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Dear Ed and Peter,

Partner opens 1NT (15-17) and I have 4♠-3-3-3 with 10 HCP. There is no intervention.
Should I, lacking ruffing values, bid 3NT?
Or is the chance of partner, if he has four spades as well, having ruffing values bigger than 50%? In that case it may be better to apply Stayman, in search of a 4-4 spade fit...

Thank you in advance,
M. Smeets

Answer Ed Hoogenkamp (South)

Dear M. Smeets,

Peter and I have extensively discussed this topic, when we made the recommended auctions for the bidding contest of the bridge magazine we used to work for.
My gut feeling was to forget about Stayman and bid 3NT. Peter, however, convinced me I was wrong.
So let's read his answer below, where he explains once more. I can do with a repetition.

Un saludo, regards from Barcelona

Answer Peter van der Linden (North)

Dear M. Smeets,

Ed is exaggerating, my arithmetic is not that good, so I cannot prove my point. I'll try to make it plausible though.
Firstly: advanced players use artificial methods to find out whether the 1NT opener has 4-3-3-3. I assume you haven't agreed with your partner about such a method (if you had, you wouldn't have asked this question...).

Suppose you apply Stayman with a 4-3-3-3 (or 3-4-3-3) and you find a 4-4 fit. Partner then has either a 4-4-3-2 or a 4-3-3-3 distribution (for the moment we assume that he doesn't open 1NT on a 5-4-2-2 — five-card minor — or five-card major).
The total chance to get a 4-4-3-2 distribution is 21,5512%; the chance to get a 4-3-3-3 distribution is 10,5361% (source: The Official Encyclopedia of Bridge).
The chance of partner having a 4-4-3-2 is therefore slightly better than twice that of him having a 4-3-3-3. Calculating this back to 100% (since we assume he opens 1NT with a four-card major on either a 4-4-3-2 or a 4-3-3-3): 67,16% of all hands on which he opens 1NT will therefore be 4-4-3-2 and 32,84% will be 4-3-3-3.

I postulate that if he has ruffing values, 4♥/♠ will never be worse and usually be better than 3NT.
Furthermore a trump suit is sometimes needed to check the opponents' suit. In a rare case even with two 4-3-3-3 hands opposite each other 4♥/♠ may prove to be better than 3NT:

		♠	A J 5 4
		♥	6 4 3
		♦	Q 7 6
		♣	K 8 2
		♠	K Q 10 2
		♥	9 7 2
		♦	A J 10
		♣	A Q 4

3NT makes if the ♦K is with East and the heart suit is 4-3 in EW (or West fails to lead it).
4♠ requires only the ♦K with East .
Admittedly, this is a rare case. Usually when both partners have 4-3-3-3 and a 4-4 fit in the major, 3NT is the superior contract.

In order to make it plausible that with a 4-3-3-3 opposite a 4-4-3-2, a 4♥/♠ contract is more often superior to 3NT than vice versa, a computer simulation is required of hundreds of NS-hands. In each case the chances of 4♥/♠ versus 3NT are to be compared. I have not done so (I can't even do it...).

But still: suppose that in three out of four cases that partner has a 4-4-3-2, 4♥/♠ is superior to 3NT. Then both possible lines of action (Stayman vs. no Stayman) are superior in 50% of all cases, a draw therefore (mind you: I suppose then, that with two 4-3-3-3's opposite each other 3NT will always be superior — which is not entirely true as we have already seen).
For those who wonder how I concluded to that draw: 3/4 x 67% = 50%.

I have the feeling, however, that with 4-4-3-2 opposite 4-3-3-3, 4♥/♠ will be superior to 3NT in more than 3/4 of all cases. So I apply Stayman!

I have four (!) more reasons.
- I did already mention the first one: sometimes 4♥/♠ is superior even with both having 4-3-3-3.
- To apply Stayman means you are consistent in your bidding. After all, each and everyone will use Stayman, when having a 4-4-3-2 and play in a major suit after finding a 4-4 fit. No-one asks himself then whether partner perhaps has a 4-3-3-3...
- The 1NT opener may have a 5-4-2-2 distribution (five-card minor). Such off-shape 1NT openings are getting more and more common, since they prevent rebid problems (for instance, if you open 1♦ on 2-4-5-2 and 15 HCP, you're in a fix if partner responds 1♠; opening 1NT is more practical, therefore).
- The 1NT opener may have a five-card major. Not applying Stayman could lead to playing 3NT with a major 5-4 fit then — not a nice contract, since the 1NT opener is certain to have plenty ruffing value...

To conclude with: please don't get angry with me if you choose to apply Stayman and subsequently see your partner go down in four in the major with 4-3-3-3 opposite 4-3-3-3, whereas he would have made 3NT! Bridge is about doing what is usually best!
(Just blame Ed, he is used to that).

En hils, regards from Orkanger