[isdarifi] 2700 + money

Consider a ratings difference of r = 70.83533779584746678944378491. In a single game, the expected score difference of two players with that difference is p = 1/(1+10^(r/400)) = 0.3994491169441985005619073685.

For a twelve-game match, the worse-rated player has a probability of sum(i=6, 12, binomial(12,i)*p^i*(1-p)^(12-i)) = 1/3 of a tie or "upset", scoring 6 or more points.

This is the basis of the simplest format of the chess world championship. Any player with a rating of within 70 points of the current champion may bid a prize fund to challenge. Whoever bids the highest (actually delivering the bid, of course), wins the right to challenge.

Hypothetically, an unscrupulous current champion might try to game the system by bankrolling a specific weaker player (whom he can beat, possibly in an arranged match) to become the challenger. However, this is where the alleged graft and corruption in FIDE actually does good: FIDE aggressively takes a cut, say 20%, of the prize fund (some of it is used to make sure the playing venue and conditions are fair, some of which might be used to fund youth and women's championshps), which means such a strategy is guaranteed to cost the current champion at least 20% of the winning bid which he bankrolled.

An additional mechanism prevent a single wealthy entity from corrupting the system for many years in a row (e.g., bankrolling a weak-ish challenger on behalf of the champion), we also allow to bid a group of candidates representing multiple sponsors who all pay in, and play a candidates tournament to select a final challenger.  The details of the candidates tournament are worked out amongst themselves before the group bid.  There are plenty of degrees of freedom.

I hope this doesn't make things worse, with the possibility of a cabal controlling the candidates process, excluding someone they don't like.  It also opens the possibility of a sponsor getting back more than they invested, a gamble.

This was originally inspired by Topalov's 2700+money proposal.