Partner opens a strong notrump, say 15.0 to 17.5 (see previous blog for discussion of half points adjustments.) When should you bid game? When should you pass? When, if ever, should you invite? These questions have been given various answers in various bridge-playing countries over the years, and depend upon the relative skill level of declarers and defenders and the form of scoring.
What most players neglect in deciding to try for 3NT is the considerable risk that 2NT will go down, or go down more tricks than 1NT. The classic advice to invite with 8 or 9 and opener accepting with "a max" is, in fact, worse than a pass-or-bash strategy of bidding game with 9 and passing with 8, even though that means you sometimes play 1NT with 25 and sometimes 3NT with only 24. The secret is you never play 2NT, the biggest matchpoint-losing contract in bridge. Slightly better than pass-or-bash is (for a typical declarer, in a matchpoint game) to invite with 8.5 to 9.0 and opener accepts with 15.5 or better, i.e., anything but a dead minimum. This agrees with the conclusions of a classic Bridge World article: "invite rarely, accept often." If partner invites with the standard 8 or 9, opener does best to accept with 16.0 or better. If opener never downgrades an ugly 15 and often upgrades 14 (due to a five card or a couple of tens or because he likes bidding notrump), invite with 9 to 9.5 and pass with 8.5 or less.
What if you use 2NT artificially, such as a transfer to diamonds? Then I have a very strong piece of advice: if you don't have interest in a major suit, use pass-or-bash. The gain from inviting is only the difference between around a 49% and 52% matchpoint expectation, for specifically 8.5 points for responder; just an occasional lead-directing double of 2C, plus the information you give the defenders about opener's hand, will more than wipe that out. Therefore, a sequence like 1NT-2C-2H-2NT ought to promise a four card spade suit, even if 1NT-2NT would have been artificial.
Messy details (most players can ignore):
Combining information from double-dummy analysis (from several sources) with some real-world data from Richard Pavlicek, I developed a complex spreadsheet to analyze this for specifically matchpoint bidding. The important thing was to set up a "field", i.e., decide what players at other tables were likely to do. I used the well-known advice given in most American textbooks: with no interest in a major suit game, bid 3NT with 10 hcp (15-17 +10 = 25-27), bid 2NT with 8 or 9 (giving us 23 to 26 total), and pass with 7 or less. Later experimentaton showed that the results below were not very sensitive to what strategy the field was using.
The data suggests that each additional high card point adds about 19% to our chances of making 3NT. As that is a fairly large swing, I interpolated the data to half-points, so each half point adds 9-10% to our chances. (Did you realize a Ten could be the difference between a poor 45% chance and a fair 54% chance?)
Double dummy, here's your chances of making at least 8 or 9 tricks at notrump:
Combined HCP: 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0
8+ tricks: 57% 67% 78% 82% 87% 91% 94% 96% 98%
9+ tricks: 21% 31% 41% 50% 59% 68% 76% 81% 86%
Now, it is well known that real-world declarers make 3NT significantly more often than double-dummy analysis suggests. Here's the same table, with the assumption that declarer makes an extra trick about 10% of the time (for percentages close to 50%.) This seems to be in line with RP's real-world data:
Combined HCP: 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0
8+ tricks: 62% 71% 80% 85% 90% 91% 95% 96% 98%
9+ tricks: 25% 35% 45% 54% 64% 71% 78% 83% 87%
So a typical declarer will show a slight loss playing 3NT with 24.0 hcp and a slight gain with 24.5 (there's that Ten!) However, reaching at least 2NT with 24.0 to 24.5 will cost you the 15-20% of the time 2NT fails; this will more than wipe out any gain you achieve from bidding thin 3NT's. Matched up with a field that is mostly following the normal "Invite 8 or 9" strategy, the biggest gain from inviting comes with 8.5, opener accepting on anything but a bare 15.0. Passing with 8.5 earns an average of 48% of the matchpoints, bidding 3NT earns 49%, and inviting earns 52%.
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