Thanks for your advice about hand-evaluation. Do you have any other good tips? I used the range "6-12 HCP" as an example, because those were the range and metric used in the original post. Regardless of whether your method of hand-evaluation is HCP, an estimate of how many tricks your hand is worth, or the Diego Garcian Special Potato Count, the point is the same. As responder's range widens, either you split his range more ways, or you lose accuracy. When you make up numbers to support a argument, you could at least take the trouble to check that they do, in fact, support your argument. If we accept these figures, when you're vulnerable bidding has an expectation of 11 * 0.25 - 5 * 0.5 = +0.25. Non-vulnerable you'd be right, though: 7 * 0.25 - 4 * 0.5 = -0.25. And I've no doubt that if you make up some more numbers for the frquency of being doubled or going two down you'll be able to "prove" your point. But I don't accept your figures anyway. In the context of ArtK's "6-12" raise with the opponents silent, if you only move on a hand which would move opposite a standard raise, you will miss game at least as often than you go down at the three level and would have been allowed to go plus at the two-level.