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# Richard Cowan's 5-4-3-2-1 Count

In 1987, Richard Cowan did some research into notrump hand evaluations, and came to the conclusion that notrump trick values of the honor cards is very close to:
```     Ace   = 5
King  = 4
Queen = 3
Jack  = 2
Ten   = 1
```
on the condition that both hands are balanced. This is a surprising result, compared to my research, so I checked his analysis.

It turns out, he is evaluating suits in isolation. He looks at all pairs of holdings that a declarer and dummy can have, then computes an average number of tricks for that holding. For example, holding A-4-3 opposite 6-5-2, Cowan says this pair of holdings is worth one trick.

Sometimes, an ace is worth more than one trick, of course, because, for example, K-x-x opposite x-x-x is worth 1/2 a trick, while K-x-x opposite A-x-x is worth 2 tricks. Under this analysis, Cowan gets the value of an ace to be 1.41 tricks (under the condition that both declarer and dummy are balanced.)

The problem with this analysis is that an ace gives the declarer not just a trick, but a tempo. For example:

North
A 3
A K Q J
A K 3 2
A 3 2
South
4 2
5 4 3
Q J 6 5
K Q J 3

The ace of spades here is the difference between making 13 tricks and being limited to eight tricks (assuming spades are 5-4.) The ace is, here, worth five tricks.

From Cowan's point of view, the spade ace is one trick.

In Binky Points, the notrump difference between A-2 and 3-2 is 2.6 tricks.

The reality is that a 5-4-3-2-1 evaluator scores very badly as an evaluator because it does not include the value of honors giving the declarer a tempo.