Doubling intervention after we've found a fit

Here's a common auction: we open 1♥, lefty passes, partner raises to 2♥ and righty comes in with 2♠.  The good news is that we have one call available that we didn't have before (double), but do we really know how best to use that call?

I once had this exact auction a number of years ago now.  It was at a sectional and my right-hand opponent had earlier given a talk to the I/N players entitled "overcalls -- how to make them safely", or some similar title.  RHO now came in with 2♠ (I think all were vulnerable but I'm not sure) and I held a hand something like the following: ♠AQT4 ♥KQ543 ♦A2 ♣K7.  I doubled and we scored 800 for a top.  It felt pretty good.

The snag is that I've played a lot of hands since then and I don't think anything quite like that has ever come up again.  If I have a good hand in that same auction, it's much more likely to look like this: ♠A2 ♥KQ543 ♦AQT4 ♣K7.  This isn't all that bad.  I can either shoot straight to game (a slight overbid but could easily be right) or I can make a game try with 3♦ or 2NT.

What do I do with this hand, though: ♠92 ♥KQ543 ♦AQT4 ♣K7?  If I bid 3♦ with this hand, how will partner tell the difference between this and the previous hand?  Some partnerships, including one of mine, play that 2NT is the "good-bad" 2NT (is there an ugly 2NT?).  This is a pretty good convention and partner will know that we don't have ♠2 ♥KQ543 ♦AQT94 ♣K7 which we would show with 3♦.

Sometimes the opponent will have the cheek to bid 3♣ (or 3♦) which will prevent us from using the 2NT treatment.

I believe there's a much more flexible call available: double!  If we happen to catch partner with a good balanced hand with useful spades, he could pass, especially if they are vulnerable (seeking the magic 200).  But most of the time, he'll either sign off in 3♥, bid 4♥ (or perhaps 3NT) or bid an available minor suit as his own game try.  The double here should show a semi-balanced hand typically with a small doubleton in the enemy suit and of course only five hearts.  It shows a little extra (it denies having made a "rule-of-20" type of opening) because every now and then partner will pass and it would be nice to set their contract!

It's basically a question of frequency and the arithmetic of the scoring table.  Let's say both sides have 20 hcp.  If you believe that, on average, the total trumps will predict the total tricks and, if you go one step further and believe in the so-called Hillyard Corollary, you will predict that our side will take the same number of tricks as our total trumps and their side likewise.  I do stress that we are talking about averages here.  In the long run!   I'm not claiming that this will work out exactly on every hand.  Far from it. I'm an LOTT-skeptic too.  But let's say that both sides have an eight-card fit in their major, with no particularly good double fit.  We'd expect each side to be able to take 8 tricks.  Now, if they can make their 2♠, we'd prefer to bid 3♥, especially if we aren't vulnerable.  So, even though we may not be close to making game, we still want to compete!

We still need good judgment.  Let's say our hand is ♠972 ♥KQ543 ♦AQ4 ♣K7.  It would likely be very dangerous to compete here.  Even if we get to play 3♥, we are likely to lose the first three tricks especially if they only have a seven-card fit.  And LHO may have some useful heart holding and double for penalties.

Those of you who play the "maximal" double will have very little difficulty adapting to this scheme.  It will now not matter at all which of the other three suits they compete in.  Double will always have approximately the same meaning.

And of course, since our direct double is essentially a cooperative double, so to will partner's be.  If we have a hand like ♠AQT ♥KQ543 ♦92 ♣K7 we will obviously be passing 2♠.  But partner may have 8 or 9 hcp, together with spade shortness and he can double.  We will be delighted to pass.  So, we may yet achieve our 800s and 1100s.

But, to reiterate, it is unusual for these competitive auctions to result in big penalties.  We therefore use the double more as a way of describing a hand that wants to compete.  And that comes up far more frequently.