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Rooting For Armageddon At The World Chess Championship

Tiebreaker games at the World Chess Championship will begin this afternoon. Over the past 19 days, Magnus Carlsen of Norway, the defending champion, fought his challenger, Sergey Karjakin of Russia, to a 6-6 tie in their best-of-12 match and the battle for chess’s top prize.

And they’re not done yet. According to the FIDE match rules, this is how the tiebreaker will go:

• First, a mini-match of four rapid games will be played. Each player gets 25 minutes for all of his moves, plus 10 bonus seconds after every move played.
• If the players remain tied after those four games,1 they’ll play a mini-match of two blitz games. Each player will get five minutes, plus three seconds after every move. They’ll keep playing those, if the two-game mini-matches are tied, for up to five total mini-matches (10 total blitz games).
• Finally, if none of that settles it, they’ll play one sudden-death game using a format known as Armageddon. White gets five minutes and black gets four minutes, but a drawn game counts as a win for black.

I’m not supposed to root from the press box, but I’d be lying if I said I wasn’t intrigued by the possibility that the World Chess Championship will be decided by Armageddon. So what are the chances of that happening?

To find out, we need to know the likelihood of draws in individual games in the rapid and blitz matches. In last year’s World Chess Rapid Championship (Carlsen won, Karjakin finished 19th), 29.9 percent of the games in the tournament were draws. So let’s suppose a 30 percent chance of draws in the individual rapid games. In last year’s World Chess Blitz Championship (Carlsen finished 6th, Karjakin 17th), 20.2 percent of the games were draws. So let’s say there’s a 20 percent chance of draws in the individual blitz games.2 I’ll also use the two players’ listed rapid and blitz ratings from the FIDE website throughout my analysis to estimate chances that individual games in the two formats are won by either player.

CUMULATIVE CHANCE OF WINNING CHAMPIONSHIP
TIEBREAKER ROUND CHANCES OF PLAYING CARLSEN KARJAKIN
Rapid Game 1 100.0% 0.0% 0.0%
Rapid Game 2 100.0 0.0 0.0
Rapid Game 3 100.0 28.4 6.7
Rapid Game 4 64.9 59.7 20.1
Blitz Match 1 20.2 68.9 24.3
Blitz Match 2 6.9 72.0 25.7
Blitz Match 3 2.3 73.1 26.2
Blitz Match 4 0.8 73.5 26.4
Blitz Match 5 0.3 73.6 26.4
ARMAGEDDON! 0.1 73.6 26.4
When will the chess end?

I simulated tens of thousands of iterations of this afternoon’s tiebreakers using the same basic method I used to forecast the 2016 chess championship before it began. We’re guaranteed to see the first three games of rapid chess, as no player will be able to clinch the match in only two games, but there’s a 35 percent chance that one player will have clinched after those first three games. That would end the mini-match and thus the championship. There’s a 20 percent chance that Carlsen and Karjakin will be tied at the end of the rapid mini-match and that we will move on to the five-minutes-a-side blitz segment. According to my simulations, the two-game blitz mini-matches would each wind up tied about a third of the time.

What all that means, sadly, is that there is just a 0.1 percent chance that Armageddon will decide the 2016 World Chess Championship.

The tiebreakers begin this afternoon, and a world champion will be crowned. I’ll be covering them here and on Twitter.

## Footnotes

1. Wins are worth 1 point, draws are worth a half-point for each player, and losses are worth zero points.

2. In the rapid and blitz championships, the time controls are similar to today’s tiebreakers, but slightly different. Players in those tournaments received 15 minutes rather than 25 for rapid, and three minutes rather than five for blitz.

Oliver Roeder was a senior writer for FiveThirtyEight. He holds a Ph.D. in economics from the University of Texas at Austin, where he studied game theory and political competition.