[Dinarius]

♥

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West leads J♦ against 3NT. No opposition bidding.

East wins K♦, cashes A♦, and plays a third diamond to your queen.

You now have 8 tricks.

Which offers the best chance of a ninth trick?

1. Play a spade and hope that east has the ace and, if he has a fourth diamond, they're breaking. And if he doesn't have a fourth diamond, you have nine tricks at least. Or, that west has A♠ and diamonds are 4/4.

2. Run Q♥ and hope that it wins.

Basically, if the lead was from five diamonds and west has A♠, he must also have K♥ and you must run the queen to make the contract.

While if diamonds are 4/4, it doesn't matter what you do.

So, I guess we have to assume that diamonds are 5/3 and decide what's the best line to deal with it?

D.

[apollo1201]

Sometimes diamonds are 35…

[pescetom]

Neat problem.
Probably in the wrong forum, although we are now so few that it matters little

But at the table against decent opps I would play on the spades, it has to be better than hearts even if diamonds are not JTxx AKxx.
If the opps are weak then play out the clubs and watch discards carefully.

[Dinarius]

I should correct what I said about the diamonds being 4/4.

If they are, you can lose three diamonds, KH and AS.

Not sure if that affects the choice of line.

The opposition were expert.

D.

[P_Marlowe]

Hi,

I am not good at those things, but it is simple math.
I am using
https://www.bridgewe...it%20breaks.pdf

Going after the hearts is 50%, i.e. a 50% shot.

Going after spades is

32.8% 44 diamond break, Ace of spade does not matter

47% / 2 = 23.5% 53 diamond break, Ace of spade is on the right side

This would make it a 56% shot.

So going after spades seems to be better, but not much.

Now the 23.5% is not correct, the Ace is more likely to be with the 3
cards, due to being more free spaces, i.e. the odds, that you survive a
53 break go up.

This gets being countered by the fact, that they did lead diamonds.
To lead a Diamond holding JTxxx with a side entry is fairly standard,
... I am not 100% sure, that it would be standard to lead JTx with a
side entry.
Depending on the auction you may also rule out AKxxx in diamonds and A of
spades in the same hand.
How you weight those factors is hard to say.
You can improve your chances of getting it right by playing 3 rounds of
clubs, so that you get to see a discard. Which may or may not be helpful.

It may also be helpful to take into account the card West played on the
Q of diamonds, if West does not play the 10, you can rule out the lead
being from JTx.
Leading from an empty suit, and I would rate JTxxx an empty suit is not very
attractive, at least without a side entry.

Going after a hearts is the simpler play.