[paulhar]

mpefritz, on Sep 19 2004, 12:45 PM, said:

Ben, if someone wins the ♥AK, then leds the J, won by EAST/WEST who then returns another heart, you MUST make up your mind too early on which minor suit to play for 4 tricks! (pitch a spade and club on the 2nd and 3rd heart). therefore MUST hook at trick 1. see below.

Yes, you make up your mind, but since the chances are about equal, it doesn't matter. You still have the chance for queen doubleton of diamonds.

Play AK of hearts (no doubleton queen), jack. Opponents take queen and play another heart. You pitch a diamond, a club, and a spade. Now, you can cash AK of diamonds and if the queen is doubleton or singleton, you pick up the suit. Otherwise you need four the club tricks. I think this is better because the lead makes Qx of hearts more likely than Qxx onside.

However, a problem comes if RHO has queen fifth of hearts and ducks a heart. Now you still have to set it up and have to pitch a second diamond from hand. Now you have to give up on the queen singleton of diamonds.

[twcho]

Why I said the hand is too complicated before is not because the hand is too difficult to play but there are so many logical lines to choose from and it is very difficult (if not impossible) for anyone to calculate the best line.

E.g. As Paul suggested above, East can strip the declarer's option when he wins the 3rd H and return a C. Now declarer can't test the D before resorting to finesse in C.

Alternatively, you can play the small H on the 1st trick and if it wins, you can continue with another small H. By doing this, since you discard a S on the 2nd H, your option in the minors will remain intact. If East return a C, you can just cash both minor Aces and then go to dummy with CK. But this line gives up the possibility of dropping singleton or doubleton HQ which the chance cannot be overlooked.

Another possible line is to try to finesse on 1st H trick and if it holds, you can try to cash the top H to pinch down the Q but this line suffers from the same drawback that your option in minors will be reduced.

Actually my gut feeling for the best line of play is not setting up dummy's H but rather take the 1st H with HA or K and play a small D to J. This line will win whenever east hold DQ or Qx or Qxx because you will have a second entry to dummy in D to establish your H (So 2S, 4H, 4D and 2C). This amounts up to 68%*0.5+28%*0.1=36.7%. If east doesn't hold the above D holdings, you still have chance to test the H with possibility of bringing down singleton or doubleton Q (I didn't include the HQ in my previous calculation for East D holdings) or with these fails but finding East with CQx or Qxx. All this will add up to (100%-36.7%)*(30.5%*2/7+0.5%+90.8%*34%)=25.3%. So the total chance of success for this line of play is 62%.