Playing a Standard American bidding system, you have three direct ways to show trump support after partner opens 1H or 1S:
A simple raise to two (1S-2S), to show 6-9 pts.
A jump to three (1S-3S), which can be played either of two ways, depending on your preference: as a forcing raise (12+ pts.), or as an invitational limit raise (10-11 pts.).
If you play the more modern system of using the jump to 3 as a limit raise, you have a somewhat awkward problem when you hold a forcing-to-game hand with trump support. One solution is to bid a new suit first, temporarily "concealing" your support, then jump to game in partner's suit at your next turn (an auction like 1S by partner - 2C by you - 2NT - 4S).
There are a number of different conventions designed to help you describe these strong hands. One of the most popular is the Jacoby 2NT, which was invented by Oswald Jacoby (who also invented Jacoby Transfers). To use this convention, your partnership agrees that after you open 1H or 1S and your partner is an unpassed hand, his jump to 2NT shows:
Forcing-to-game strength (12+ points)
The 2NT response forces you to at least game level. It is not a suggestion to play in notrump; it shows support and asks the 1H or 1S opener to further describe his hand.
Note that the Jacoby 2NT convention is "on" only if
responder has not previously passed in the auction. If you are
a passed hand, your jump to 2NT is natural, showing a balanced
hand of 11-12 points.
In addition to giving responder a direct way to show a forcing hand, the Jacoby 2NT improves the accuracy of your slam bidding. Its biggest advantage is that it gives opener room to further describe his hand. There are a number of different meanings you can assign to opener's rebids. Here's one of the most commonly used structures:
If you open 1 of a major and partner responds 2NT:
If you have a second 5-card suit (a semi-strong one -- QJxxx or better), show it by jumping to 4 of the suit.
With any other hand that has a singleton or void, bid 3 of that short suit.
If you have extra values (but no singleton or void), describe your strength and pattern by rebidding 3NT with a fairly balanced hand or 3 of your suit with extra length (a 6+-card suit).
For example, after you open 1S and partner responds 2NT, the meanings of your rebids are:
3C, 3D or 3H = Singleton or void in that suit.
3S = good 14+ pts. with extra length in your suit (or 19+ pts. if you're balanced), no singleton.
3NT = 15-18 pts., balanced (no singleton or void).
4C, 4D, 4H = Decent 5-card side suit (QJxxx or better).
Once responder has this information, he can decide how to proceed.
If he's not interested in a slam, he can just jump to game. If
he wants to explore further, he can cuebid a new suit to show
an ace. This requests opener to cuebid an ace.
(1) KJ832 A10764 A65 KQ5 10 872 A954 K7 Opener Responder 1S 2NT 3D 4NT 5H 6S
After responder uses the Jacoby 2NT, opener bids 3D to show his singleton. This is encouraging news for responder because it means his club and heart honors will fit well in partner's hand. Knowing that his xxx suit is covered by opener's singleton -- and that opener's outside strength is in clubs and/or hearts -- responder can use Blackwood to check on aces, and then bid his 24-point slam.
Note that responder would evaluate his hand very differently if
opener's answer to the Jacoby 2NT had been 3C or 3H. Singletons
in these suits wouldn't be helpful because responder's kings may
well be "wasted" cards opposite the singleton. Over
opener's 3C rebid, responder would just jump to 4S to show that
he no longer had interest in slam.
(2) QJ10543 AK72 AKJ 105 32 KQ54 K9 A62 Opener Responder 1S 2NT 3S 4C 4H 6S
Opener's 3S rebid denies a singleton, but promises a good (somewhat distributional) opener. Responder shows slam interest by cuebidding his club ace and opener cooperates by cuebidding 4H. This shows the heart ace and denies the diamond ace (since he'll cuebid his cheapest ace). Responder now knows that the partnership has extra values, control of every suit and exactly three aces. Since he doesn't need to use Blackwood (a grand slam is out of the question), he jumps to 6S.
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