There are several situation in bridge where a pass can be forcing. There's the forcing pass bidding system in which you pass as dealer with all good hands and bid something with bad hands. That system is illegal in most duplicate bridge games.
A forcing pass situation occurs more frequently in normal bidding when your side has bid a game and the opponents have taken a sacrifice, or at least what appears to be a sacrifice. In an auction such as 1H-3D-4D-P; 4H-P-P-5D; P here by opener is forcing. Opener's side has bid game with the intentions of making it (The cuebid of 4D indicates strength and heart support whereas 3H and 4H would not have shown as much strength), so we have to either double them or bid again. How do we decide what to do? With my regular partners, we tend to double with hands that do not think 5H has much chance to make, usually based on slow values or lots of values in the opponents' suit. We bid again with particularly distributional hands. We pass with hands where we don't have a strong opinion either way - more or less an average hand for the auction so far. We also pass with hands that are interested in slam. This pass and pull (pass 5D now but then pull partner's double to 5H) shows interest in slam and probably first round control in the opponents' suit.
Since slams can often be made on much fewer than 33 points with such distributional hands, it is often useful to have a way to distinguish between bidding 5H to make and bidding 5H as an invite to 6. But we must know for sure that a forcing pass situation in in effect. As a general rule, passes in direct position are forcing when we have bid game and expect to make it and the opponents take another bid. In the auction 1H-1S-3H-3S; 4H-4S-P, this pass is not forcing for responder has not shown any values. 3H was a preemptive raise so if responder does have some good defensive values, he needs to double to show that because opener will not be expecting responder to have any defensive values. A situation that is a little ambiguous is if the auction starts 1H-1S-2S where responder has made a limit raise and opener has declined to accept the invitation to game. If the opponents later bid 4S, is passing over 4S by either partner forcing? I think so, but many good bridge players think it wouldn't be forcing because we never bid game or were in a game forcing auction. My thinking is that this is a very distributional hand for the opponents to be sticking their neck out at 4S when we have announced that we have over half of the high cards. So, if they can make 4S, surely we can make something so we must double to protect what we could have made or bid on to 5H.
Forcing passes may also occur after a 1NT opening is doubled for penalty. Many strong notrumpers play stayman and transfers on after their 1NT is doubled in direct seat, but when responder has a balanced yarborough, it can be very difficult to find a playable suit. I am a big fan of weak notrumps and the following runout structure, and I don't see why usign the same structure over strong notrumps wouldn't work well. We will assume an 11-14 1NT range. After 1NT-X:
Pass = forces redouble to sign off in 2C or 2D or 2H (with a 5 card suit) or leave 1NTXX in (with 9+hcp)
XX = please bid your lowest ranking 4 card suit. I have no desire to play 1NTX with 4333 shape or possibly 4432.
2C = 4-4 in clubs and another suit. opener passes with 3+ and bids 2D with a doubleton.
2D = 4-4 in diamonds and a major.
2H = 4-4 in the majors
2S = to play
You will almost always be able to find at least a 4-3 fit and be relatively safe if the opponents double again. Knowing your runout system is crucial when playing a weak notrump because all too often you will open a flat 12 and catch partner with a flat 3 count and desperately need to escape to a better contract.
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