[Cyberyeti]

You reach a slam, you have no side suit loser, this is the trump suit:

Dummy: KQ109

Hand: xxxx

entries are not an issue, you play small to the king and it holds

you come back to hand and ?

a) your RHO is an expert
b) your RHO is not very good

[shyams]

The only combinations that matter are:

1. AJxx vs. x
2. Axx vs. Jx
3. Jxx vs. Ax

*** A finesse in round 2 is about 1.8x more profitable.

*** Even for a non-expert RHO, it is not improbable to duck holding Ax (for random reason or no reason at all). If you assume that a non-expert RHO will withhold the Ace only half as often as an expert, the second round finesse is still 1.35x more profitable.

[DavidKok]

Spoiler

If RHO is not very good, play small to the queen. This loses to Ax offside or x offside (so AJxx onside), but the former case is unlikely as weak defenders have a habit of covering the king here. And AJxx opposite x is slightly less likely than Axx opposite Jx.
Against an expert play small to the ten (or nine). Now you have a pure guess between Ax offside or Jx offside (if AJx(x) is offside you can never win), but small to the ten also picks up AJxx onside.

[steve2005]

 shyams, on 2023-December-04, 04:12, said:

The only combinations that matter are:

1. AJxx vs. x
2. Axx vs. Jx
3. Jxx vs. Ax

*** A finesse in round 2 is about 1.8x more profitable.

*** Even for a non-expert RHO, it is not improbable to duck holding Ax (for random reason or no reason at all). If you assume that a non-expert RHO will withhold the Ace only half as often as an expert, the second round finesse is still 1.35x more profitable.

4) xxx vs AJ

[Cyberyeti]

 steve2005, on 2023-December-04, 07:39, said:

4) xxx vs AJ

Impossible when the K fetches a small one from both hands

[Cyberyeti]

I wonder if there's a corollary to this.

4 experts at the table, and it goes x-x-K-A.

If you assume the expert would duck Ax, the key holdings are A and AJ and AJ is slightly more likely so you should play the Q next.

Therefore should you win the A from Ax occasionally to induce the play of the Q ?

[mikeh]

 Cyberyeti, on 2023-December-05, 04:23, said:

I wonder if there's a corollary to this.

4 experts at the table, and it goes x-x-K-A.

If you assume the expert would duck Ax, the key holdings are A and AJ and AJ is slightly more likely so you should play the Q next.

Therefore should you win the A from Ax occasionally to induce the play of the Q ?

It’s just another variation on a theme, arising (so I’ve read) from game theory. If one always plays the same card from certain combinations, in specific situations, then declarer can rely on simple probabilities. By varying one’s play, one adds an element of uncertainty into declarer’s calculations. While this is valid in theory, in real life one rarely encounters these situations more than once or twice against any one declarer (this may vary according to where you play) such that declarer may not expect you to vary your play, especially if neither declarer nor defender are expert.