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A double here (or any time pard opens with a pre-empt) is for penalty. I'd worry that we don't have a game, let alone slam - xx xx xx KQTxxxx
Note that even when partner has that hand, the bad guys are not making three diamonds, so a penalty double isn't the worst thing in the world here. (They're making the club ace plus whatever diamonds they have, assuming the spade king is with RHO -- most likely result is down one, maybe two.)
I am not concerned in the slightest about missing slam. If partner has a stiff diamond (unlikely) and the club ace (less than 50%, after a first chair nonvulnerable preempt), and the spade king is onside, we'd still some luck, as we'd probably be short on entries to hook the spade.
One reasonable plan is 3S, following that up with 4H if either 4C or 4D swings around to you. That's probably superior to 4D (I'm assuming you wouldn't play that as keycard for clubs, though you could), because when pard holds Kx or Q9x (or so) of diamonds you may get to 3NT.
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Re the double being penalty: people get confused, because on their convention card they've written that doubles are negative through 3D (or 4D, or 4H, or sometimes 4S, or even 6H if you play with me), so they figure this one is too -- but ctj is still correct that this one is penalty. Why? Because there is no reason for a negative double in an auction in which partner has already described his hand. Partner has announced with his preempt that he has a one suiter, so asking for his second suit doesn't make a lot of sense. Deals like this one, in which you want partner to take out even though you know he doesn't have a second suit, are uncommon; on the other hand, auctions in which the opponents are pressured by the preempt into making bad bids are pretty common. If you play negative doubles through 3D (it really should be through at least 4H, but whatever), then you are referring to auctions like 1S (3D) X, not 2S (3D) X.