Board 5

Our side vulnerable

Our side vulnerable

♠ A K 8 5 2 ♥ 8 ♦ A J ♣ K 9 8 7 5 |

Two passes to me. I know some people open one club with this pattern, and I used to be one of them. But I never had much success with that approach. (I can recall one deal where it did work spectacularly well. At rubber bridge, I opened one club with six-six in the black suits, LHO overcalled one spade, and partner made a negative double. Even with that result, however, I still think I've been a net loser opening one club.)

I open one spade, partner responds one trump, I bid two clubs, and partner corrects to two spades. I'm glad I'm not playing forcing notrumps, since I have only

*one*more club than I've promised rather than two more. If partner weren't a passed hand, my advantage over the Eastern Science Fiction players would be even more pronounced, since my partner's upper limit in high cards would be lower. I would probably pass anyway, but I pass a bit more comfortably in my style.

LHO passes as well and leads the three of diamonds:

NORTH
♠ 7 3 ♥ Q 9 7 5 3 ♦ K 7 2 ♣ A 10 3 |
||

SOUTH
♠ A K 8 5 2 ♥ 8 ♦ A J ♣ K 9 8 7 5 |

West |
North |
East |
South |

Pass | Pass | 1 ♠ | |

Pass | 1 NT | Pass | 2 ♣ |

Pass | 2 ♠ | (All pass) |

East plays the queen, and I take the ace. Frequently, when one is concerned about a bad break in a side suit, it is right to start the side suit before touching trumps. If the side suit splits badly, you may be able to compress your trump losers and your side suit losers. With only two trumps in dummy, however, this doesn't look like the right approach. If someone ruffs the second club and plays a trump, I may be sorry I started clubs early. I cash the ace and king of spades. West plays ten-jack; East plays four-six.

*A priori*, the odds are about four to three that trumps are four-two rather than three-three. Has West's carding changed that? West could have begun with (A) jack-ten doubleton, (B) queen-jack-ten, (C) jack-ten-nine, or (D) queen-jack-ten-nine. Let's assume that, initially, each of these four cases is equally likely. (Yes, (B) and (C) are

*slightly*more likely, but not by enough to make much of a difference in our analysis.) The principle of restricted choice dictates that the true relative frequency of each case is the

*a priori*frequency divided by the number of ways West might play his cards. In theory, West could play his cards in any order with any of these holdings. Certain orders, however, wouldn't make sense. For example, queen-ten, queen-nine or, to a lesser extent, jack-nine would be a poor choice, since declarer would be disinclined to play West for a doubleton after such a sequence. So let's assume that West would always choose touching cards if he played his cards in descending order. That means he has two ways to card from (A), five ways from (B) or (C), and nine ways from (D).

The number of cases where the suit can split three-three, then, is one fifth (for B) plus one fifth (for C): a total of .40. The number of cases where the suit can split four-two is one half (for A) plus one ninth (for D): a total of .61. Thus the odds of a four-two versus a three-three break are roughly three to two. Of course, I didn't go through this calculation at the table. I already know that the odds of a four-two break go up when restricted choice comes into play. And on this particular deal, I don't care by how much. I included this calculation in the post only because I've never seen anyone discuss the touching-card assumption before or how it affects the calculation.

I cash the diamond jack--four--seven--eight, and play a club to dummy's ace. West plays the deuce; East, the four. I play the king of diamonds--ten--heart eight--five, then lead the ten of clubs. East plays the six. I doubt West has a stiff club, but it probably won't hurt to let this ride. Even if West wins and gives his partner a club ruff, it will probably be with a natural trump trick. I play low. West wins with the jack and plays the nine of diamonds, on which East pitches the queen of clubs.

I ruff, and I'm down to:

NORTH
♠ -- ♥ Q 9 7 5 ♦ -- ♣ 3 |
||

SOUTH
♠ 8 5 ♥ -- ♦ -- ♣ K 9 8 |

West was either 3-3-5-2 or 2-4-5-2. If I play a trump now, I'll make five in the former case or go down one in the latter. If I play clubs, I guarantee making four. Since this looks like a normal contract and since declarer can be held to three on a heart lead however trumps split, I suspect making four is above average. So I see no reason not to settle for that result. I play the king of clubs. Making four:

NORTH
♠ 7 3 ♥ Q 9 7 5 3 ♦ K 7 2 ♣ A 10 3 |
||

WEST
♠ J 10 ♥ K 6 4 2 ♦ 9 6 5 4 3 ♣ J 2 |
EAST
♠ Q 9 6 4 ♥ A J 10 ♦ Q 10 8 ♣ Q 6 4 | |

SOUTH
♠ A K 8 5 2 ♥ 8 ♦ A J ♣ K 9 8 7 5 |

Because of the favorable position in the black suits, we can make five clubs. But I can't see getting there even if I bid three clubs over two spades. Plus 170 turns out to be worth nine out of twelve matchpoints. Three other pairs were plus 170, two were plus 140, and one reached four spades and went down.

Me: +170 (9 MP)

Total: 39 MP (65%)

Current rank: 1st