[Hanoi5]

Imp pairs:

♠8xxxx
♥AQx
♦xx
♣xxx

♠AQJT
♥xxx
♦AK
♣AKxx

♦Q led.

Say you win. Play the heart finesse, which loses and get the ♥J return. You win on the table and finesse spades, which wins, no 9 in sight. What's the best way to continue?

[Fluffy]

Endplay is better, lets explain the line:

Cash ♦AK ♣AK and play a heart.

-If the defence plays a ruff and discard without cashing third club you are home (discard club from dummy, losing at most 1 trump and 2 hearts)
-Given that 3-1 and 2-2 are almost equal, there is no big gain or lose if RHO ends up playing a 4th club, this means you win if spades 3-1 (ruff in dummy and finese) and lose if 2-2.
-There is also no gain or lose if RHO cashes third club, they are 3-3 and he plays a triple heart ruff, you are back to a 3-1/2-2 guess.
-if clubs are 3-3 defence is suposedly able to unblock and give entry to RHO who has hearts left to avoid endplay, but this might not be possible or they might fail.
-LHO has a killing defence if clubs 4-2 and hearts 2-5 and spades 2-2 ruffing third heart and promoting partners spade


So after a cash otu and a heart play we are in this position:

RHO wins ♥, and has no clubs to play -> win
RHO wins ♥, gives partner a third club -> win
RHO wins ♥, plays 2 clubs -> tie
RHO wins ♥, wins a club, plays a heart -> tie
RHO wins ♥, wins a club, but has no heart left -> win
LHO wins ♥, plays 2 clubs -> lose
LHO wins ♥, wins a club -> win
LHO wins ♥, gives partner a club who plays a heart -> tie
LHO wins ♥, has no clubs to play -> missdefence (impossible)<br class="Apple-interchange-newline">



The math is complex and the lines are complex as well.Also heart 9 is very important and the pips played so far also, because it will change liekllyhood of LHO being able to win third round.

I will assume some things for simplicity:

- spades 2-2 or 1-3 are right now equal in %.
-If after the cash out RHO plays a heart for triple ruff we are on a 50% guess so we didn't win nor lose anything (Can try to win in dummy discarding or ruff in hand and try 2-2)
-They won't unblock clubs if they are 3-3 (this is probably assuming too much, but justto be able to start calculating)
- to compensate this LHO will always find the killing defence of ruffing third heart if he has 4 clubs
-RHO has ♥10 and the heart pips played so far are all low.
-Heart distributions aproximatelly then 3 way: stiff 9, stiff low and void with LHO. I will assume they are equal (33% each)
-club percentages are no longer the classic, singleton clubs are very likelly to have been played at tricks one or three, so the percentages are now 54%(4-2)/42%(3-3)/4%(5-1)
-diamonds aren't 8-1
the line of cash out and play hearts to end play fails misserably when:

LHO has 4 clubs and wins the third heart with ♥9 (LHO will play 4 clubs making his partner ruff) (24% clubs and 33% of being able to win third for a total 6%)

or when

LHO has 4 clubs and wins the third heart by ruffing (24% clubs, 50% spades, 33% hearts 2-5 for a total 3%)

or when

clubs are 5-1 (very rare given the defence so far) for a total 4% (note, they might end up in an endplay even after ruffing a top club so this might be lower)



The endplay doesn't matter when

RHO has 4 clubs (this is counterintuitive, but after cashing his tricks he will be forced to play 4th club, and now we make if spades 3-1 and go down if 2-2. Won the same than we lost except for some vacant spaces thing)

The endplay line works when

clubs 3-3 (42%) and the club is won by LHO or the club is won by RHO but has no hearts left to play (RHO will win third club and have a heart left 30% of the time) for a total 29.4%

or when

clubs are 4-2 (27%) and LHO is unable to win third heart (33% low pip + 33%*50% of the time he has void and no trump=50% total) for a total 13.5%


I am starting to have a headache, can't even think if this percetages are dependant, but with my assumptions endplay is far better unless the vacant spaces are more important than I think.


EDIT: I made a mistake, since I am giving RHO a % for having 3514, but in my assumptions diamonds are not 8-1, so there is a small % that is wrong, probaby I made worse mistakes anyway.


EDIT: made a mistake on last percentage, now corrected.

[nige1]

Hanoi5, on 2012-April-11, 06:07, said:

Imp pairs: Contract 4♠ ♦Q led.
♠ 8xxxx ♥ AQx ♦ xx ♣ xxx
♠ AQJT ♥ xxx ♦ AK ♣ AKxx

IMO ♦A, ♣AK, ♦K. Then exit in ♣

Hanoi5, on 2012-April-11, 06:07, said:

Say you win. Play the heart finesse, which loses and get the ♥J return. You win on the table and finesse spades, which wins, no 9 in sight. What's the best way to continue?

From here, I guess to cash ♠A immediately, Then.the minor tops. Finally exit in ♥