DON'T look at the whole deal below. See only the North–South cards and observe the bidding, whether you agree with it or not.
Assume you are North and the lead is ♠ 8. You play the ace and throw your diamond. The contract is watertight if only you could avoid losing two hearts. Plan the play.
The “normal” play, i.e. absent any bidding or lead inferences, is pretty obvious: take ♥ A and follow with &hearts 5, planning to finesse the ten. This play, it turns out, would be successful no less than 87.6 % of the time. It loses only when the hearts are 5–0 or East holds ♥ Q J x x. You can do nothing about a 5–0 break, but you can remedy the latter, by coming to hand (preferably via a diamond ruff) and running the ♥ 10. The question is: Should you?
When this deal was played on BBO, declarer rejected the “normal” line in view of the double, and—you can see the East–West cards now—went down, to bag −14.73 IMPs, generating a swing of 27.93 IMPs. (Scoring was by cross IMPs.)
As dummy, my first reaction was that declarer had made a horrendous mistake. You, however, can see that declarer's line is not absurd. That notwithstanding, I am of the opinion that the “normal” line was the correct line here, because the double merely suggests a strong heart holding with East, and the alternative line fails against any other 4–1 break. Second, East's profile marked him as an expert (not that that necessarily means anything); could he have doubled (on a hunch) merely to deflect declarer from the normal line? Third, he could have read the auction as gone awry or have expected to get a spade ruff after leading his singleton spade to partner's (phantom) ace, despite South's 5 NT. Or he may belong to the school of thought that demands doubling slams because of the a priori improbability of a hand being a slam hand, especially “since partner has nine tricks in his hand”.
To elaborate a point about deflecting declarer from his normal line of play, one should always be suspicious of indications from the opponents that direct one towards an unnatural action which fails against a normal lie of the cards; it could be a falsecard or have been an intelligent psych. That said, can one humanly resist the temptation to expose a sucker double? All in all, I don't think it was a big blunder to play East for ♥ Q J x x.
If you think people don't double on the “a priori” theory, let me tell you that the same East, two boards later, doubled 7 NT on an auction that began on his left: 1♣ –1 ♥–2 ♦–4 NT–5 ♥–5 NT–6 ♦–7NT, holding ♠ Q 5 2 ♥ J 8 7 6 4 ♦ 10 7 2 ♣ 5 4—perhaps heady from his earlier victory, not recognizing that the contract had been very sound.
Let's consider the auction now. What are your feelings on North's 4 ♥ overcall? I think it's an unwise call, though I cannot claim to know a good solution in this situation. I'd be very uncomfortable hiding the clubs. Let's look at the options.
3NT: Are you nuts? 4 ♣: A distortion of course, but 5 ♣ may be the best spot, which can now be reached. 5 ♣: slightly better than 3NT, but not much else. 4 ♥: Fine except that it completely buries the club suit. Dbl: Represents the best chance of finding the correct spot, but partner may jump in diamonds (you'll correct 4 ♦, of course); also, your hand is aceless and has only 2 AK controls. Pass: Though partner rates to have some points, he will also likely have spades, in which case he might not balance and a cold game might be missed.
My choice would be to double. Please note that, holding hearts and diamonds, you will definitely double. If you're wondering why, you better read about the Equal Level Conversion principle. Even if you don't want to play it at lower levels, to my mind, it would be insane not to play it in this kind of situation.
Next, how do you in general show two-suiters over an enemy 3-level pre-empt? One idea would be to use the cue-bid as a top–bottom cue-bid, i.e. to show the lowest and the highest ranking of the unbid suits; the double should be used in accordance with the equal-level-conversion principle (i.e. the highest ranking unbid suit and diamonds or, in case 3 ♦ is the pre-empt, clubs) and flexibly whenever the alternative action takes the partnership too high. 4NT should show the two lowest unbid suits. Please do share your opinion on this.
[Update: In these last minutes before posting, clarity hits me. As declarer on this deal, if you rule out a 4–1 where West has heart length, odds are actually 3:2 against West having a singleton honour, assuming exactly four hearts with East and taking no inference about suit quality. Added to that, East is surely more likely to have doubled holding the Q–J than not. Since you can overcome any 3–2 break, I now think the percentage line is to try the finesse. Declarer did, however, make a minor tactical mistake, in my opinion. He tried to run the seven instead of the ten. The ten is more likely to induce a problem-solving cover.]
