With 9 trump, missing the K and Q but not the J or 10, I have always felt comfortable simply banging down the A and continuing the suit. I have read and been told specifically, that the odds of a double finesse are a little better than the odds my way. However, there are other considerations besides how those 4 outstanding cards stack up, the most important being maneuvering to get in position to lead toward the Ace -- twice. Then there are secondary considerations such as fiddling with side suits where the opponents may find a ruff. Also, I may find it necessary, on a defender's lead, to take a finesse I'd rather put off a few tricks. And just in general I don't like to delay the drawing of trump perhaps up to trick 5 or 6, and all this while risking a double hook into K Q tight! So I just bang away and know pretty quickly how trump stack up.
The worst thing one can do is to start the finesse, losing to the hand behind the ace, and then second round to bang down the ace. This works on 2-2 trump, of course (but then, what doesn't?), but not on 3-1, where you get neither the advantage of dropping a stiff honor, first round, nor that of finessing through an honor third round. In any event, this hand is a cakewalk if declarer subscribes to that above philosophy. If you get a club lead, you'll want to ruff that lone club first, of course, and might even want to take care of clubs without a club lead, since your entries are limited. On a spade lead, which you let ride to the closed hand (you would let it ride, wouldn't you?), that suit is taken care of. But on a diamond lead, you've got the fourth round of spades to be concerned with and perhaps had better not count on the third round of diamonds for sluffing a second loser on an uneven heart split. Hence, on a diamond lead, it looks as though you'd be fairly safe cashing the A of clubs, ruffing a club, then the A of hearts and hearts continued. If we drop an honor first round, the 10 should knock out the other honor, leaving the J for the third round.
A glance tells you that there aren't many entries to dummy. In fact, there are only two. Plus dummy has a powerful side suit. So you're going to want to preserve those entries, except when there's a sound reason for using one up. But you will have to take care of one low club and one low spade. And this proved the undoing of a sprinkling of declarers.
Here's one who got a spade lead and went up with the Queen! ! ! That's a certain entry that you want to preserve until you've unblocked diamonds and can use it. This is all the more bizarre in that declarer has A K 10 in the closed hand and by letting it ride, wouldn't need to sluff a spade by way of diamonds. Evidently declarer wanted to lead toward the ace, for he took one heart lead, East covering the 10! So if that was a stiff Q, instead of declarer controlling the third round, West would with the 9! Which I guess is another reason for two quick heart leads. (Declarer doesn't really have a sound double finessing position here, with the J and 10 in different hands, lacking the 9.) Now he unblocked the diamonds, cashed the A of clubs and ruffed a club . . . oh, oh, oh! I presumed he was ruffing a club since there's no other reason for cashing the ace, and was looking to see what he did next. But he wasn't on lead! He didn't ruff his club! He sluffed the 8 of spades on it! ! That's such a bizarre play that I guess it can only be considered a mismouse. But the spade was two cards over from the lowest heart. Well, I dunno.
Actually, that declarer was only in game and made an overtrick, and declarers sometimes get lazy when the contract isn't at issue, only overtricks. But here was one in 6 hearts: Opening lead a club, now the club was properly ruffed, the 10 of hearts covered by East! I still don't like that lead. Let's suppose East does hold K Q 9 or K Q 5. There's no advantage. After the 10 of hearts is covered, what does declarer do? He returns to dummy with the Q of spades and leads another trump toward his Jack. East goes up and cashes a club! Oh, declarer forgot to figure that there'd be no more trump if you ruff once and lead twice? Now he cashed his diamond ace, spade to the Q, king of diamonds, sluffing a spade. So far, so good. A heart lead to West's K, the Q of clubs, declarer sluffing the A of spades! That's too bizarre also to work out. But here, a low trump is several cards away from the A of spades, and that's difficult to understand.
Well, lemme go to the declarer down two in 7 hearts. Of course, he had no chance, but why down two? Well, believe it or not, after getting the favorable lead of a diamond, willy-nilly unblocking the suit, this declarer in four tricks wiped out his entries to dummy -- without cashing the K of diamonds! This one clearly wasn't a mismouse, though it's almost as difficult to understand. Here's what he did: trick 2: spade to the Q. Trick 3, club to the A. Now since he hardly needed to be in dummy to cash that round of clubs, he clearly doesn't have his eye on the ball. Now a club was ruffed at trick four. He can still make 12 tricks if he'll just cash the K of diamonds sluffing a spade. But trick 5 saw a lead to the A of spades! Well, actually, I didn't realize this at first, but he still had a chance for a 12th trick by ruffing the third round of spades. But what he actually did was to cash the K of spades, sluffing a diamond. It was a winner he could well have waited to cash, no? He could have ruffed the third round of spades, and now he doesn't even need the diamonds.
Well, I must admit that this isn't the best illustration of a failure to use entries wisely. The first two declarers made totally bizarre and incomprehensible plays, and the third came close. Of course he was in a totally unmakable contract and didn't have quite the motivation the 6 heart bidder had to pick up 12 tricks. Hafta look him up and see if he regards himself as an expert.