I'll write a longer response, Helene and I recently discussed this topic as well.
Personally I really dislike the 'borrowed king' theory. The idea is that partner won't be able to overcall with many relatively strong hands, so that we might still have a good score even if the balancing hand is a bit weak. So we 'borrow a king', i.e. lower all our requirements by 3 HCP or so, and in return trust partner to treat their hand about 3 HCP weaker and respond lower compared to when facing a normal double or bid.
In my experience this approach does far more harm than good, and stems from a different era of bridge. We overcall lighter, make takeout doubles on hands with neither shape nor decent strength, even open lighter. As a result, 'pass' becomes more defined. Let's go through partner's options over 1
♣ (I am giving my own system below, if yours is very different that might play a role here):
- Pass: none of the below. In particular: 1) any weak (0-8) hand not worth a weak jump overcall; or 2) 9-11 balanced no 5 card suit; or 3) 12-14 (semi)balanced, no 5 card suit, not 4-3 or better in the majors; or 4) a penalty pass of clubs.
- Double: 1) 11+ with 4-3 or better in the majors, desire to be in the auction and no other bid; or 2) a hand too strong for an overcall (typically 18+).
- 1♦: 5(+)♦, approx 7-17 HCP, if 7-8 then needs a decent suit.
- 1♥: 5(+)♥, approx 7-17 HCP, very little other requirements.
- 1♠: 5(+)♠, approx 7-17 HCP, very little other requirements.
- 1NT: 15-18 balanced with a club stopper.
- 2♣: 55+ in the majors, approx 7-20 HCP.
- 2♦: 5(+)♦, approx 4-10 HCP, offensively oriented hand.
- 2♥: 5(+)♥, approx 4-10 HCP, offensively oriented hand.
- 2♠: 5(+)♠, approx 4-10 HCP, offensively oriented hand.
- 2NT: 55+ in the red suits, approx 9-20 HCP.
- 3♣: 55+ in the pointed suits, approx 9-20 HCP.
Some of the specialised bids don't matter that much, and most people will require a 6-card suit for a weak jump overcall, but it's really the 1-level responses that matter.
If partner didn't have an overcall and didn't have a takeout double apparently there's a hole in one of the majors, so what are we aiming for by keeping the auction open? Once in a blue moon partner has the penalty pass, but realistically partner is limited to the weak notrump type hand with a doubleton in a major. If you hold, say, 8-9 HCP and no five card suit, do you really want to push the opponents to their likely major suit fit, or at any rate push them to the long suit of the weak hand? We probably don't even have the balance of strength. In my experience most of the time opener will have some 19+-count and responder was afraid of showing their suit and being taken too seriously, and stretching to keep the auction open primarily helps them find their best contract.
The trick to competing is to compete immediately, with light requirements for overcalls and takeout doubles and openings. The main reasons are that you might not get another bid and also the opponents are most likely to rescue you if you make your mistakes early, while they haven't described their strength and shape yet. As a bonus such aggressive action relieves partner of the need to take light action in balancing position.
Personally I think the case is actually far stronger than this - even if you play sound overcalls, healthy takeout doubles, and sound openings, I think it is likely anti-percentage to then come in light later in these balancing positions. Especially over their 1m opening, where partner had all the freedom in the world to compete and also it is unlikely to be the best spot for the opponents.
I would personally therefore not shift your ranges by much, if at all. If you do follow the 'borrowed king' approach you'd shift all your responsive ranges up by 3 HCP, to not hang partner.
As for the exact ranges and the system itself - there are several different approaches to continuing after partner's takeout double at the 1-level. If you are curious I'm happy to share mine, but be aware that different options exist.
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