Most players overcalled 1NT with this hand.
You have 16 HCP and a balanced hand. This is a perfect 1NT opening bid.
BUT you did not get to open the bidding. Your RHO opened the bidding and they opened the bidding 1♦. You are now OVERCALLING 1NT rather than OPENING 1NT.
What's the difference?
Not much. You need the balanced hand. You also need the 15-17 HCP (though most players play you could also have 18 HCP to overcall 1NT). However to OPEN the bidding 1NT you do not need a stopper in the Opponent's suit. (Mostly because the Opponents haven't bid yet so they have no suit!)
To OVERCALL 1NT you are supposed to have a STOPPER in the suit the Opponent opened.
What is a stopper?
Basically a card that will STOP the Opponents from taking the first five or six tricks. In other words, a GUARANTEED winner in the suit the Opponents opened.
Holding in the ♦ suit that would guarantee a trick:
♦A83
♦KJ64
♦QJT6
♦AJ65
♦KQ4
Heck, even:
♦JT98
if we are desperate.
On ALL the above holdings, if the Opponents lead a ♦ we are sure to take a trick.
Why? Why do we need a stopper?
Mostly because it is assumed that the Opponents will lead their suit. You need to make sure that they won't take the first six or seven tricks with that suit! Extreme example, but I did have a six card suit to the AKQJ one time when the Opponents bid up to 3NT. Needless to say they did NOT make that contract!
So that means that this hand probably should not overcall 1NT.
Is there a better bid?
How about a Take-Out Double?
That would be my choice.
Don't play Take-Out Doubles?
Sure, Overcall 1NT and hope that Partner doesn't leap to 3NT. Or if they do, hope the Opponents don't lead a ♦. Or if they lead a ♦ hope Partner can win a trick. Or maybe the Opponents only have a four card suit....You might get away with it and then you can resolve to learn Take Out Doubles!
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