Suppose your partner opens 1NT and you hold a 4441 hand with specifically a singleton club. If you have invitational values or better, no problem really - you just wheel out Stayman (or, if very strong, the Baron convention if you play that) and take it from there. But suppose you have a hand of less than invitational values. Now it is quite tempting to bid Stayman and then pass pard's response. This will work jolly well if pard responds 2/2; but if pard responds 2 you might well be in a 4-3 or even (ugh) a 4-2 fit. Thus, whether Stayman is a good idea on these weaker hands comes down to a question of probabilities. The purpose of this article is to try to assess these probabilities by examining a couple of simplified models of general 1NT opening styles. We will make the commonsense assumption that any 4-4 fit is significantly better than 1NT in this case, a 5-4 fit very much better, a 4-3 fit significantly worse and a 4-2 fit very bad.
Model 1: partner always opens 1NT on any 4333 and 4432 hands in the right point range but never on other hands. (a) If pard is any 4333, he will have 4 spades/hearts/diamonds 75% of the time. Thus you will land in a 4-4 fit 75% of the time, a 4-3 diamond fit the remaining 25% of the time. (b) If pard is any 4432, you are guaranteed to hit a 4-4 fit. (In fact, in the 4432 cases you will end in 2 only where pard is 4-4 in the minors, which occurs one-sixth of the time.) Now, 4333 and 4432 hand shapes occur roughly in the ratio 1:2. Thus, putting all this together, we see that employing Stayman will lead to a 4-4 fit 92% of the time and a 4-3 diamond fit only 8%. Stayman is overwhelmingly the winning action.
Model 2: partner always opens 1NT on any 4333, 4432 and 5332 hands in the right point range but never on other hands. The above analysis still holds good for 4333 and 4432. For 5332, as 4333, he will have spades/hearts/diamonds 75% of the time, landing you in a 5-4 fit in those cases. In the remaining 25% of 5332 hands partner will have 5 clubs and either 2 diamonds (one-third of the time) or 3 diamonds (two-thirds). So of the 5332s, you'll land in a 5-4 fit 75% of the time, a 4-3 diamond fit 17% and a 4-2 diamond fit 8%. The relative frequencies of 5332, 4432 and 4333 hands are roughly 3:4:2. Combining all this we see that employing Stayman will lead to a 5-4 fit 25% of the time, a 4-4 fit 61%, a 4-3 diamond fit 11% and a 4-2 diamond fit 3%. As with Model 1, Stayman emerges the clear winner. It's interesting that in Model 2 Stayman leads to an improved contract 86% (25% + 61%) of the time whilst the dreaded 4-2 diamond fit is an almost negligible risk of 3%. It is true, of course, that many people are more likely to open 1NT with a 5card minor than with a 5card major, but that is a question of style and we won't pursue it here.
The conclusion has to be that you should employ Stayman on these weakish 4441 hands and I will definitely do so in future. If it turns out badly, you have the consolation that you took the percentage action - though I can't guarantee that your partner will be supportive.
[Somehow practice isn't quite as convincing! One point to remember is that if we bid to 2, opponents know not to compete in a major, whereas if we pass 1NT they may well get into trouble in some As(p)tro sequence. (ed)]