# 2016 Carlsen - Karyakin world champs outcome according to math

These are my predictions of the upcoming Carlsen-Karyaking match:

- After 9 rounds, the standing will 5.5 -- 3.5 to Carlsen
**Carlsen wins**after 11 rounds**with 7 -- 4**

In contrast to my (spot on) predictions of the last two WC matches, this time the predicted result is not as clear mathematically. There are two about as likely scenarios for the match outcome. These second most likely scenarios are: Carlsen winning after 10 games with 6.5 -- 3.5, and Carlsen winning after 11 games with 6.5 -- 4.5.

**How the prediction is made:**

The prediction is done purely by crunching numbers.

Carlsen is rated 2853 FIDE and Karyakin 2772. The rating difference between the players is 81 points. This corresponds to Carlsen (statistically) scoring an average of 0.6166 point in each game (the number is from interpolating the FIDE rating table). This expected result is all we need to make statistical guesses of the match.

After 9 games we are expected to see Carlsen at ~5.55 points ( 9 games with 0.6166 each ). Since a chess game can only give 0, 0.5 or 1 point, the closest result is 5.5p.

After 10 games we the expetated score is 6.166 points for Carlsen ( 10 x 0.6166 ). The closest possible result is 6p, but there is already a chance (maybe 30%) to obtain the needed 6.5p.

After 11 games there are two almost as likely scenarios. Carlsen is expected to have 6.776 points. Here both 6.5p and 7p are almost as likely, but the 7p case is a tiiiny tad closer.

And unlike some recent election, the statistics here are hopefully more reliable -- chess ratings are not weighed by what skin colour or social group the players have / belong to.