Likelihood

K J 5
A 9 4
A Q J 10 8 2
K
8 7 3 Q 6 2
K 7 6 2 Q J 10 8
5 3 K 9 4
J 7 6 3 9 5 4
A 10 9 4
5 3
7 6
A Q 10 8 2

I'm not much of an odds junkie, particularly when I read in one bridge column that one line of play figures to be 1 7/128th% better than another. I don't think many people want to reduce bridge to such calculations -- and to me it would be a reduction. Frankly I doubt if many experts could come up with such a close call in the moderate haste we are normally subject to, though sometimes their games are much, much slower. C'mon, we just want to enjoy the game.
However, I am certainly not opposed to figuring the odds and indeed have elsewhere offered two reminders, to wit: first, everyone should be familiar with the common axiom that an even number of cards will tend to split unevenly, while an odd number will tend to split as evenly as possible. Thus six cards figure to split 4-2 more often than 3-3, while 5 cards and 7 cards are favored to split 3-2 and 4-3 respectively. And secondly, though you may like to see yourself as too free and imaginative a spirit to be bound by anything so unimaginative as mathematics, there is a point where a disregard of the odds simply becomes bad bridge. Would you rather see your partner happy 60% of the time or 35% of the time? If you have trouble with that question, then, no, I don't suppose I have much to say to you.
Anyway, here is a hand where a little play with the odds would have steered anyone in 3 no to a makable contract, while those who went contrary to the odds (and common sense) wound up disappointed.
Opening lead was the deuce of hearts. Take note right away. In newspaper columns, this always indicates that West has a four-card suit, as indeed it does here. True, some people will lead 3rd and 5th best, which would allow for 5 cards in either hand, and you're entitled to ask, but getting a straight answer (or assuming 4th highest) should leave you feeling pretty good.
Anyway, just about all no trump declarers ducked two rounds, willy-nilly winning the third, and now a choice has to be made. Declarer might just be able to bring the contract home with any of the three remaining suits, one of them clearly inferior, one clearly superior and the third in the middle. Let me go through them.
Several tried to make hay out of the club suit -- indeed, every one who went down in three no that I checked had pursued that line. Now that has to be the least appealing of the three suits for a couple of reasons. One is that it goes against the odds to find the jack in the short hand on a 4-3 split. You don't even know you're going to have a 4-3 split to begin with -- you can't live on a 5-2 even if the jack falls short -- and to go beyond that to look for the jack to fall in three leads is to put yourself at a distinct disadvantage.
The second reason clubs are the least appealing suit is that if you're wrong, you can't recover unless you've already finessed successfully against the Q of spades. That would allow you three clubs, four spades and two aces.
In the middle lie spades. Yeah, if you guess right, you can win four spade tricks, 3 clubs and the two red aces. But there is a two-fold problem with that, one being that if you guess wrong on the queen of spades, you again can recover only if you pick up the diamonds without loss, which would have allowed the contract in the first place, and the second reason is that this allows for no overtricks -- unless you wanna try a diamond hook after establishing your contract.
Which brings us to diamonds. First of all, you can recover on a losing finesse -- which right there puts the suit in a more favorable light than the other two. You can recover if hearts were originally 4-4 as indicated by the opening lead, and if they were 5-3, with the finesse being into the short holding, now exhausted. And secondly, they offer a chance at an overtrick.
Hence, after winning with the ace of hearts at trick 3, I would cash the king of clubs and finesse a spade in the closed hand. If it loses, I'm going to hope a 4-4 heart split spares me from a setting trick right there -- and that I'll have success with the diamond hook. In essence, I would be banking on either the spade or the diamond finesse to work. Then take the diamond hook. If it holds (and at least one defender did hold up there), I'd come to the ace of spades, cash the A of clubs and repeat the finesse. If the finesse is off after all, the defense can cash out a fourth winner, but I've got my nine winners, and if on, I should have two overtricks: two clubs, 6 diamonds, two spades and a heart. (Yes, that's if diamonds are 3-2.)
Why, if I'm taking that spade hook as soon as I get the lead, why don't I stick with spades for four spades, three clubs and two aces? Well for the possible overtricks, without risk, which of course wouldn't pan out, but are worth a try.
A fairly simple hand that lends itself to a look at the odds, or at likelihood if you prefer. A few incidentally, were in 6 diamonds -- making. Without defensive error. The opening lead of a heart was won, the king of clubs cashed, a finesse of the 10 of spades, two club leads got rid of heart losers, and now the diamond hook settled the contract.
The daring declarers won't always come out ahead, but timidity has its own dangers and will often invite defeat when success stared declarer in the face. Compare the chances that declarer took in 6 diamonds with the chances of those who so feared taking that diamond hook that they tried to avoid it by testing clubs -- and thereby uncovered the jack of clubs as a winner, leading to their defeat.
You've got to go with the most promising line even if that means taking a chance you wish you didn't have to take. Do you want a game where every contract is cut-and-dried? I don't think so.
[years later] Aside from noticing that I'd referred to "the red-suit finesses" when I obviously meant diamond and spade finesses (corrected above), I found that I didn't like my analysis at all. It would've made better sense if we trade the 10 of diamonds for the 5. In that case, we'd need a 3-2 diamond split. But declarer has a virtually guaranteed contract (on a 4-4 heart split) and can live with any 4-1 diamond split. After winning with the A of hearts, cash the K of clubs, then the A of diamonds and lay down the Q of diamonds. If both defenders followed to the A of diamonds, you now only hafta sweat out a heart lead -- and when both defenders play a heart on the fourth round, you're on claim with adequate communication in spades. You'd have three clubs, 5 diamonds, one heart and two spades, except that the opponents have three tricks, so you cannot pick up 11. And if hearts were originally 5-3? Well, I still have a chance that the short hand in hearts has the K of diamonds. But no.
Another possible line: Forego the spade hook, come to the closed hand with the A and take the diamond finesse. This has the advantage that the diamond hook might be on. But no, wait a minute. We won't have a later entry to the clubs, so we'd have to cash out the top winners. This has the advantage that you might drop the J of clubs in three leads, but the disadvantage that you might lose a club in addition to three hearts, which isn't such a good idea.
No, I like the one where declarer holds up on the hearts, sluffing a club on the third round, then (after unblocking the K of clubs) bangs down the A of diamonds and continues with another top diamond. When hearts break evenly, nothing can prevent declarer from establishing 5 diamonds, etc. And the reference to the odds is pointless. Mea culpa.