Wikipedia:Reference desk/Archives/Mathematics/2018 April 20

= April 20 =

Bridge events
In a bridge "tournament" where the same deals are played at multiple tables, one way of scoring is, for each pair who had the same cards as you that you got a better result than, score 2 points, for each pair with the same result, score 1 point.

The results for one deal and the score it produces, (pairs are numbered 1 to 8) 1 v 2   +400 for 1    (-400 for 2) 3 v 7   +400 for 3    (-400 for 7) 8 v 4   +430 for 8    (-430 for 4) 6 v 5   -50 for 6     (+50 for 5) where 1,3,8,6 had the same cards and 2,7,4,5 the same cards

Thus 8 beat 1,3,6 and gets 6, 4 beat no one and gets 0. 1 beat 6 and equaled 3 for 3, 2 beat 4 and equaled 7 for 3. 3 beat 6 and equaled 1 for 3, 7 beat 4 and equaled 2 for 3. 6 beat no one for 0, 5 beat 2,7,4 for 6.

Then you add it all up, and assuming all pairs played the same number of times, the highest total wins.

My question: Given this, it is possible to have a tie for top score. Is there a fair tie-break scheme? One possibility is to look only at the scores when the equal tops played each other - would this work?

-- SGBailey (talk) 21:21, 20 April 2018 (UTC)
 * Well, what do you mean by "work"? It's a possible tie-break scheme.  It's "fair" in the sense that it doesn't arbitrarily privilege any particular pair.  It won't always break ties (because for example there might be two top parterships, and they might have split evenly the boards where they played each other), but it will in many cases.
 * If you're asking whether it will break ties in the "right" way, then I think we need to inquire deeper into what that means. --Trovatore (talk) 21:48, 20 April 2018 (UTC)


 * I'm a director in the American Contract Bridge League. This is matchpoint scoring, except in North America we use 1/2 point for each tie and 1 point for each you did better than, which is equivalent to what you have.  And yes, ties for first place can happen.  Generally there is no tie-break system.  If two pairs tie for first place, they add the reward for first place and second place together and give each pair half of that total.  There might be some events, say a national pairs championship, where they would want a single winner, and then they might use some sort of tie-break, but I don't know.  But I don't think they would use anything like you are suggesting. Bubba73 You talkin' to me? 22:10, 20 April 2018 (UTC)


 * Another point that just occurred to me: In most matchpoint rotations, you stay either North–South or East–West for the whole match.  So if for example the pairs tied for first are both East–West, then they never play each other at all. --Trovatore (talk) 22:24, 20 April 2018 (UTC)
 * That's right and it can happen. Bubba73 You talkin' to me? 22:40, 20 April 2018 (UTC)


 * It is always possible that the tied pairs actually had identical scores on every board of the event. (This is true even if they played each other in one round.  Maybe they passed out each of those boards, getting half of the possible matchpoints because half of the other tables went +100 EW and the other half were +100 NS.)  In that case even if you wanted to break the tie, there is no way to do it based on their records in this event. --69.159.62.113 (talk) 22:39, 20 April 2018 (UTC)


 * Well, of course, you have to define a criterion to decide what "works", but we can still answer. I cannot answer as to what is usually used for bridge, but for chess (where the fact that most pairs of players do not meet each other and all games are different compounds the "two EW pairs never meet" effect), there are a lot of options. Tigraan Click here to contact me 16:48, 21 April 2018 (UTC)