Unfortunately, when I "improved" the forecasting computer program, it started giving me results that could not possibly be correct (i.e., Karjakin has a better chance of winning the tournament than Carlsen). I haven't been able to identify the bug yet, but luckily we can still do the calculations by hand.
The critical game will be the Round 10 battle between Carlsen and Caruana. If Carlsen wins, then he is guaranteed at least a tie for 1st regardless of what happens in his game with Radjabov. Based on games between 2700 players with a similar rating gap, this event happens 43% of the time. Case 2: Carlsen loses to Caruana (16% chance). But Carlsen can still secure 1st place if he beats Radjabov (55% chance) while Caruana draws or loses to Mamedyarov (72%). Even if Carlsen draws Radjabov, he can still win the tournament if Caruana loses (22%) and no one on 4/8 wins twice. Case 3: Caruana and Carlsen draw. Then Carlsen is assured 1st place if he doesn't lose to Radjabov (89.5%), but even a loss doesn't always cost him the tournament. After adding up the probabilities, we see that Carlsen has about an 85% chance of tying for 1st. This seems like a reasonable figure: yesterday Carlsen was around 90%, but now his main pursuer is Caruana, who is much higher rated than Radjabov. Thus, Carlsen's chances should have declined slightly from 90%, and they did.
Most of Caruana's chances rely on him defeating Carlsen, but there are ways for him to win if he draws Carlsen and prevails against Mamedyarov. Caruana has about a 20% chance of tying for 1st.
Radjabov, Karjakin, and Nakamura face far steeper odds. There is about a 95% chance that the winner of the tournament will need to score at least 6/10. They need to win both of their last games and hope that the leaders stumble. Their chances are less than 10%.
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