In most systems, a redouble of a takeout double of partner's opening is made on pretty much any hand of nine points or more other than one with a fit for opener's suit, and is part of what is effectively a new bidding system, since new suit responses are no longer forcing. Apart from being unnecessarily complicated, this leads to some strange contortions.
Consider this hand from Precision in the 90s by Barry Rigal:
| West | North | East | South | ||
|---|---|---|---|---|---|
 7 | 1 | dbl | |||
 KQ72 | ? | ||||
 Q1093 | |||||
 A963 |
with KQJ842106K42Q5, and you will have swapped a juicy penalty for an unsure part-score. So he suggests you pass with this hand, and double on the next round for penalties. Just make sure you have agreed with partner that this double is for penalty...This is all very un-Chilli, and indeed this hand is a perfect example of the only type of hand on which we would redouble. With eleven points, we categorically hold the balance of power, but we know there is no major suit fit and game is unsure; and any two-level contract by them will struggle badly. Redouble and prepare to take the money.