The push double

A situation often arises in competitive bidding where one side pushes the other side into (usually) a game contract and then the pusher doubles.

Like many aspects of bridge logic, this one can be interpreted by looking at the scoring table. Let's take a look at an example:

South suspected that he could not defeat 3♠️ so decided to push the opponent into a game that he hoped he could defeat. If the push was successful, then plus 50 would be a much better matchpoint score than -140.  There would be absolutely no good reason to risk the double here. If the push was unsuccessful, then, without a double, -420 would probably have company. But -590 would clearly be a lot worse than the -170 that the opponents were probably going to make without the push.

So, it seems to me that the double cannot be to increase the penalty. Often going from 50 to 100 doesn't even change your matchpoints! It must be lead-directing. But to what?

Without the double, you were going to lead a club, right? If partner was happy with you leading a club, why would he double? 

So, what's the best lead here? Not a trump--that cannot be right. How about a diamond? It could be right but it doesn't look right with this holding. So, you lead your singleton heart, partner wins the ace and gives you a ruff. We will come to a spade, a heart, a heart ruff and we must score the ♦️K. +100.  Dummy is void in clubs so your trumps will be drawn before you can score a heart ruff (if you led a club).

Actually, I told a little white lie here. Partner didn't have the Ace. But declarer failed to go up with dummy's ace and partner won his King and you still got your ruff.

Sound unlikely? Well, yes. Declarer went up with dummy's ace, drew trumps and bye-bye heart ruff. Scoring -590 for 0%.  Pushing them without doubling would have scored 16%. Failing to push? Hard to know. Dummy had six spades, a club void, the ♥️A and the ♦️Q. Would they have raised to 4? Quite possibly not. So, the push strategy was misguided this time.

But the principle of the "push double" being lead-directing is eminently sound.