# On Breaking Ties and Making Offers that Can be Refused

Benasque is an odd tournament in its tiebreak system. While most open tournaments avoid head-to-head playoffs (it’s simply not practical to have a 20-player round-robin for 3rd prize and so on), there is no general agreement amongst tournament organizers about how to break ties.

In the US, they generally get around this by simply aggregating the monies for the tied places and then dividing it equally. Thus, if 5 players tie for first, and the prizes go down from \$5000 to \$4000 to \$3000 and so on, they each get \$3000 for their effort.

However, this does not seem all that equitable to me, as it’s quite possible for players to play very different fields to get to the same score. The player who starts out on fire will likely have played all his closest competitors, while someone who loses the first game and comes from behind will likely have played weaker opposition (because they are playing opponents with 0/1, 1/2, and so on).

Many European tournaments eschew pooling money together for a group of tied players and instead assign mathematical tiebreak scores to each player to differentiate those in the same score group. The usual metric is the sum of the opponent’s scores (often a trimmed version, with the high and low scores tossed out). There can also be conditions to calculate an opponent’s score in case the player withdrew from the tournament before finishing.

Benasque does something extra strange, though, in that the tiebreak order is determined by a lottery. Thus, they have a group of 3 tiebreak metrics (sum of opponents’ scores, performance rating, and number of wins), and then essentially randomly determine which one serves as the first tiebreaker and so on.

This also seems unfair to me. The idea that number of wins, in an open tournament, could serve as a primary tiebreaker is ridiculous. For players who lost their first game, they almost necessarily player a weaker field and so can put up many wins to reach the same score as someone who won early and then faced tougher opposition and drew. Thus, for example, after the last round, Players A and B both had 7.5/10. Player A had faced a field with an average rating of 2373 and Player B had faced a field with an average rating of 2174 FIDE. Player A had a higher sum of the opponents’ scores, 45 to 38.5. However, because Player B had lost two games against lower rated players, he continued to play down in all his games and won 7 games. Thus, in the number of wins tiebreaker, he led Player A by a tally of 7 to 6.

Does this seem fair? Admittedly, it is not easy to beat lower rated players, but I would think you’d want to reward a stronger performance (as reflected by the rating or scores of the opposing field).

In a round-robin, using the number of wins as a tiebreaker makes more sense since everybody plays everyone else. Wins generally equal more exciting chess, and from a sponsorship point of view, it makes sense to reward that fighting spirit. In an open tournament though, it makes no sense to me as a primary tiebreaker.

The idea of using a lottery system to choose the first tiebreak is an interesting one though. I think the motivation is so that it makes it more difficult to “fix” the results in the last round, as without knowing which tiebreak will be first, you will be less likely to offer money for someone to lose. I wouldn’t particularly mind if the lottery was only between opponents’ scores and performance rating, with number of wins as the third tiebreak regardless as this seems to strike some balance between preserving the integrity of the tournament and providing a more meaningful separator amongst tied players.

This has special implications for Benasque because of the practice of buying games in the last round. Rumors swirled last year when GM Felix Levin beat GM Azer Mirzoev in the last round to finish on 8/10, and then took first place on the fixed tiebreaks with GM Tamaz Gelashvili of Georgia (the Republic, that is). I don’t have definite proof that Levin bought the game, but I have it on good information that he referred to Mirzoev as a “chess prostitute” after the game. Gelashvili seemingly won his game fair and square, but because Levin won and beat him on tiebreaks, he left with 2nd place and 1000 less Euros than he would have otherwise.

This year, I know an offer was made to my roommate prior to the last round. GM Levan Aroshidze was playing GM Rashad Babaev of Azerbaijan. After the pairings went up the previous night, I received a visit at our hotel room from Mirzoev who was asking about whether Levan was around. While Levan wasn’t, I knew immediately why Mirzoev had come calling. Levan walked in maybe 20 minutes later and said that Babaev had been waiting in the lobby and an offer was made – if either player wanted to “win” the game without it being a real struggle. A win by either player would take them to 8/10 and possibly a tie for first (but even if not first place, at least more money), along with a few extra rating points for the win.

Aroshidze’s response was quite good – he essentially flipped him the bird and told him he’d see him at the board the next morning. Despite having the black pieces, Aroshidze proceeded to beat Babaev and finish on an honest 8/10. Given the tournament tiebreak system, number of wins popped out as the first tiebreak, and with 7 wins (he started the tournament one-round late), he was the leader amongst the 8-point scoregroup and so finished in 2nd place.

Having an actual tiebreak system (unlike in the US) would seem to help dissuade cheating, since the money is not guaranteed. You may know how your opponent’s are doing up through round 9, but you can’t know in advance how they’ll do in round 10, and even more importantly, you don’t even know which tiebreak is going to be in place after the end of the tournament. The organizers are clearly thinking about this problem, but I think it would be bring a seemingly more equitable outcome if the tiebreak choices were tweaked slightly.

Update: Somebody pointed out that an opinion piece about the Benasque tiebreak system was written at: http://www.ajedreznd.com/2008/nvictorias.htm (the author essentially agrees that number of wins is a poor first tiebreak)

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