# With which "non-trump" holdings is a 4-4 fit superior to a 5-4 fit?

If a partnership has both a 4-4 and 5-4 holding on one deal, I could see why it would make sense to have the 4-4 holding be the trump suit. The 5-4 holding can take "long" tricks with the fourth and fifth cards (on the 5 side), while the only way to "lengthen" the trump holding is through ruffs.

But suppose that you have the 4-4 and 5-4 holdings in separate deals. And suppose that you have no other "long" (seven card or longer) suits in either deal, so that the eight card (4-4) holding is distributed 8-6-6-6 in the four suits, and the nine card (5-4) holding is distributed 9-6-6-5 in the four suits.

In this case, wouldn't it be better to have the 5-4 holding with the extra trump than the 4-4 holding? Especially since the ninth card guarantees a ruffable imbalance, e. g. 5-3-3-2 opposite 4-3-3-3, whereas the eight card holding could be 4-3-3-3 opposite 4-3-3-3? Or is there something I am missing?

• I have no idea what you are getting at. Perhaps give a specific example of the two hand shapes you are trying to compare. Also, it is important to note that all non-trump suits are identical - why should, or even how could, you care which is which? Nov 8 '15 at 15:57
• @PieterGeerkens: If I have 5-4-3-1 opposite 4-4-1-4, I prefer the 4-4 fit in hearts to the 5-4 fit in spades, because spades is a "long suit that might yield an extra trick. But If the shapes were 4-3-3-3, opposite 4-3-3-3, the 4-4 fit doesn't seem to do me much good, and I'd prefer a 5-3-3-2 opposite the 4-3-3-3 with the extra trump and an "imbalance. Put another way, I might be inclined to bid one higher with 5-3-2-2 opposite a (presumed) 4-3-3-3 than with 4-3-3-3 opposite the same 4-3-3-3. In the other deal, the trick-taking potential was maximized by the 4-4 fit.Or am I missing something? Nov 8 '15 at 20:38
• If both hands are 4-3-3-3 why aren't you playing the 9-trick NY game? Play a contract that requires one less trick, to compensate for having a trick less playing potential due to the unfortunate distribution. Nov 8 '15 at 21:05
• @PieterGeerkens:Then a 4-4 fit needs an "imbalance" in side suits to shine. Ideally a partnership holding of 8-8-5-5 (or better), rather than 8-6-6-6 (unless the latter were something like 4-2-4-3 opposite 4-4-2-3). That was the point of the question. Nov 8 '15 at 21:13

This is sort of an odd question. The cards you get are the cards you get, and you should do the best you can with the cards you have. You don't get to decide whether you have a 4-4 fit or a 5-4 fit, so in a sense this information doesn't help you. But as a way to improve your hand evaluation, let's consider this.

One answer comes from the law of total tricks, which basically says, if you add up the tricks your side can get when declaring in your best trump suit to the tricks your opponents can get when declaring in their best trumps suit, it'll add up to the number of trumps you have plus the number of trumps they have. Of course, this isn't actually a law (it's easy to construct counterexamples), but it's a good rule of thumb. In this case, you're comparing 8+7=15 to 9+8=17, so it seems likely that your 9-card trump fit will have more trick-taking potential for the same number of high card points.

You can also look at this from the losing-trick-count point of view. If you move a spot in a 2- or 3-card suit into a suit that already has 4 cards, you're removing a loser from your hand (in losing trick count, you count the number of cards that will lose to an A, K, or Q not in your hand, so AKx, AKxx, and AKxxx all have one loser, while xxx has 3 and xx only 2).

Even good old high-card-point evaluation methods typically give some sort of value to distribution -- either adding a point for the fifth card in a suit, or adding points for having doubletons instead of tripletons, singletons instead of doubletons, etc.

So this is a lot of ways to say, your intuition is correct. All things being equal, in a pair of hands that only have one fitting suit, having more cards in that suit tends to increase the number of tricks you can take.