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?

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.