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A Bridge Too Far (Posted on 2013-06-19) Difficulty: 3 of 5
In the game of duplicate bridge, the idea is to get a better score than the other pairs who, during the course of the session, play the same hands at different tables. A pair will get one point for every score they beat, and half a point for every score they tie.

One particular hand was played eight times. All pairs playing North-South scored either +420 or +450. (The derivation of these scores doesn’t matter, although they are common and result from a contract of, say four hearts.)

One of the pairs that scored +420 noted that this score was worth 2.5 points at the end of the session.

How many points would this pair have received had they scored +450 instead?

No Solution Yet Submitted by K Sengupta    
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Solution Valuable overtrick (spoiler) | Comment 1 of 2
I'm a duplicate bridge player, so I had better get this right.

If the hand was played 8 times, then there are 7 other pairs.

If we got 2.5 points for +420 (the lowest score), then that means that we tied 5 pairs (calculated as 2.5 / .5) who also got 420.

That means that 2 pairs got +450 (the highest score).  If we had gotten +450 instead of +420, then we would have tied 2 pairs (earning half a point each) and beaten 5 (earning one point each) for a total of 6 points.  Final answer

Another way of calculating is that if there are only two different results, then getting the higher score instead of the lower one is always worth an extra half a point for each of the other pairs who played the hand.  (Either we beat a pair instead of tying them, or we tie a pair instead of losing to them).  2.5 + 7*(.5) = 2.5 + 3.5 = 6. 

  Posted by Steve Herman on 2013-06-19 14:20:51
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