[Knurdler]

My first post here. If it is in the wrong place, someone please tell me.
I did search for this topic but found nothing.

My question is on the solution to Bridge Master Level 2, Deal B19.

The solution says the only play is to drop Q&J of trump. That is true for the given distribution.
However, if the cards out were to lie 4/1 with a singleton honor, then the standard play for this combination (K, then low to 10) would succeed and playing K,A would fail. I estimate (not proper math) the probability of the given distribution is about 6.8% and the probability of 4/1 with singleton honor is about 11%. I would love a second opinion on this. Question 2: after leading the K and dropping the J, should one apply the principle of restricted choice and assume a 4/1 split?

[smerriman]

The solution outlines why playing for a 4-1 trump split with a singleton honor does not succeed. You will lose the 4th round of trumps even after you take a successful finesse on the second round.

The only way you can ever take four trump tricks is when QJ is doubleton.

[shyams]

If you notice the small cards held by opponents in, if they split 4-1 you will definitely lose one more heart trick. Having already lost a diamond trick with the opening lead, you cannot afford to play any layout where you are saving yourself an extra one undertrick.

You are correct that the odds favour a finesse as per restricted choice. However, after your restricted choice finesse has won, you will still have the following card layout in trumps,

..Dummy
♥94

.........East
........♥Q8

Declarer
♥A3

... and you will find you cannot repeat a finesse to avoid a loser.

[LBengtsson]

smerriman, on 2021-February-14, 13:09, said:

The solution outlines why playing for a 4-1 trump split with a singleton honor does not succeed. You will lose the 4th round of trumps even after you take a successful finesse on the second round.

The only way you can ever take four trump tricks is when QJ is doubleton.

Yes. The small cards ♥876 emphasize how important they are. If either East/West have ♥Q876 or ♥J876 then contract can not be made. Change the opps ♥ to QJ875 then you can might make the contract if ♥ 4-1 and ♥Q or J drop singleton on first round of trump with good guess and ♥6 in right hand. Probability less than dropping ♥QJ as doubleton, so solution of problem on Bridge Master is right.