Gambling 3N is a hand with a solid 6-8 card minor suit and stoppers in 0-3 side suits. Both of these numbers depend on partnership agreement.
Responder's bids
With a weak hand:
Pass with stoppers in three suits; otherwise - 4 and opener will pass or correct to 4.
With a strong hand:
4 asks opener to bid his singleton or void, if any.
Opener's replies:
4 = a singleton or void in the major bid. 4N = 7222 shape. 5 = short Diamonds if Clubs is his suit. 5 = short Clubs if Diamonds is his suit.
4N = A in 2 suits and A or KQ in a 3rd suit plus an extra sure trick.
Opener bids slam with an 8+ card suit.
Is it worth it?
The following comments have surfaced on BridgeBase.com (no kin to CardShark Bidbase).
While the convention calls for partner to leave 3N in with the 3 side suits stopped, most people expect just 2 stopped and hope defenders choose the wrong lead, hence the "gambling". After all, if partner has all side suits stopped and opener has 7 running tricks, where's the gamble?
Another idea is for opener to bid 3 for a gambling 3 notrump. Partner can bid 3N with a suitable hand or run to 4, etc. This right-sides the contract, but it takes away preempts in Spades on the 3 level.
A minority say that hands suitable for Gambling 3N come up fairly often.
The majority say that such hands rarely come up. Some have tried for years. On the other hand, 26-HCP hands for a natural 3N rarely come up either.
3N can be used to show a strong 4 preempt. (Responder bids 4 and opener passes or corrects to 4.) It's hard to see the need for this. There's a big advantage if a minor suit preempt can be converted to 3N, but not so much of an advantage in converting a major suit preempt to 3N, plus Namyats is good for major suit preempts.