[seqfan] Mathematics of bridge

Charles Greathouse charles.greathouse at case.edu
Wed Nov 20 03:14:42 CET 2013

A new user registered recently
and asked this question. As I have no knowledge of the game I leave this
here without comment:


I'm now playing around with a simplified method of converting rubber bridge
scores to Victory points. There is one such table dreamed up more than 25
years ago. It lacks any mathematical foundation.

I've tried a variety of mathematical combinations and my latest method is
based on the Fibonacci series: 1-2-3-5-8-13-21-34-55-89-144-233.... It has
yielded a new sequence that might be interesting. It is not intended to
replace the International Matchpoint Scale, but could be used by social
bridge players using the 4-deal method to determine has done best after
6-10 rounds.

After the completion of each round of four deals one calculates the net
score difference between the two pairs at each table and converts this
number to Victory Points based on this scale, where the winning pair gets
the higher of the two numbers listed for each range. The Victory Point will
vary from 10 to 0 and cover the score difference from 0 to 3850 or higher.

The spread 0 to 3850 is divided up based on the Fibonacci series
1-2-3-5-8-13-21-34-55-89-144-233... as follows. 0-10, 20-40, 50-80, 90-140,
150-230, 240-370, 380-590, 600-940, 950-1500, 1510-2400, 2410-3850. Note
that each range is a multiple of 10 times the above Fibonacci series. Note
there is a 10 point step between the high number of each range and the low
number of the next range.

Now take the sum of each range and divide by 10 and you'll get the
sequence: 1-6-13-23-38-61-97-154- 245-391-626-1005....

Having only rudimentary math know how I would like to ask if this series
can be expressed with a simple formula to allow calculation of the nth
term. Would somebody care to do this?

Charles Greathouse
Case Western Reserve University

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