[MrAce]

Antrax, on 2011-September-14, 23:27, said:

I'm not sure I understood the solution. Could you explain how you play when hearts are 4-1 with a Q singleton?

He takes Q with A in hand, plays ♣, he is hoping for 2-2 ♣ or 3-1 A stiff or 3-1 they can not find ruff. Assume they took ♣ A and

1- They played another ♥, he wins with J, ♠ A and ruff, ♦ ruff to hand clear trumps and claim

2- They played ♣ back, then it must be 2-2 , he takes and plays as above

3-They played ♦, wins A, cashes ♥J, ♠A and ruff, ♦ ruff again, basically same line

[kgr]

Note: I don't want to criticize your problem or solution. I find this defense and play problems interesting.

mck4711, on 2011-September-14, 14:17, said:

OK, this is my first problem, it might be that I took some shortcuts and that there is some space for improvement...

From the very start we have two ways of playing for the 12th trick, the finesse or ruffing.

IMO the finesse has a simple 50% chance. Yes, it might be that E does X only with KJxx in ♠, we dont know. But in case we want to finesse we come to a PRACTICAL problem. We need to enter the dummy, either via ♥J or ♣K. Playing ♥J is IMO dangerous because playing low protects us against ♥Q singleton with E (mentioned earlier). Meaning we play from dummy at trick 1. 2nd option is then ♣K. But as already explained earlier playing ♣ before ♥ requires that ♣ either split 2-2 or ♣A is singleton.

But in this case then we DO NOT NEED anymore the finesse. So, why to take an - now unnecessary - risk? Therefore the line of play is clearly via ruffing ♠.

Even from a mathematical point of view this line of play is supported:
Finesse: 50%, you may argue that the probability is higher, that E needs to have ♠K, and we can for sure finesse (in this case look at the practical problem)
Ruffing: around 58%: 40% (2-2) + 12.5% (♣A singleton) + 5.6% (4-1 ♥distribution with Q singleton, 28% 4-1).

I still don't understand why the ♠-finesse needs ♣2-2:
You play 3 rounds of ♥ followed by 3 rounds of ♣. If ♣ are 3-1 then ♣A will be out now.
You can then overtake ♣9 with ♣K and discard a ♠ on the 5th ♣ and a ♠ on ♦A. And end with ♠-finesse.

[mck4711]

Here it is trick by trick:

Trick 1: ♥7, low, low, T
Trick 2: ♣Q, low from dummy, one opp wins
Now a:
Trick 3: ♣return, winning in hand (♣2-2)
Trick 4: ♠A
Trick 5: ♠ ruff
Trick 6: ♦ ruff
Trick 7/8: drawing ♥ and claim
Now b:
Trick 3: ♦return (♣A singleton), winning with A, pitching ♠
Trick 4: see above
Now c:
Trick 3: ♠return (♣A singleton), winning with A
Trick 4: ♠ ruff
Trick 5: ♦ ruff
Trick 6/7: drawing ♥ and claim
Now d:
Trick 3: ♥ return, winning in hand with A
Trick 4: see above

If ♥Q singleton:
Trick 1: ♥7, low, ♥Q, ♥A
Trick 2: ♣
Trick 3: ♣ return
Trick 4: ♠A
Trick 5: ♠ ruff
Trick 6: ♥J
Trick 7: ♦ ruff
Trick 8/9: drawing ♥ and claim

If W should win ♣ and return ♥
Trick 3: ♥, J, doesnt matter, low
Trick 4: ♠ to the A
Trick 5: ♠ ruff
Trick 6: ♦ ruff
Trick 7/8: drawing ♥ and claim

Important: Only small ♥ from dummy at trick1 protects against 4-1 with Q singleton. If you play the J then W has 98x behing ATxx is making one trick.