Deciding to pass partner's takeout double
The bidding when your LHO opens and your partner makes a takeout double is asking your to show your longest suit and your hand strength. When the RHO passes, you are left with two options. You can pass, try to convert the contract to a penalitized contract. You can bid your hand. Remember, when responding to Takeout you bid your best(longest) suit. Bidding at the 1-level (minimal bid) only shows 0-7 HCP. So, you the weaker you are the more pressure is on you to bid. Hands with 8-11HCP can show the extra strength by jumping the bidding up one level with their response. However, sometimes, your best suit is the opponents bid suit.
If the number of cards you hold in the opponent's suit added to the number of power cards (Ace thru Ten) in that suit plus the level of the contract equals or exceed 9, passing will likely produce the best possible score for your side.
That seems a bit complicated, let's examine some examples.
After 1♣--Double--Pass--
Which hand would you like to try for setting 1♣-Dbled? Which would you be happier to try for 1NT (and maybe it goes down 1)?
The first hand seems like a no brainer to try penalize clubs. Opponent's
look to be in trouble in clubs. You have 6 clubs, 3 power cards (KJT) for
a total of 9 points. The contract is only at the 1-level, but using the above
rule, that make a score of 10. The best possible score (at this point) will be
to set 1
X. You have 7 HCP and don't have any good fit with partner. So, likely,
1NT is your ultimate contract. If this makes (not certain) it likely gets only 90 or 120
points. Setting 1C could produce 100 or 200 points (maybe more if opponents are
vulnerable). The mostly likely case here, though, is that the Opener will realize
how much danger their are in trying to play 1♣ and will probably make an SOS
redouble. You are happy with that. You can always balance back in with 1NT or
leave the new contract up to your partner to penalize.
The second hand scores 4 for 4 cards in club and 3 more for the power cards, the
contract level is only at the 1 level. This makes the score only '8'. Likely, not
much reward for letting opponent's play 1x. This is a case to call 1NT instead.
Generally, we'd like to have a minimum 8HCP to call 1NT. If you have strict
HCP requirements for the 1NT response to TO Doubles, then you will have to bid
1♥. Partner shouldn't bury you.