[bravejason]

Playing SAYC or similar, the bidding begins 1 minor - (1 suit) - 1NT . By 1 suit, I mean an overcall at the one level in any permissible suit. What sort of shape and strength should 4th seat have in order to bid assuming 4th seat does not have the support necessary to raise partners overcall? What is the meaning of double?

I left the bidding generic because I’m interested in the general bidding principles for this type of auction.

[HardVector]

This sequence will tend to deny holding any 4 card suit between the overcall and nt. It will tend to deny holding any 4 card major that is not biddable by the failure to make a negative double; i.e. 1m-(1s)-1n tends to deny hearts. It will show a slightly better hand than is normally required. Normally you need 6-9 to bid nt (6+ in 2/1), here you should now have 8-10. You must have values in the opponent's suit. Partner with a good hand should not have to guess whether to bid 3n or not because THEY don't have anything in their suit. You may be concealing a fit for partner's minor. This is where you should use some judgement. When deciding to bid nt or raise partner's minor, the things to consider are how good is your holding in the opp's suit and overall how good is your hand?

So, holding KQxx xxx Axxx xx and hearing 1d-(1s)-? You first look for a negative double, not there. Holding good spades and appropriate values tend to bid nt. Change this to Jxxx xxx AKJx xx and I would raise diamonds. Now the spades are not quite good enough. Change again to KQxx xxx Jxxx xx, and again I would raise diamonds. Here you don't have the values to bid 1n (you should be 8-10).

This is all by partnership agreement, and may be contrary to some people's teachings. By the way, the "tends to" remarks allows you to use your judgement in making these decisions. If you hold 9xxx KQxx Axx xx and it goes 1d-(1h)-? You may not want to introduce that spade suit and highlight your heart holding by bidding 1n instead of making a negative double.

EDIT: Sorry, misread the question.

[Stephen Tu]

I think bravejason was asking about advancer's (4th seat) actions, not the 1nt call by responder to the opening.

In any case, new suit should be long and shapely, something that expects to do better declaring than defending.
Double is up to partnership agreement, personally I like it as a responsive double showing the unbids typically 5-5. (responder often has not other major from failure to bid it / negative double and some degree of minor fit for opener, so good to get the other major in picture if it's our side that has it)

[apollo1201]

Same as Stephen.

Given that opener, partner and responder each found a bid other than pass, the likelihood that you have enough to penalty-X opponents’ NT is quite small (unless you play with a 50-points deck, or unless each of them is at the lower range of their bids, but even in that case, points would be close to 20-20 around the table).

So the free X bid can be used to show the 2 other suits, 55 preferably or more, to avoid misfit issues as much as possible. Opponents bid NT and advertised values, so could X for penalties any soon. Min strength 6-7 concentrated values with good suit texture if min.

2-level bids should show a 6-cd suit and deny fit for partner.

[bluechip10]

I feel that double can be used in two ways. One, if one doubles, it would deny top honor (Q, K, or A), but show at least 3+ support. Direct raise would show 3+ and a top honor.

Another way: treat it as a support double.