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Suppose my RHO opens one of a minor. I can "overcall" in a major suit with a five card suit and a minimum of seven or eight high card points, provided that those points are concentrated in my suit. That's true even though my hand is weaker than my opponent's opening hand. Here I can plausibly fight for a part score (or a sacrifice) because I have a higher ranking suit to offset my weaker hand (depending on what each person's partner has).

If RHO bids one spade, I have to overcall at the "two" level. Since I'll have to take an extra trick, my guess is that I will need an extra trick (king) to overcall, bringing the required strength of my hand to 10-11 high card points), close to opening hand level, as well as a reasonably good five card suit.

But most of the literature I've read suggests that the above is not enough; that to overcall at the two level, one needs a six card suit* or a very strong five, say AKJxx or AQJTx (AQJxx is not good enough), and/or 12-13 high card points. Is this greater strength (versus the previous paragraph) necessary for a two level overcall, and if so why?

*On the other hand, my understanding is that if you are making a "jump" overcall with six cards (in a sequence of one minor, two spades), you can do so with strength approaching a "weak two" bid.

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Joe's answer gets to the most important reason for the difference.

In addition, there is also much more risk in overcalling at the two level. Opponents won't usually be able to double your one-level overcall for penalties. It is very rarely correct to defend a doubled contract at the one level (if you can take eight tricks in opponent's chosen suit, collecting 300 NV or 500 V, you can likely make at least game in your own strain). Also, the opponents usually have very little idea of their own side's assets, so they must communicate to their partner instead of trying to penalize opponents.

All this means that you are able to make one-level overcalls with worse hands, potentially helping partner to make a good lead or find a good sacrifice. On the other hand, it is more often possible to penalize a two-level overcall when opponents have stepped out of line, so your two-level overcalls should be strong enough to reduce this risk.

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The big problem with overcalls at the 2 level is you have a lot less room to stop before game, so it's harder to get to anything useful. Thus, it's important that partner have a good sense of your strength. If you could overcall with QT743 and 9 points 2H over 1S, or you could have KQT754 and 12 points and make the same call, how is partner supposed to know whether to pass or bid on with A32 A86 Q8432 T4? In the first hand you probably make at most 2H, and on the second hand you might have a decent shot at game, especially if you're short in diamonds, with something like K8 KQT754 K9 J85 or one of a number of other possibilities.

As such, 2 level overcall promises more, so that partner knows how to bid effectively. Different partnerships have different lines here - some will absolutely require 6, some will require a very good 5 or decent 6, some care more about points than others - but the point is that you want a better (smaller) defined range of possible hands, so you can get to the effective games more easily.

This focus on games is because that's where the actual value is in these overcalls. When you have the inferior suit, it's harder to compete for part scores - if this is a hand where opponents and you can both take 8 tricks, you're not going to end up with the contract unless opponents don't realize their strength. If you both have 20 points, then 1S-2H-2S-ppp isn't going to help you any.

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