Cue Bid Limit Raise
A limit or invitational raise normally shows 10-12 HCPs and invites partner to bid game with appropriate strength of his own.
A non-conventional limit raise is just a jump in the suit, such as 1-P-3, in noncompetitive bidding.
In competitive bidding, it is advantageous to bid as high as you can based solely on trump support in order to jam things up for the opponents. Generally, it is safe to bid for the same number of tricks as the minimum number of trumps you and your partner are known to have.
For example, after 1-Dbl-??, partner is known to have at least 5 Hearts (unless you open 4-card majors), so if you have 3, you can bid for 8 tricks (2). If you have 4 of his suit, you can bid 3, etc.
Since partner can open 1 of a minor with 3 cards (or fewer) in the suit, it takes more support to make a Total Tricks raise. After, say 1-1-??, you should have 5 Clubs to raise to 2. If he opens 1, you could raise with 4 Diamonds, since a 1 tends to show more cards in the suit than 1, on average.
Since direct raises of partner's suit are preemptive, meaning you could raise to 3 with 4 Hearts and NO points, you have to find some other way to show a hand of invitational strength. This is done by cue bidding RHO's suit.
Since 3 would be preemptive (weak),
bid 2 to show 4+ Hearts and 10-12 HCPs.
Opener bids 3 with a minimum
or 4 with a good hand.
Also see Cue Bid Raise and Cue Bid Strength Showing.
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