Balancing at the 3-level

It is often a difficult problem to bid directly over a 3-level preempt, and it is just as hard to balance, although at least in balancing, some inference should be available from the previous 2 passes.

I heard 3♥ -P-P and looked down to find:  ♠ K8♥ A♦ AJT82♣ KJT83.

What to do?

Well, I could pass…  as I am likely to go plus, but at Imps, Vul vs. not, there is just too much risk against not scoring a game bonus.

Double?  If a minor suit card were a spade, I think this would be my first choice, but as is, what to do when partner bids 3S or 4S?  I suppose we could bid 3N or 4m over 3S, and pass 4S hoping partner has at least 5 — although under the general principle that suits break badly after preempts, would we really want to play in a 5-2 spade fit?

4m?  First of all which one?  If partner is 3-1 or 4-1 the way we don’t pick, we could go down in 4m when cold for 5 of the other.

3N?  Hamman’s rule?  RHO’s failure to raise at favorably strongly suggests that partner has some heart length.  A simple Txxx after an honor lead should be enough of a second stopper if we need to knock some card out — imagine pard with QJxx Txxx KQxx x :  8 tricks after knocking out the spade, and a ninth if they persist in hearts, or give me time to lead a club up.

In fact 9xxx might do if west leads an honor from KQhxxx(x) and their partner has a singleton or doubleton Jack or Ten.

4N?  Pick a minor?  As I just suggested, partner may have heart length, and if they also have spade length, they may be 2-2 or worse in the minors.

Sadly, at the table, 4N is all that occurred to me, and partner had ♠ AQxxxx♥ Jxxx♦ 97♣ 9.

5D was not a success.  4S turns out to be a very difficult contract, even though spades cooperate 3-2, as the preempter was 2=6=5=0 with one diamond honor.  Of course since spades break, 3N is cold with a successful club finesse, and the other bad breaks not mattering.

Would you pull 3N with these cards?  Partner did not double, so they may be 1-3-3-6 or 7 with a running or one loser minor and a single or double heart stop — and then 4-2 or 5-1 spades will not bode well for 4S.