From                  3rd May, 2006, Board 11

                                          Theme               Combining Chances

                                          Difficulty           * * * *

                                          Dlr West           None Vul

After the opening Heart lead, you are up to ten top tricks, with chances for more in each of the other three suits.  In what sequence do you go after those extra tricks?

SOLUTION

Line A

If you play AK♦, and out a Diamond, you have excellent chances of scoring 3 Diamond tricks, but also the possibility of immediate defeat if North has Q9xx or QTxx of the suit.  If the Diamond play works, then you can try for 3-3 Clubs (or the Jack coming down), and if that fails there is always the Spade finesse to fall back on.

Line B

Can you do better by playing Diamonds differently?  You might cash just one top Diamond, and then lead towards the Jack.  This reduces your chances of 3 Diamond tricks, but also avoids the ignominy of instant defeat when North has Q9xx or QTxx.  So, the line of play would be:

- Win the Heart

- A♦ and a Diamond towards the Jack, let’s say it loses to North’s Queen (if the Diamond play isuccessful,

  we’ll revert to Line A)

- The return is immaterial, now test Clubs and Diamonds, if both suits work, we are home

- If one of the minor suits does not work, you can try the Spade finesse.

Both lines look pretty reasonable to us, we wouldn’t fault either line of play.  But just for the heck of it, we calculated the odds … Line B turns out to be the winner by a narrow margin, 67% to 65%.

We don't suppose that many players are able to calculate these odds at the table (no, neither can we), so instincts come into play.  One good instinct is to keep as many irons in the fire as possible, something which Line A does not do, it risks everything on the Diamonds.  On the other hand, Line B keeps things alive longer, giving the opponents more opportunities to mess up (yes, it has been known!).  Also, there are squeeze possibilities for Line B, which we won't enjoy if we go down early by putting all of our eggs in the Diamond basket.

	♠ Q953 ♥ Q4 ♦ QT95 ♣ 876
♠ A4 ♥ J62 ♦ J876 ♣ KQ93	North    West           East            South	♠ KJ76 ♥ AKT ♦ AK2 ♣ AT2
	♠ T82 ♥ 98753 ♦ 43 ♣ J54

Keys to Success

   - Taking the non-committal line, all the better to combine your chances in more than one suit

   - Taking the non-committal line, if only to give the opponents a chance to mess up

   - Taking the non-committal line, sometimes if you don't go down early, a squeeze materializes.