Opener bids one of a major and Responder does not have a fit
Some thoughts on what each partner is trying to do
So far, the partnership has had a fit right from the beginning. That allowed both partners to use some very precise bids to tell each other about their point counts: a weak hand (with or without a fit), a minimum response with a fit, an invitational response with a fit and a game-forcing response with a fit.
When the partnership doesn't have a fit the partnership has to make bids which not only tell what kind of responding hand they have, but also they have to try to find out where the partnership might have game (if the partnership has enough points, of course). There are some generalizations which help you think about what to bid and then there are some specific things that Standard American-Yellow Card uses (mainly the Standard American part of it).
When you don't have a fit for partner, you should attempt to let her know your point range first. Although you won't have a lot of choices, the ranges are the same as if you had a fit. Remember that a weak responding hand has 0 to 5 points with 10 or more losers, a minimum responding hand has 6 to 9 points with 9 or so losers, an invitational responding hand has 10 to 12 points with 8 or so losers, and a game-forcing hand has 13 or more points with 7 or fewer losers. So as far as points go, you have already learned these ranges. However since you don't know if the partnership has a fit, do not add support points. [Support points are only added when you know the partnership has a fit.]
While telling her about your point range, you should attempt to tell her something about your hand. This might be cards in the other major suit or cards in a minor suit (trying to find out if NoTrump) is possible. You continue the search for the best contract for the partnership.
Sometimes you will be able to accomplish some of both tasks with one bid. Sometimes you will not. If you cannot do both, make sure you tell your partner the truth about your points. That way the partnership can stop bidding if the partnership doesn't have enough points for game.
Lastly, if it becomes obvious to you that the partnership's hands don't have a fit anywhere and don't have enough points for game, you should do your best to stop the bidding in the closest suit that might work. You might "stop" in a suit where you're pretty sure that the partnership has only seven cards. You might "stop" in 2NT because you think that the partnership doesn't have enough points for game even though you have stoppers in all the suits.
Opener in her rebids will also be trying to do the same things: telling you her point range, telling you about what suits she holds (and stoppers if she has them), and trying to stop when the partnership doesn't have enough for game or doesn't have a fit.
Some specifics about bids after your partner has opened one of a major
First, any non-PASS from you means that you have at least 6 points. Unless the bid puts a top range on your hand, you could have as many as 27 points. But you can't have anything less than 6. If you have 0 to 5 points (with 10 or more losers), you should PASS even though you know the partnership doesn't have a fit. So with the following hand, after partner opens 1♥
♠87432 ♥void ♦T742 ♣Q953
you should PASS. You don't expect partner will be very happy with your hand if everyone else PASSes [which is unlikely, believe it or not]. But partner will not be much happier than if you bid 1♠ and she bids 2♥ which you regretfully PASS [stopping since you know game is impossible and you have no idea what suit the partnership has a fit in, if any.] If everyone PASSes in this case (somewhat more likely) she'll have to take an extra trick (2♥ requires her to take 8 tricks while 1♥ requires her to take 7 tricks). Your hand is unlikely to be of any help.
So with a weak responding hand you should PASS even if you have a void in your partner's suit.
Second, any suit bid at the 2-level shows at least an invitational hand or more (10 or more points with 8 or fewer losers). [Some bids show much more than this.] So if your partner opens 1♠ and you bid 2♣, you have just told partner that you have 10 or more points with 8 or fewer losers (and that you hold at least four clubs in your hand).
Suppose your partner opens 1♥, your right-hand opponent PASSes and you hold the following hand? What do you do now?
♠ KQJ84 ♥T4 ♦T73 ♣876
You have seven points (six for high cards and one for length in spades) so you shouldn't PASS. You don't have a fit for partner's hearts, so you can't use any of those responses. But you can bid 1♠! You didn't bid spades at the 2-level so your partner will not be expecting you to hold more than six points. And you were able to tell her about your spade suit. Very nice and convenient!
What do you do with the following hand after your partner opens 1♠ and your right-hand opponent PASSes?
♠T4 ♥KQJ84 ♦T73 ♣876
You still have seven points so you shouldn't PASS. You don't have a fit for partner's spades, so you can't use any of those responses. You want to bid hearts, but you'll have to bid 2♥ to do so and that would be telling your partner that you have 10 or more points. You mustn't do that. It sure seems like you're stuck. That's ABSOLUTELY correct! You have only one bid you can make: 1NT! This may seem to be too many lies to be telling: you don't have a stopper in either clubs or diamonds. True, but your partner knows that you have 6 or more points (since you didn't bid) and fewer than 10 points (or sometimes 10 points if it's a 'bad" 10 points) since you didn't bid something at the 2-level. So she'll know quite a bit about your hand even though she has no idea that you have those nice hearts. The point is that you've told her the truth about your points first and she will have some idea of whether a game is possible or not.
Finally, suppose your partner opens 1♥, your right-hand opponent PASSes and you hold the following hand?
♠T73 ♥T4 ♦KQJ84 ♣876
You don't think the partnership has a heart fit, you don't want to tell her about spades, you have seven points and you'd love to bid diamonds if you can. Unfortunately, the lowest diamond bid you can make is 2♦ which lies about your points. So you're stuck again! 1♠ lies about your spade suit (and lying about major suits is not good) and you can't bid anything at the 2-level. So, guess what? You'll have to bid 1NT with this hand too! You shouldn't be happy about it. But that's all that's left.
So with a minimum responding hand you will bid a suit at the 1-level if you hold that suit [actually, you only have to hold four cards in the suit]. If not, you will make the least possible lie (very often 1NT).
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