My long-standing and long-suffering partner sent me an email the other day to say that Andy Robson, writing in the Times, had advised eschewing Stayman in response to 1NT with a 4333 shape.  My partner wrote that he didn't entirely agree with that, as the 1NT opener may have a weakness not covered by responder; he said on balance he preferred to be in the 4-4 major suit fit.
Amazingly, I am in agreement with partner.  Sorry, Mr Robson.  In fact, Justin Corfield & I wrote about this very issue in Why They Win, as follows:

Is it wrong to look for the major suit fit with a 4333 hand opposite a 1NT opening?  
Not at all.  Just because your hand is 4333, it doesn’t follow that notrumps will play just as well as the major.  Your hand may not gain a trick by ruffing something, but your partner’s might be able to.  If your 4333 is opposite something like 4234, then potentially there is a club ruff in your hand and a heart ruff in his, gaining two tricks against players in notrumps. And let’s not forget that partner might have opened 1NT on a 5332 hand with five spades. If that is the position, then a 4sx contract could easily roll home with overtricks while 3NT is hopeless.

Andy Robson apparently gave a hand where 4â™  would not make but 3NT had nine tricks on top. All well and good, but two can play at that game!



North
â™  K 9 7 4 
♥ A Q 6 
♦ 7 5 
♣ A 10 6 2 


South
â™  A 10 6 5 
♥ K J 7 
♦ 9 8 3  
♣ K Q 4 



North opens 1NT (12-14) and if South eschews Stayman to bid 3NT he risks going down as the diamonds are wide open. In 4â™ , on the other hand, you can afford to lose two diamonds and a trump. 
In general, therefore, I'd say it is sensible to look for the 4-4 fit, even if you have a 4333 shape.  With one caveat: if your 4333 hand is so stuffed with points that it is unlikely your combined hands have a weakness, then by all means try 3NT as that will probably succeed on raw strength whereas 4M might come unstuck on an unlucky distribution. Add ♦Q to South's hand above, for example, and 3NT is a good shot because you know you have at least 28 points between the two hands.

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