Stayman with Weak Hands ("Junk Stayman")
Using Stayman often promises enough strength to invite to game. But even if that is your understanding with your partner, you can play "Garbage Stayman" -- you can bid Stayman with a weak hand and pass whatever partner bids. The ideal is a 4-4-5-0 distribution.
The more modern convention is Nonforcing Stayman -- over the 2D negative answer, 2H and 2S are weak and should be passed. So, when you are weak but 5-4 in the majors, you can try for a 4-4 fit and still play in your 5 card suit if you don't find the 4-4 fit. You lose the ability to invite to game with 5-4 in the majors, but weak hands occur more often than invitational hands. So Nonforcing Stayman is more useful at match points, but I guess it is worthwhile even at IMPs.
(There is one small advantage to nonforcing Stayman in bidding games -- with 5-4 in the majors, you might want to invite to game if you find partner with 4-card support, but not invite to game in NT. You can do this with Nonforcing Stayman but not with Forcing Stayman.)
As an aside, most people apparently play nonforcing Stayman over a 1NT opening and forcing Stayman over a 2NT opening.
You can improve on Nonforcing Stayman with what is called "Crawling Stayman" -- after the bidding 1NT - 2C - 2D - 2H, the 1NT opener converts to 2S when holding only 2 hearts (and hence 3 spades). Now you can bid 2C when you are 5-5 in the majors, maybe find a 5-4 fit, and always end up in at least a 5-3 fit.
With Crawling Stayman, you give up the chance to look for a 4-4 fit when you have six hearts and 4 spades. But you should probably use Jacoby transfer with a 6-4 distribution anyway. (There is likely to be a 6-3 heart fit; Jacoby transfer makes the strong hand the declarer; Stayman gives away information and allows more doubles of artificial bids; and you get your long suit in right away if there is competitive bidding from your left-hand opponent.) When you are 4-5 in the majors, partner will convert your 5-2 heart fit to a 4-3 spade fit. That presumably is okay.
When to Use?
So, there is a collection of techniques for using Stayman with weak hands -- Garbage Stayman, Nonforcing Stayman, and Crawling Stayman. For want of a name, and because I am going to to suggest using Stayman with worse than 5-4 in the majors, I will call this collection of techniques Junk Stayman.
When should you use Junk Stayman?
4-4 in the Majors
When you are 4-4 in the majors and your partner opens 1NT, you have (about) a 52% chance of finding your partner with a 4-card major.
How do I know this? I had the computer deal random hands given that you had a 4-4-3-2 distribution and 0 HCP. I found 20,000 hands where your partner had 15-17 HCP and a balanced (4-3-3-3, 4-4-3-2, 5m-3-3-2) distribution. Partner had a 4-card major 52% of the time. (That's enough hands to be accurate to about .7 of a percentage point.) The percentages change slightly depending on where your HCP are located -- if your high cards are AQ of hearts, you have a 50% chance of finding a 4-4 fit; if you have the AQ of clubs, there is a 54% chance of finding a 4-4 fit. So the probability of your partner having a 4-card major isn't exactly 52%, but it's around 52%.
What if your partner responds 2D? I am assuming now that you are 3-2 in the minors. If you are playing Nonforcing Stayman with your partner, you can bid 2H. If you are playing Crawling Stayman, partner will take you to 2S with only a two-card heart suit. So you always end up in at least a 4-3 fit.
If the 4-4 fit is always better than no trump, and if the 4-3 fit is always worse, Junk Stayman is essentially an even gamble when you are 4-4 in the majors. You are shooting (going against the field) with a very slightly higher chance of succeeding than failing.
The 4-4 fit is not always better, but it usually is. (In his book Matchpoints, Kit Woolsey writes "A four-four major suit fit is virtually always superior to notrump at the part-score level.") But I think there is a reasonable chance of the 4-3 fit being as good or maybe even better. If your 4-3 fit does not produce an extra trick, it is a worse contract. If 1NT was going down, 2 of a major has to produce 1 extra trick to break even. If 1NT was going to make, an the extra trick improves your score.
It is very difficult to analyze whether the 4-3 fit will produce an extra trick. You have seven trumps and the opponent's only have six. That's a slim advantage, compared to your eight to five advantage in a 4-4 or 5-3 fit, but it's still an advantage. At the game level, a 4-3 fit usually does not produce an extra trick, which is why bridge players usually do not look for a 4-3 fit. But apparently a trump fit is more valuable the weaker you and your partner are -- you have less high cards to control the hand, so you need trumps to control the hand.
The most important factor is probably your communication problems. If your partner is strong and you are weak, partner will have trouble getting to your hand, to take finesses or to cash winners in a long suit. One way or another, your fourth trump is probably going to be a trick. Maybe the suit breaks 3-3; maybe the opponent with 4 trumps ruff; maybe a jack or queen just finally is good; or maybe you will get a ruff in your short suit. This trick is an entry, so it is probably worth at least a trick and a half (taking a trick and letting partner take a finesse). If the opponents try to draw trump so you can't ruff, then they are systematically leading your suit, a courtesy you were probably not going to get in no trump.
Another key factor in getting an extra trick in a 4-3 fit is if the short hand (the hand holding only three trumps) has ruffing value. I will assume that if the 1NT opener with 3 trumps also has a flat hand with no doubleton, the 4-3 fit won't work. But when you are 4-4 in the majors, there is only a 14% chance that you end up in a 4-3 fit and his hand is flat. The remaining 34% of the time, partner has a doubleton. Of course, a doubleton is not necessarily a ruffing value, but it is probably a ruffing value.
Kit Woolsey again: "The requirements for a four-three major suit fit to be superior to notrump at the part-score level are not nearly as strict as at the game level. All that is usually neeeded is a reasonable trump suit and any kind of potential ruffing value in the short hand. The reason is that it is not necessary to keep control of the hand at the part-score level. Declarer can often scramble home on a semi-crossruff for an extra trick." He suggests using Stayman with
That's the basic idea of Junk Stayman. The mechanisms are in place for the safe hands, but they work even for hands that aren't quite as safe. You take a gamble, maybe find a 4-4 fit, but also maybe find a good 4-3 fit.
The 4-4-4-1 distribution with a singleton minor is ideal for Junk Stayman, because a singleton is more valuable for any trump fit. When you are 4-4-4-1 with 4 diamonds, you have the added option of just passing 2D if partner does not have a 4 card major. Should you pass 2D? The computer can tell us many diamonds partner is likely to have. The percentages, once partner bids 2D, are:
Passing when partner has 2 diamonds is not good, but that has only a 11% probability. When partner has 4 or 5 diamonds, you would rather be in the diamond fit, and this is a 48% probability. A 4-3 diamond fit is inferior to a 4-3 major fit if you are going make your contract. But if you are going down, it doesn't matter whether you are playing a major or a minor. So a pass is clearly indicated when you have a weak hand, and borderline when you are strong. (But if a 4-3 major fit has a very high probability of beating the field at matchpoints, then that is your safe route.)
4-3 in the Majors with 5-1 in the Minors
Do want to use Junk Stayman to deliberately search for a 4-3 major fit? Now you have, roughly, only half the chance of finding a 4-4 major fit. But finding a 4-3 fit in your 3-card major is probably good, because you have a strong ruffing value in your singleton. You will be the short hand, so that singleton is very valuable. Because you now have only 7 cards in the majors, the probability that partner has a four-card major is now about 56%.
It's better if your 4-card major is hearts, because partner will bid hearts with 4 cards in both majors. Put another way, if you have 4 spades and partner has both majors, partner will bid 2H and you will play there. The probabilities when you have 4 hearts and 3 spades:
With 3 hearts and 4 spades:
When partner answers 2D and you have 5 diamonds, pass. Diamonds is your better trump suit, except when partner is exactly 3-3-2-5, and even then you are just playing a 5-2 fit instead of a 4-3 fit. And you are not guaranteed a 4-3 major fit if you press on, because partner might have a 2-card heart suit and bid 2S with just 3. Your percentages (for when you have 4 hearts):
There is one more wrinkle in Crawling Stayman. Suppose your 5-card minor is clubs and your 4 card major is hearts. After the unwanted 2D response, you bid 2H. If your partner crawls to 2S, you should bid 3C. 3C is still weak. You have at least an 8-card club fit, which has to be better than your 3-3 spade fit. Your percentages:
You cannot protect yourself with clubs if your 4-card major is spades, because your partner always passes 2S. Your percentages:
So, being long in spades and clubs is the worst 5-4-3-1 distribution for using Junk Stayman. But it is still good probabilities on your side. On the bad side is an 25% chance of playing the 4-2 spade fit or a 4-3 fit when partner is flat, compared to a 57% chance of a 4-4 fit or a good 4-3 fit and an 18% chance of an okay 4-3 fit.
4-3 in the Majors, 4-2 in the Minors
Being 4-2 in the minors is not as good as 5-1. Now you don't have a singleton, and your 4-card minor is not as good of protection. The worst case (again) is being long in spades and clubs, because you have to bid 2S over 2D and you will play there even with a 4-2 fit. The percentages are almost exactly the same as for the 4-3-1-5 distribution, it's just that the outcomes aren't as good:
Now the obviously positive result, the 4-4 fit, does not quite balance the negative results of the 4-2 fit and the 4-3 fit with the balanced hand not having any doubletons. But usually, 51% of the time, there is a 4-3 fit with a doubleton in the short hand. If that is neutral, you can do what you want with the 4-3-2-4 distribution.
If you have 4 hearts and 3 spades, you get the increased chance of being in your 4-card fit, plus you can run to 3 clubs in partner converts to 2S. 3C cannot be worse than 2S. Your percentages:
Now the obviously good 4-4 heart fit comes in at 30%, and the bad outcomes of a 4-3 club fit or 4-3 heart fit and partner is flat have a combined percentage of only 19%. So even if the 4-3 fit is neutral, Junk Stayman is probably marginally better.
If you have 4 diamonds, should you pass 2D? As noted above for the 4-4-4-1 disribution, when you were guaranteed a 4-3 major fit, passing 2D with a 4-card diamond suit was marginal or good. Now your 4-3 fit isn't guaranteed, so you should pass 2D.
If you are 4-3 in the majors with a flat hand (3-3 in the minors), don't use Junk Stayman. You have a small chance of finding a 4-4 fit, but when partner bids your 3-card major, you have no ruffing value. You also have no minor for protection.
3-3 in the majors, long in diamonds
Finally, consider the hands where you are only 3-3 in the majors, but you are long in diamonds. Suppose first you have 6 diamonds and a singleton club. Your 4-3 fit is very good. On the other hand, you have at least a 6-2 diamond fit, and a 69% chance of a 6-3 fit or better. When you are strong, the ideal play of a 4-3 fit is to use the short hand for control, draw trumps, then run a long minor. But that isn't going to happen when you and your partner do not have a good majority of the HCP. So when you play your 4-3 fit, you are probably giving up on your diamond fit.
Of course, compared to leaving partner in 1NT, all of these choices are better. With a 6-card diamond suit, you hopefully would take partner to 3D. However, you now have a 39% chance of being in 2D. If 3D makes, it doesn't matter if you are in 2D or 3D, but if 3D is not going to make, 2D is better. And now the balance of power falls to playing a 4-3 fit on the two-level versus a 6-2 fit on the 3 level. If the 6-2 fit doesn't produce an extra trick, it is worse. If it produces an extra trick, that is only neutral.
I think the balance here is to bidding 3D and probably (69%) playing a 6-3 fit or better.
When you have only 5 diamonds (and hence a 3-3-5-2 distribution), your 4-3 fit is not as attractive. But your diamond fit isn't as attractive either. You are not going to 3D, so the comparison is to 1NT. Your five diamonds will probably be more useful in no trump than a 4-3 fit. But it will not be useful if partner has two or you are so weak you don't have an entry. So it is reasonable to think about Junk Stayman. The percentages:
Finding a 5-4 or 5-5 diamond fit is probably good. Finding a 5-2 diamond fit (5%) is probably not good, because producing an extra trick is just neutral. I would guess that your 5-3 diamond fit is better if you don't have the strength to make 1NT, or neutral otherwise. Playing a 4-3 major fit might be good if diamonds are 5-2, and not good when diamonds are 5-3 or 5-4. So if you have a very weak hand, Junk Stayman might be good
If you pass 1NT, the strong hand is always declarer. With Junk Stayman, the strong hand is the declarer more often than not, but a fair number of times the weak hand is the declarer
Another factor is your skill in playing 4-3 fits, and the opponents' skill in defending.
These probabilities are not correct if partner deviates from my assumptions in opening 1NT. But the two most obvious deviations favor the majors. One common deviation is opening 1NT with a 5-card major. This increases all of the probabilities of finding a major fit and means sometimes you will be finding a 5-4 major fit or a 5-3 fit that you thought was going to be 4-4 or 4-3. Another possibility is that your partner does not open 1NT with a 5 card minor and a distributional arrangement of HCP. This too increases your chance of finding a major suit fit.
I have not considered the possibility that opponents will compete, or whether that competition is good or bad.
Several factors influence whether you should play a 4-3 fit. Unfortunately, most of them are your partner's decision. I suspect that also moreso to making game. For example, when playing a 4-3 fit in game, ruffing value in the long hand isn't very valuable, because it is not an extra trick and you lose control of the hand whenever trump are breaking 4-2. If you are in 2S and trying to go down 1, two ruffs out of a weak hand probably is great, even if these are two ruffs in the long hand. Another factor is that queens are jacks in a suit usually decrease the chance of ruffing value.
I have analyzed this from the perspective of matchpoints. At IMPs, if you have enough points that 1NT will probably make, then you do not want to take a gamble that might end up in a 6-card trump fit. If 1NT is not going to make, then maybe you do want to gamble on finding a fit. And if you are so weak that nothing will make, then maybe your goal is to play any contract undoubled.
There are a number of weak hands where you can profitably use nonforcing Stayman. I think Stayman is a good gamble when you are 4-4 in the majors or 4-3 in the majors and 5-1 in the minors. Stayman might also be useful when you ar 4-3 in the majors and 4-2 in the minors, or when your distribution is 3-3-5-2, but it is not obviously better. The value of Stayman on any of these hand depends on the value of playing a 4-3 fit rather than 1NT.
I have so far collected two examples. Here's a great success for Junk Stayman. Only 7 pairs of 63 used nonforcing Stayman to find their 4-4 Spade fit. (Three other pairs found their fit when the opponents competed in diamonds.) Because of the singleton diamond opposite the ace, the fit played very well. And, it was very helpful to be in dummy to try all the finesses. Reasonable declarer play scored 90-98%, and the pairs only making two got 85%. 1NT had only about a 27% chance of making, and if the opponent's bought the contract in diamonds you also receive a minus score.
Here is another hand for Junk Stayman. Down 1 is a likely result in 1NT (if hearts break 3-2). The club doubleton in dummy is worthless for ruffing clubs. However, if the opponents do not lead spades at trick 1, the ruff can be shifted to spades and you will probably make 2H. The doubleton diamond in declarer's hand is also of no value for ruffing (except if both the K and the J of diamonds are off-side. But an opening diamond lead might erase your diamond loser, and now the doubleton is valuable and 2H is very likely.