What does this redouble really mean?

Can you identify which of the four proposed hands matches North’s bidding in the sequence shown — and say what you would have done with the other three?

A free bid, made in a competitive auction where the player is not forced to bid, must be constructive. And it must not hide anything!

Here, after West’s double, North is no longer obliged to complete the Texas transfer. North can therefore take the opportunity to show whether they hold a Heart fit, in case East bids 3♦. This allows South to decide whether to compete further.

With Hand 2, the only one containing just two Hearts, North must pass, which denies a fit. With the other three hands, all supporting Hearts, North should bid.

In this situation, there are different ways to show Heart support. Everything depends on the choice of the declarer, and therefore on which hand will receive the opening lead.

After the opponent’s intervention, it is no longer obvious that the “right hand” to declare is opener’s hand. If South holds, for example, the King-doubleton in Diamonds, it may be useful for South to declare in order to protect that holding from the opening lead.