 draws. That's about as decisive a position as you can get in high-level chess. Yes, with perfect play, Caruana might have reached a draw, but Carlsen was in an overwhelmingly strong position. And this isn't even truly accounting for the time pressure Caruana put himself in at that point. He would have been defending from an incredible time deficit. > Meanwhile, Carlsen made absolutely the correct choice (best strategic choice) to draw in Game 12. Numerous grandmasters disagree with you, including at least Anand, Nakamura, Hess, Kasparov, and Kramnik. The computer results also suggest he should have at least played on several moves before offering, because he was in a position where his likely worst case result was a draw and his best case was a decisive win.

Isofarro 8y ago
> It's currently +3-18=14. That's 3 wins for Caruana's position, 18 wins for Carlsen's, and 14 draws. That's about as decisive a position as you can get in high-level chess. Except that +3 would mean three chess engines, supposedly stronger than Carlsen, have managed to lose Carlsen's position. That's eye-opening, and perhaps justifies Carlsen offering a draw than risking being in that +3 column. Caruana was supposedly without counter-play. +3 is far too high a score to support that claim.
- TangoTrotFox 8y ago
  There's one important nuance here. Those machines are playing against super human defense. In human chess there are countless positions that computers can easily defend whereas even the best players in the world would lose nearly every time. Finding only moves in very complex positions is not really that hard for most modern programs. Doing this over and over for humans, let alone with limited time and with mental fatigue a very real issue, is just not possible to consistently do. This position hadn't reached that critical of a juncture yet, but that's largely because Magnus just started winging it long before the final position. His position was much stronger earlier on. But even in the final position he was very much the attacker and Fabiano's clock was starting to run low. In practical chess, Fabiano definitely faced an uphill battle to try to draw that position.
notyourday 8y ago
> It's currently +3-18=14. That's 3 wins for Caruana's position, 18 wins for Carlsen's, and 14 draws. That's about as decisive a position as you can get in high-level chess. Yes, with perfect play, Caruana might have reached a draw, but Carlsen was in an overwhelmingly strong position. And this isn't even truly accounting for the time pressure Caruana put himself in. If this was not the game 12, they would have had a point. However it was the game 12 and upon a draw Carlsen would have enormous advantage in a tie breaker -- he is much stronger in rapid games.
- stouset 8y ago
  Humans are not computers. And the fact that computers won some of those games is further evidence that, while Carlsen had winning chances, the position was complicated enough that one or two suboptimal moves might be enough for Fabi to capitalize and win. A slight advantage in a complicated position with lots of tension and many ways for the game to continue is wildly different from a slight advantage in a quieter position with many of the pieces traded down. In the latter, a mistake might cause you to draw rather than win. In the former, a mistake might cause you to lose outright.
  - emmelaich 8y ago
    Agree. The last 50+ years of 1-1 contests (chess, boxing, tennis, mma, ..) have tended towards the defensive(1), for good reason. In the old days a bit of flair and risk might have taken you a long way. 1. or at least the minimisation of mistakes.
- msbarnett 8y ago
  Sure, but we're kind of wandering off the point here. Carlsen is widely recognized to have been in a great, likely winning position in game 12, and arguably got himself into several other, if not cleanly decisive positions, very strong ones in several other games, where Caruana never quite seemed to. OP suggested they were dead even in play in "what he considers" chess (classical time controls). I'm suggesting that the results may have been even, but that Carlsen seemed to be stronger all along, based on the chances he got himself into, even though it never quite converted until rapid.
Someone 8y ago
”It's currently +3-18=14. That's 3 wins for Caruana's position, 18 wins for Carlsen's, and 14 draws. That's about as decisive a position as you can get in high-level chess.” Today’s games stand at +3-0=0 or, taking the last game as the draw it would have been if Caruana didn’t have to win, at +2-0=1. I haven’t done the math, but I’m sure taking a “best of four” sample from the distribution that was taken from gives you better odds than taking a n=1 sample from the distribution that gave you +3-18=14 (about 9% chance of losing, about 50% of winning’, followed by (if that draw is a tied game) that n=4 sample. And that’s ignoring the fact that that +3-18=14 is from machines that are way different from humans. When given a chess position that’s like a minefield, with a single winning sequence of 40 moves, and all other moves a loss, a computer will happily declare the position a certain win, but chances are no human will find that winning sequence.

Isofarro 8y ago

> It's currently +3-18=14. That's 3 wins for Caruana's position, 18 wins for Carlsen's, and 14 draws. That's about as decisive a position as you can get in high-level chess. Except that +3 would mean three chess engines, supposedly stronger than Carlsen, have managed to lose Carlsen's position. That's eye-opening, and perhaps justifies Carlsen offering a draw than risking being in that +3 column. Caruana was supposedly without counter-play. +3 is far too high a score to support that claim.

TangoTrotFox 8y ago
There's one important nuance here. Those machines are playing against super human defense. In human chess there are countless positions that computers can easily defend whereas even the best players in the world would lose nearly every time. Finding only moves in very complex positions is not really that hard for most modern programs. Doing this over and over for humans, let alone with limited time and with mental fatigue a very real issue, is just not possible to consistently do. This position hadn't reached that critical of a juncture yet, but that's largely because Magnus just started winging it long before the final position. His position was much stronger earlier on. But even in the final position he was very much the attacker and Fabiano's clock was starting to run low. In practical chess, Fabiano definitely faced an uphill battle to try to draw that position.

notyourday 8y ago

> It's currently +3-18=14. That's 3 wins for Caruana's position, 18 wins for Carlsen's, and 14 draws. That's about as decisive a position as you can get in high-level chess. Yes, with perfect play, Caruana might have reached a draw, but Carlsen was in an overwhelmingly strong position. And this isn't even truly accounting for the time pressure Caruana put himself in. If this was not the game 12, they would have had a point. However it was the game 12 and upon a draw Carlsen would have enormous advantage in a tie breaker -- he is much stronger in rapid games.

stouset 8y ago
Humans are not computers. And the fact that computers won some of those games is further evidence that, while Carlsen had winning chances, the position was complicated enough that one or two suboptimal moves might be enough for Fabi to capitalize and win. A slight advantage in a complicated position with lots of tension and many ways for the game to continue is wildly different from a slight advantage in a quieter position with many of the pieces traded down. In the latter, a mistake might cause you to draw rather than win. In the former, a mistake might cause you to lose outright.
- emmelaich 8y ago
  Agree. The last 50+ years of 1-1 contests (chess, boxing, tennis, mma, ..) have tended towards the defensive(1), for good reason. In the old days a bit of flair and risk might have taken you a long way. 1. or at least the minimisation of mistakes.
msbarnett 8y ago
Sure, but we're kind of wandering off the point here. Carlsen is widely recognized to have been in a great, likely winning position in game 12, and arguably got himself into several other, if not cleanly decisive positions, very strong ones in several other games, where Caruana never quite seemed to. OP suggested they were dead even in play in "what he considers" chess (classical time controls). I'm suggesting that the results may have been even, but that Carlsen seemed to be stronger all along, based on the chances he got himself into, even though it never quite converted until rapid.

Someone 8y ago

”It's currently +3-18=14. That's 3 wins for Caruana's position, 18 wins for Carlsen's, and 14 draws. That's about as decisive a position as you can get in high-level chess.” Today’s games stand at +3-0=0 or, taking the last game as the draw it would have been if Caruana didn’t have to win, at +2-0=1. I haven’t done the math, but I’m sure taking a “best of four” sample from the distribution that was taken from gives you better odds than taking a n=1 sample from the distribution that gave you +3-18=14 (about 9% chance of losing, about 50% of winning’, followed by (if that draw is a tied game) that n=4 sample. And that’s ignoring the fact that that +3-18=14 is from machines that are way different from humans. When given a chess position that’s like a minefield, with a single winning sequence of 40 moves, and all other moves a loss, a computer will happily declare the position a certain win, but chances are no human will find that winning sequence.