198 18.
Arithmetic
Chapter 18 Here are the 13 one-suiters with 6 or 7 spades:
(5) 2] HS
(3) 2NT MS
Arithmetic (2) 3{ even even
(1) 3} 6-3-3-1 6-3-1-3 6-1-3-3
(1) 3[ 7-2-3-1 6-3-2-2 7-2-1-3 7-1-2-3 6-2-2-3
Leonardo Fibonacci was the first notable Christian mathematician
(1) 3] 7-3-2-1 7-2-2-2 7-3-1-2 7-1-3-2 6-2-3-2
of medieval Europe. The Fibonacci sequence, which governs the
rate of growth of some organisms and populations, is named after Another neat structure1 – a Fibonacci collection of common shapes
him. This is the sequence: split into five streams, all ending by 3].
(1), 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 .... Fibonacci and system design
After a scratchy start, each number is the sum of the previous two. In the Fibonacci sequence, each number is the sum of all the earlier
Roy Kerr and Walter Jones used this sequence to devise the ones, excluding the one just to its left.
structure of symmetric relay. Take this Scamp relay auction: Consider positive responses to 1{. There are 300 hand patterns
1[ that need to be described. Fibonacci shows that there is room to do
1]R 2{ balanced this below 3NT.
Opener can have one of 8 patterns (3 x 5332, 4 x 4432, 1 x 4333)
The efficient way to describe these shapes is to split them into Bid Hands Bid Hands
streams that all end at the same low point. Fibonacci dictates how Pass 610 2[ 13
this should be done. 1{ 377 2] 8
(8) 2{ 8 balanced hands 1} 233 2NT 5
1[ 144 3{ 3
(3) 2[ five hearts
1] 89 3} 2
(2) 2] [&}
(1) 2NT 2-4-3-4 2-5-3-3 1NT 55 3[ 1
(1) 3{ 3-4-2-4 2-4-4-3 3-5-2-3 2{ 34 3] 1
(1) 3} 3-4-3-3 3-4-4-2 3-5-3-2 2} 21 3NT 1
This Fibonacci split (3-2-1-1-1) ensures that all the streams end at
3}. If we add an extra shape to the eight balanced hands, one The Hands column represents the maximum number of patterns
stream would overflow to 3[. The ideal number of hands to place in that can be relayed out by 3NT, starting at the bid alongside. For
each box is a Fibonacci number – eight and five are good, four is not instance, you can put 144 patterns into the 1[ box and still get to
ideal. show them all by 3NT.
However, it's logical to deal with some patterns in groups of four. Add the numbers from 144 down and you get 377. Thus responder
Take Roman hands with a known shortage. There are four of them, to a strong 1{ opening has enough bidding space to show 377
which we resolve in one go, rather than make more streams – you
need five shapes to make that worthwhile.
1 Okay, I fudged by ignoring 7330 (3NT) but that's okay. You can tack any number
of rare shapes at the end of a stream – resolve all the way to 12-1-0-0 if you wish.
There's no value in trying to accommodate them lower down.
