[Antrax]

(W) xxx opposite (E) KQT9x in isolation, no entry problems, need to play for four tricks.
(I'm asking because in another thread, it was mentioned S with Ax should duck the first round and I can't figure out why)

[GreenMan]

Start by playing low to the King. It wins. Come back to your hand, lead another small one, LHO plays small, and ... you have to guess whether to play the Q or the 10.

That's why South should duck with Ax; if he wins the A right away then you'll finesse the 10 on the second round and run the suit. If he gives you a guess, then half the time you'll get it wrong by random chance.

Alan Truscott wrote once that when you're facing this guess, assess the relative strength of your opponents. If one of them is a stronger player than the other, assume that one has the Ace; a less skilled player will have probably played it by now.

(By now you've figured out that if you're the defender you want to duck your Ace the first time because it's almost always the right play. Courage.)

[Antrax]

Makes sense - I was stuck because I thought "well, this loses to AJ". But there is only one AJ and three Ax combinations, so probably this is better.
What about Jx though? Don't those offset the Ax combinations?

[MickyB]

In isolation, you'd play to the ten on the second round in that suit, because that picks up AJxx onside as well as Jxx onside, but sometimes you know RHO doesn't have a singleton so that layout isn't relevant. I've not seen the original thread to comment on the assertion made there, but it is generally good technique for RHO to duck.

Let us instead assume that you need to take only two tricks in the suit, but that you need to do so without losing two tricks. Perhaps you are in a suit contract with no shortage of trumps and no need for the pitches.

If the defence follow low in tempo, you have a straight choice between Axx/Jx and Jxx/Ax.

If the defender takes the ace on the first round, there are four possibilities -

He has AJx or longer - what you do now is irrelevant
He has stiff ace
He has AJ tight
He has Ax or longer

If we knew that RHO would always duck with the last of these, we would play for the drop on the next round, because AJ tight is more likely than stiff ace. [Say we have 8 cards in the suit - we assume LHO has the three small ones and RHO has the ace - there are now 12 unknown cards in RHO's hand and 10 unknown cards in LHO's hand, so it is 12:10 that RHO has the jack. This logic is known as "vacant spaces"].

However, in practice you will usually finesse on the next round, because it only needs RHO to play to play the ace from Ax a very small proportion of the time in order to swing the odds.