"Drop-dead Stayman":
On what shapes and strengths is it appropriate?

Gordon Bower

Stayman was invented to help your partnership reach 4 or 4 rather than 3NT. But as soon as it was invented, people discovered that there was an extra benefit: with a hand like K543 8643 98654 —, responding 2 and passing opener's rebid, regardless of whether it was a natural 2 or 2 or the possibly-artificial 2, led to a better result than staying in 1NT did.

A few people resisted this use of Stayman. Some people championed "Extended Stayman," where responder promised invitational or better values and opener was allowed to use responses all the way up to 3 to show his strength and distribution in more detail. Others decried the use of 2 on weak hands as an illegal risk-free psychic bid. Beginner's bridge books will still sometimes say "after a one-notrump opening bid, a response of two clubs requires 8 or more HCP." But the vast majority (including the author's of those beginning bridge books, who are just trying to keep things simple for beginners) found it was a useful addition to standard bidding.

The standard textbook advice is to do this only when responder has 0-7HCP and 4-4-4-1 or 5-4-4-0 shape, with a singleton or void in clubs. It's clearly right to do so on those hand patterns. But it may also be a reasonable gamble on hands that don't have 4 cards in all three unbid suits. If responder is weak and distributional, a 4-3 major fit is often better than 1NT.

We investigated all reasonable shapes and strengths of hands, to see which hand patterns showed a profit by bidding 2 rather than passing 1NT. The two fundamental conclusions are having three cards in a suit is okay, but having only two is bad and the weaker responder's hand is, the larger the profit from using Drop-Dead Stayman.

Summary of findings

• 4441, 4351, 3451, 3442 - always
• 4432 and 4342 - always (but if you have 7 or 8 HCP, rebidding 2NT is better than dropping partner in your 3-card suit.)
• 4423 - always (but much less profitable than 4432/4342. Rebidding 2NT is better with 7 or 8 HCP, and also with 6HCP if opener is very likely to pass 2NT rather than raising to 3.)
• 4414 - always profitable at matchpoints; 0-5HCP at IMPs. (At either form of scoring, rebidding 2NT is better with 6+ HCP.)
• 2452 - always (but with 7 or 8 HCP, rebidding 2NT over 2 is better.)
• 4252 - only with 0-6 HCP at pairs, 0-5 HCP at IMPs. (With 7 or 8 HCP, rebidding 2NT over 2 is profitable.)
• 2443 - only profitable with 0-4 HCP
• 4243 - only profitable with 0-1 HCP at matchpoints, 0-2HCP at IMPs
• 3433 - only profitable with 0-2 HCP, not holding the Q
• 4333 - only profitable with 0 HCP
• 3343 - never profitable
• 3361 - Always profitable!
• 3352 - only profitable with 0-7 HCP (and pass, don't raise to 2NT, with 8.)
• More extreme distributions (3460, 4361, 4450, 3370) were not analyzed (but Stayman is clearly correct on the first three of these.)

If you play very old-fashioned conservative 1NT openings -- especially if you rarely or never hold a 5-card major when you open 1NT -- you need to also be more willing to pass 1NT. I did some short supplementary simulations to find out just how much more so: if you never open a 5-card major, use Stayman on all your 4441, 4351, 3451; the intermediate shapes only if weak (3361 and 3442 up to 6HCP; 4432 and 2452 up to 5; 4342 and 3352 up to 3; 4414, 2443 and 4252 up to 2.); the worst hand patterns (4243 and 4423) not at all.

More detailed analysis

Generally speaking, using Stayman shows a large profit if it uncovers an 8-card fit; shows a small profit if it lands you in a 7-card fit; and incurs a large loss if you play in a 6-card fit, or if you get too high in notrump with a weak hand.

Not surprisingly, having hearts is most important, since opener will rebid 2 when holding both majors. The matchpoint benefit of bidding 2 on a 3-4-5-1 hand, for instance, is about 2% greater than on a 4-3-5-1 hand. The difference becomes more pronounced as the suit lengths grow farther apart (over a 10% difference between 2-4-5-2 and 4-2-5-2 hands). See how rare the 2 response becomes when responder is short in hearts in the table below:/P>

Frequency of opener's rebids

If your majors are split this way:	Opener's rebid is:
	2	2	2
4-4	26%	31%	43%
4-3	24%	39%	37%
3-4	31%	32%	37%
3-3	29%	38%	32%
4-2	22%	46%	32%
2-4	36%	32%	32%

The overall success of the the 2 response is a weighted average of how successful 2, 2, and 2 contracts will be, given that opener makes that particular response. In only a few cases (4351 and 3451) were all three contracts always better than 1NT. More typically, we are exchanging a substantial gain in one area for a modest loss in another. A typical example is responding with a 4-4-3-2 pattern and 4HCP:

If we play:	Matchpoints:			Net IMP Expectation
	Gain	Lose	Net	NV	Vul
2	77%	6%	+71%	+2.46	+3.47
2	77%	5%	+72%	+2.55	+3.61
2	20%	59%	-39%	-1.16	-1.84
Overall	53%	28%	+25%	+0.97±.06	+1.29±.09

In those cases where returning to 2NT rather than dropping opener in a possible misfit has merit, I compared the expectation of "always pass" as calculated above with the expectation of "pass 2M if you find a 4-4 fit, rebid 2N if not" from my previous study on responding to 1NT with balanced 8-counts (for which I actually did calculations for 6-10 HCP responders.)

Uniformly across all hand patterns and forms of scoring, weaker hands gain more from using Stayman than stronger hands do. This is a simple reflection of the fact the way notrump contracts go down is by having the opponents run their long suit after knocking out declarer's only stopper. The stronger the declaring side is (and the more balanced dummy's hand is!) the less likely the opponents are to be able to set up so many tricks on defence. (In my study of 3NT success I found 1 extra point was worth about half a trick to declarer in notrump.) Suit contracts benefit from extra face cards too but to a lesser extent, such that the 4-4 major fit's large advantage at the partscore level disappears completely somewhere around 29 or 30 HCP. (I am not the first person to notice the "1 HCP = half a trick in notrump, 1/3 of a trick in a suit" pattern, but despite it appearing on the web before, it is far from common knowledge.)

The importance of the heart suit is spectacularly illustrated when you compare the results for 4423, 4243, and 2443 distribution: the first and last are both far better than the hand with only two hearts.

I was surprised to see that, after the classic 4441, 4351, and 3451 hands, the next-most-profitable hands to use Stayman did not contain a 4-card major at all: 3361 and 3352! Prior to running this simulation, it would have never occurred to me to use Stayman on this hand pattern. I did a separate analysis of whether Stayman is better than transferring to 3 on 3361 hands (and found that, on average, it is.)

Presented below is the expected gain from using Drop-Dead Stayman, as a function of responder's strength and distribution. Matchpoint estimates are good to ±1%, NV imp estimates to ±.07, and vul imp estimates to ±.10 or better at the 95% confidence level.