Correct contract bridge / by E.V. Shepard ; including the official Laws of contract bridge adopted by the Whist Club, New York, and by all the leading clubs in America.

FOUR CARD BIDS

I47

In the first place, 59 in ioo times, at least one ad.
versary will hold as many or more than your 4
trumps. To be "efficient" means that a suit need
lose no trick to an adversary, either because the
latter holds more trumps or because he has one
honor trick. "The net efficiency" of a trump suit
consists of its average chances to find normal support in dummy, minus the average chances of finding an opponent able to win at least one trump trick.
Really the term "normal support," as scientifically used, means that the declarer and the dummy
jointly hold 8 trumps (Whether divided between
them 4-4, 5-3, 6-2, 7-I, or 8-o, does not matter;
there are held against their side just 5 trumps, standing 68 in ioo chances of being divided 3-2), or 7
trumps, in case dummy holds a missing high honor.
Sometimes a player having small regard for facts,
states that the strongest possible arrangement of
these 8 trumps is when declarer and dummy each
holds four. Of course this is absurd; the A K Q
X X X X X held by the declarer, with none in
dummy averages to be worth 8 tricks, which is 3
more tricks than an average division is worth.
Your chances to find normal trump support in
dummy are, in I,000: 44I for a 4 card suit; 6I7 for
a 5 card suit; 79I for a 6 card suit. Chances for
an efficient trump suit are in I,000: 3I3 for a 4 card
suit; 593 for a 5 card suit; 79I for a 6 card suit.
With relative efficiencies of 3, 6, and 8 chances in
IO, for 4, 5, and 6 card suits, respectively, it should
be evident that when reasonably possible 4-card
bids should be avoided.