@Splorer said in #3:
> Nepo has 2 wins, 1 loss, and 7 draws in standard games versus Carlsen (
ratings.fide.com/chess_statistics.phtml?event2=1503014&event=4168119). They will play up to 14 games, with someone reaching 7.5+ points to win. The probability he wins at least 1 out of 14 games [1-(9/11)^14=~0.94], multiplied by the probability that he doesn't lose any of 14 games ((10/11)^14=~0.26), gives him a ~24% to win.
It's hard to estimate the chances of win/draw/loss against Carlsen, so let's roll with 2-7-1. (Even though I don't believe in this distribution and the results are not independent between games.
The probability computed was 24% chance to win without dropping a single game, which is a bigger ask.
The probability that Nepomniachtchi wins outright in the classical segment can be computed by expanding (0.1 + 0.7X + 0.2X^2)^14 and summing all the coefficients greater than 14. (This simulates 1 point for a draw and 2 points for a win, >= 15 points needed for an outright win).
Wolfram Alpha tells me the polynomial expands to ... + 0.0149792 x^20 + 0.040118 x^19 + 0.0851857 x^18 + 0.143065 x^17 + 0.189072 x^16 + 0.195351 x^15 + 0.156878 x^14 + 0.0976753 x^13 + 0.0472679 x^12 + 0.0178832 x^11 + ...
Mentally summing the terms gives me about a 67% that Nepomniachtchi wins outright in the classical section.