What is the value of a fourth trump? #1
By Mike Lawrence

When you are evaluating a hand for play in a suit contract, you routinely add your high cards and your distribution. Then you make some adjustments. You deduct something if you have a balanced hand. You adjust your estimate for high cards in the suits the opponents are bidding. And, you adjust your estimate for high cards in the suit or suits your partner is bidding.

If you do all these things accurately, you should be able to make a decent decision about your next bid. NOTE that I did not say a perfect decision. No one makes perfect decisions. It is impossible, due to the vagaries of bridge, to avoid looking like a loony every now and then.

Here are some evaluation questions for you. Put your sliding scale to work on them. You are South.

NUMBER ONE.

West

North 1H

East Pass

South ?

What are these two hands worth in support of hearts?

Q 9 8 6 3 J 10 3 A 8 7 10 4

Q 9 8 3 J 10 6 3 A 8 7 10 4

If you follow traditional evaluation, both hands are worth eight points. Seven in high cards and one in distribution. Do you agree with that?

I agree. There is a difference. Let's ignore how many points these hands are worth. Instead, decide how much difference there is between the two hands. Which hand is better, and by how much? We'll come back momentarily.

NUMBER TWO.

West

North 1S

East 3H

South ?

What are these two hands worth in support of spades?

A K 2 5 3 K 8 7 6 2 10 7 4

A K 3 2 5 3 K 8 7 6 10 7 4

Again, an initial evaluation suggests both hands are worth eleven points. But are they? Which is the better hand, and by how much?

9 4 K Q J 10 9 4 9 4 Q 8 2

A K 2 5 3 K 8 7 6 2 10 7 4 Q 8 7 6 5 A 8 2 A 5 K J 6

J 10 3 7 6 Q J 10 3 A 9 5 3

In this layout, South is in four spades. Can he make it with the king of hearts lead? You can fiddle with this for awhile. Then, before deciding, take a look at the next hand.

9 4 K Q J 10 9 4 9 4 Q 8 2

A K 3 2 5 3 K 8 7 6 10 7 4 Q 8 7 6 5 A 8 2 A 5 K J 6

J 10 7 6 Q J 10 3 2 A 9 5 3

In this layout, South is also in four spades. Can he make it with the king of hearts lead? Doesn't take much fiddling, does it? You win the heart lead, draw trumps, and play on clubs to see if you have one or two club losers to go with your heart loser. On this hand, you make ten tricks. Even if spades divide three-one, you take ten tricks without effort.

What is the difference between the two hands? The difference is that on the second hand, dummy had four trumps instead of three. This brings us to the theme of this article. Traditional point count has both of the possible dummy hands valued at eleven points. Yet one of the dummys gave you little play for game while the other gave you a 99% play for game plus a comfortable play for an overtrick. Scary. Adding the three of trumps to dummy changed a terrible contract into a great one. So what do you think the value of the fourth trump was? One point? Three points? More? Less? I don't know exactly how to measure it, but it seems to be worth lots.

Going back to the first pair of hands, it is clear to me that the second hand with its fourth trump is worth more than its companion hand. The amount that it is worth is not possible to determine, but it must be a value that you consider when making your decisions.

Larry Cohen wrote a book recently called The Law of Total Tricks. It is an elegant book that says, in effect, that the more trumps your side has, the better off you are. I agree. It says a lot more too, but I won't give any more secrets away here.