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Odds on Doubling
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In a round-robin match in the Open trials, you must decide upon the right competitive action opposite your partner's weak notrump.

None vul, South deals. As East, you hold:

East
K102
Q8
A87
K8752
W
N
E
S
P
1NT
X
?

1NT: 10-12

DBL: Penalties

Your runout structure is as follows:

Pass: Non-committal. Might be desire to play 1NT doubled, or might be least of evils. If fourth seat passes, opener is on his own. He is permitted to pass it out if he so judges. If he runs, redouble would show two places to play while a suit bid would be a single suit.

Redouble: Single-suiter in clubs, diamonds, or hearts.

2, 2, 2: That suit and a higher suit.

2 and higher: To play

Your call?

East
K102
Q8
A87
K8752
W
N
E
S
P
1NT
X
?

Your side has the balance of strength. You are content to play 1NT doubled or redoubled. There is no need to run.

You pass. The bidding continues:

W
N
E
S
P
1NT
X
P
2
P
P
?

Double would be penalties. 2NT would be takeout.

Your call?

East
K102
Q8
A87
K8752
W
N
E
S
P
1NT
X
P
2
P
P
?

You don't have enough strength to expect to make game opposite a 10-12 NT, you don't necessarily have a club fit, and your defensive prospects vs. 2 are pretty good. It is clear to defend. The question is whether or not to double.

On some auctions it might be wrong to double for fear the opponents will run to a better spot or partner will pull. That isn't likely here. The opponents bypassed all other strains at the 2-level, and they aren't now going to the 3-level just because you doubled. Partner has bid his hand, and he is out of the auction. If you double, you can be confident it will end the auction.

On other auctions, doubling might tell declarer how to play the hand. Not on this auction. Declarer knows that you are doubling largely on power. If anything, if the opponents are in a 5-2 fit, the double may cause declaer to think the trumps are 4-2.

What are the odds on doubling? We have all been taught that doubling the opponents into game is the greatest sin at IMPs, and you need a virtual lock to do it. However, if we put away our fears and look at the cold IMPs, another picture will appear.

Let's suppose we think the most likely result is down 1. That would mean a distribution something like:

2 makes 25% of the time

2 is down 1 50% of the time

2 is down 2 25% of the time

Suppose these are the frequencies. Then the IMP swing on doubling is:

2 makes. The double costs 8 IMPs (-470 instead of -110).

2 is down 1. The double gains 2 IMPs (+100 instead of +50).

2 is down 2. The double gains 5 IMPs (+300 instead of +100).

Putting this all together, if the hand is played 4 times the IMPs are -8, +2, +2, +5 for a net of +1 IMP. Thus, under these assumptions, doubling is just about a break-even proposition.

The conclusion is that if you believe down 2 is a more likely result than making, doubling is a winning proposition. If you believe making is a more likely result than down 2, doubling is a losing proposition.

What is the assessment on this hand? Your side has at least 22 HCP, maybe as much as 24. Your side has at least 5 trumps, maybe 6. Even if the opponents have an 8-card fit and 18 HCP, they probably aren't making. If they have a 7-card fit or less than 18 HCP, down 2 looks reasonably likely. All things considered down 2 appears more likely than making, so doubling is the percentage action.

You choose to pass, ending the auction.

W
N
E
S
P
1NT
X
P
2
P
P
P

Partner leads the queen of diamonds.

North
53
A9
KJ102
AQJ64
East
K102
Q8
A87
K8752
W
N
E
S
P
1NT
X
P
2
P
P
P

Dummy covers with the king. If you don't win the ace, your agreements are that your card is suit-preference. A high spot is suit-preference high. A low spot is suit-preference low. A middle spot is encouraging.

What do you play?

North
53
A9
KJ102
AQJ64
East
K102
Q8
A87
K8752
W
N
E
S
P
1NT
X
P
2
P
P
P

Partner's lead must be from a doubleton, as there is no way he would be leading the queen from Qxx on this auction. This allows you to get a complete count of the hand. Declarer is known to have 5 spades and 4 diamonds. He must have 4 hearts, since partner wouldn't be opening 1NT with a 6-card heart suit. Declarer's shape is 5-4-4-0, and partner's shape is 3-5-2-3. There are 13 HCP outstanding, and partner is marked with at least 10 of them.

There doesn't appear to be any rush to do anything. It looks right to duck and keep control of the hand, forcing declarer to commit himself.

You have the queen of hearts, and that may be the card partner needs to know about. Best is to play the 8, the best suit-preference signal for hearts available.

You play the 8, declarer playing the 3. At trick 2, declarer leads the ace of clubs from dummy, discarding a heart as partner follows with the 3. Declarer now leads the queen of clubs off dummy. Do you cover or not?

North
53
A9
J102
QJ64
East
K102
Q8
A7
K875
W
N
E
S
P
1NT
X
P
2
P
P
P

There is no doubt that if you duck, declarer will discard. You might as well cover and force declarer to spend dummy's ace of hearts in order to collect his jack of clubs. Also, by covering you prevent declarer from leading a spade from dummy, which might be to his advantage.

You cover with the king of clubs. Declarer ruffs with the 4, and leads a diamond to the 6, jack, and ace. How do you defend?

North
53
A9
102
J64
East
K102
Q8
7
875
W
N
E
S
P
1NT
X
P
2
P
P
P

You might as well give partner a diamond ruff. He should come back a heart, which will force declarer to cash the jack of clubs. This will put the defense in position for an overruff on the fourth round of clubs.

You lead a diamond. Partner ruffs with the 7, and shifts to a heart. Declarer wins the ace of hearts, cashes the jack of clubs discarding a heart, and leads a spade off dummy. Do you go up king or play small?

North
53
9
10
64
East
K102
Q
87
W
N
E
S
P
1NT
X
P
2
P
P
P

Partner is marked with ace and another spade. It is clear to play small, and let partner beat whatever spade declarer plays. This will leave partner with another spade, and possibly your 10 will come in play later.

You play the 2. Declarer plays the queen, and partner wins the ace. Partner leads a heart to your queen, declarer following. What now?

North
5
10
64
East
K10
87
W
N
E
S
P
1NT
X
P
2
P
P
P

Of course you put a club through. Partner has another trump, and might be able to overruff declarer.

You lead a club. Declarer ruffs with the 8. Partner overruffs with the 9, and leads a heart. Dummy ruffs with the 5. Is there anything you can do?

North
5
10
6
East
K10
8
W
N
E
S
P
1NT
X
P
2
P
P
P

Unfortunately, there is nothing you can do. If you ruff with the king of spades, declarer discads and has the last two tricks. If you ruff with the 10, declarer overruffs, leads a diamond forcing your king of spades, and gets the last trick. If you discard your club, declarer discards a diamond and has you in a trump coup. Thus, you defeat the contract 1 trick. The full hand is:

West
A97
KJ765
Q6
1093
North
53
A9
KJ102
AQJ64
East
K102
Q8
A87
K8752
South
QJ864
10432
9543
W
N
E
S
P
1NT
X
P
2
P
P
P
D
2 South
NS: 0 EW: 0
Q
K
8
3
1
1
0
A
2
2
3
1
2
0
Q
K
4
9
3
3
0
4
6
J
A
2
3
1
7
5
7
2
0
3
2
5
A
8
3
1
4
2
J
5
4
10
1
5
2
3
2
Q
A
0
5
3
6
9
Q
10
2
5
4
8
8
9
4
0
5
5
K
5
11

How was declarer's line of play?

West
A97
KJ765
Q6
1093
North
53
A9
KJ102
AQJ64
East
K102
Q8
A87
K8752
South
QJ864
10432
9543
W
N
E
S
P
1NT
X
P
2
P
P
P
D
2 South
NS: 0 EW: 0
Q
K
8
3
1
1
0
A
2
2
3
1
2
0
Q
K
4
9
3
3
0
4
6
J
A
2
3
1
7
5
7
2
0
3
2
5
A
8
3
1
4
2
J
5
4
10
1
5
2
3
2
Q
A
0
5
3
6
9
Q
10
2
5
4
8
8
9
4
0
5
5
K
5
11

Declarer had to scramble every trick he could get, so going after clubs with the ruffing finesse looks right. There wasn't anything he could do about the diamond ruff, so leading the second round of diamonds himself was okay. One improvement would have been to duck the heart shift. This prevents East from getting in with the queen of hearts to put the fourth round of clubs through.

How was West's lead and defense?

West
A97
KJ765
Q6
1093
North
53
A9
KJ102
AQJ64
East
K102
Q8
A87
K8752
South
QJ864
10432
9543
W
N
E
S
P
1NT
X
P
2
P
P
P
D
2 South
NS: 0 EW: 0
Q
K
8
3
1
1
0
A
2
2
3
1
2
0
Q
K
4
9
3
3
0
4
6
J
A
2
3
1
7
5
7
2
0
3
2
5
A
8
3
1
4
2
J
5
4
10
1
5
2
3
2
Q
A
0
5
3
6
9
Q
10
2
5
4
8
8
9
4
0
5
5
K
5
11

From West's point of view, there wasn't much hope to defeat 2 by going passive. West's queen of diamonds shot looks reasonable. He has trump control, and needs to hit his partner with something good in order to have a chance, so setting up a third-round diamond ruff or overruff is a good idea.

After that, West's heart plays were pretty routine. West knew where the queen of hearts was from East's play at trick 1.

How about the N-S auction?

West
A97
KJ765
Q6
1093
North
53
A9
KJ102
AQJ64
East
K102
Q8
A87
K8752
South
QJ864
10432
9543
W
N
E
S
P
1NT
X
P
2
P
P
P
D
2 South
NS: 0 EW: 0
Q
K
8
3
1
1
0
A
2
2
3
1
2
0
Q
K
4
9
3
3
0
4
6
J
A
2
3
1
7
5
7
2
0
3
2
5
A
8
3
1
4
2
J
5
4
10
1
5
2
3
2
Q
A
0
5
3
6
9
Q
10
2
5
4
8
8
9
4
0
5
5
K
5
11

North's double of 1NT is okay. If North doesn't double, his side may get frozen out of a game.

South has to run, of course. We don't know the N-S agreements, but assuming South's bids are natural, 2 looks reasonable. A better fit might exist, but it is difficult to find.

One of the faults of many good players is that they don't double aggressively enough. Perhaps they are uneasy with the volatility which is created by marginal doubles, and are not willing to risk the occasional bad result when they double the opponents into game. In this day and age it is important to take any advantage one can find.

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