Responding to partner's 1NT opening is usually a fairly mechanical process, but there is some room for judgment, especially with marginal hands: should you stretch the bounds of your bidding system in an effort to improve the contract, or go quietly in 1NT? Two typical dilemmas are deciding whether an 8-point hand is worth a raise to 2NT, and deciding whether to risk Stayman on a hand like xx Kxxx xxx KJxx where you'd like to find a 4-4 major fit if one exists, but dread having to rebid 2NT and possibly get raised to 3 if you don't find a fit.

I have previously written about this, and said that with 8HCP, you should pass if 4333, pass with 4432 if both 4-card suits are minors, and a 4432 with 1 4-card major was a borderline decision. My regular partner and I have also been experimenting with an agreement that 1NT-2-2any-2NT shows a 5-7HCP hand that wanted to explore a 23-point game in a major but refuses to try 3NT. We've benefited from finding additional 4-4 fits, but our results at the table have been inconclusive about the wisdom of staying out of game.

This study of double-dummy results implies that my experimental treatment may be flawed -- that those 23-HCP major suit games don't happen as often as I thought they did. Instead my results point toward responding 2 and dropping opener in his major much more often than I expected. More on that below, and in my companion article on responding 2 intending to pass no matter what partner's response is.

Before we plunge into the math, our assumptions:

- Opener's 1NT range is 15-17HCP. A 5-card major, 5422 pattern, or a 6-card minor
*is*allowed. A singleton ace or king is*not*(always balanced or semibalanced.) - The opponents always pass.
- Responding to Stayman, opener responds 2 if he has both majors.
- We do not search for 5-3 fits where opener has the 5-card major (though we might occasionally play in them, if responder drops opener in what looks like a 4-3 fit.)
- 1NT-2-2any-2NT is invitational to game in notrump; 1NT-2-2M-3M is invitational to game in the major. We will compare several different responding styles. After an invitational 2NT rebid, we consider:
- A) Opener always passes
- B) Opener goes to 3NT with 17
- C) Opener goes to 3NT with 17, or with 16 and a 5-card suit
- D) Opener goes to 3NT with any 16 or 17
- E) Opener always goes to 3NT.

- A) Opener always passes -- actually, we consider "responder never raises to 3M".
- B) Opener goes to 4M with 17
- C) Opener goes to 4M with 17, or with 16HCP and a doubleton
- D) Opener goes to 4M with any 16 or 17
- E) Opener always goes to 4M.

Textbook advice is close to "C." Real-life expert practice is closer to "D" (with some good 15s upgrades and some bad 16s downgraded.) Future simulations could, in principle, encode a detailed upgrading/downgrading procedure; in the major-raise case I intend to investigate LTC-based raises eventually. For the present, accept the methods given above as a limitation of the study. (One of the big lessons of *all* studies of this type is how ineffective HCP are for making close decisions.)

We will investigate both matchpoint and IMP expectation of bidding on vs. passing out 1NT.

If responder has no 4-card major, obviously we are not seeking a major fit, and our decision is solely whether to pursue the game bonus for 3NT.

If responder has one 4-card major, we will have a 4-4 fit in it about 32% of the time; if responder has two 4-card majors, we will have a fit in one of them about 56% of the time. (The exact percentage varies by about 1% depending on responder's exact shape. It would also change slightly if we changed our rules about allowing 5-card majors and 6-card minors in a 1NT opening.)

We expect to see our largest gains when we succeed in finding a fit. It may be profitable overall to use Stayman if we gain when we find a fit but suffer a small loss when we don't.

Without a 4-card major, **up to and including 8HCP, never raise to 2NT.** The only possible exception is vulnerable at IMPs, where raising with the 3352 and 2254 8-counts is about break-even if opener is using rule "D" (accept invitation with any 16 or 17).

**With 9HCP, simply bid 3NT.** Inviting to 2NT shows a profit with all balanced shapes if you accept often enough, but "always accept" shows the largest profit of all ... ergo, just go directly to 3NT as responder, and find a better use for the 2NT response (or, at any rate, a better question to ask opener than "do you have a maximum or minimum point count?" if you want to invite game.)

If you've been in the habit of responding with 8HCP, here's how much you have been costing yourself, compared with passing out partner's 1NT -- a quarter of a board at matchpoints, and at least half an imp a board at teams (MP percentages are good to ±1% at the 95% confidence level; IMP estimate precision as indicated):

Shape | Acceptance style | Matchpoints: | IMPs: | |||
---|---|---|---|---|---|---|

P(gain) | P(loss) | Net | Net NV | Net Vul | ||

3343 | B | 13% | 37% | -24% | -.66±.06 | -.54±.10 |

3343 | C | 13% | 37% | -24% | -.68±.06 | -.57±.10 |

3343 | D | 25% | 49% | -24% | -.62±.09 | -.22±.13 |

3244 | B | 13% | 39% | -27% | -.73±.06 | -.65±.10 |

3244 | C | 13% | 39% | -26% | -.68±.06 | -.57±.10 |

3244 | D | 25% | 51% | -26% | -.68±.09 | -.32±.13 |

3352 | B | 14% | 39% | -25% | -.63±.06 | -.50±.10 |

3352 | C | 13% | 38% | -25% | -.61±.06 | -.50±.10 |

3352 | D | 27% | 50% | -23% | -.47±.09 | .00±.13 |

2254 | B | 13% | 41% | -28% | -.74±.06 | -.69±.10 |

2254 | C | 13% | 40% | -27% | -.67±.06 | -.60±.10 |

2254 | D | 25% | 51% | -26% | -.61±.09 | -.26±.13 |

And if you've only been inviting with 9HCP, notice the extra gains you were missing out on (compare line "E" with the appropriate invitational style.) If you *do* only invite, the standard advice to accept aggressively is good advice; but "always accept" is worth another half an imp per board vulnerable.

Shape | Acceptance style | Matchpoints: | IMPs: | |||
---|---|---|---|---|---|---|

P(gain) | P(loss) | Net | Net NV | Net Vul | ||

3343 | B | 17% | 20% | -3% | .22±.06 | .68±.10 |

3343 | C | 17% | 19% | -2% | .28±.06 | .77±.10 |

3343 | D | 35% | 31% | +5% | .73±.09 | 1.78±.13 |

3343 | E | 51% | 49% | +2% | .67±.11 | 2.08±.16 |

3244 | B | 16% | 23% | -7% | .08±.06 | .49±.10 |

3244 | C | 17% | 23% | -6% | .12±.06 | .55±.10 |

3244 | D | 35% | 34% | +1% | .63±.09 | 1.61±.13 |

3244 | E | 50% | 50% | +1% | .64±.11 | 1.96±.16 |

3352 | B | 17% | 22% | -5% | .18±.06 | .62±.10 |

3352 | C | 17% | 22% | -5% | .21±.06 | .67±.10 |

3352 | D | 34% | 32% | +3% | .70±.09 | 1.71±.13 |

3352 | E | 52% | 48% | +4% | .67±.11 | 2.25±.16 |

2254 | B | 16% | 27% | -11% | -.06±.06 | .28±.10 |

2254 | C | 16% | 27% | -11% | -.04±.06 | .31±.10 |

2254 | D | 35% | 35% | 0% | .61±.09 | 1.59±.13 |

2254 | E | 50% | 50% | +1% | .67±.11 | 1.98±.16 |

For the moment we are assuming that responder intends to rebid notrump if no 4-4 major fit is found. (With weaker hands, a Stayman response intending to pass any rebid from opener may be correct, as discussed here.)

Once again we find that the invitational sequences are not very useful. This surprised me in the case where we do find a fit; I intend to revisit this question, with some kind of suit-oriented invitation criterion (LTC for instance). But, as the results currently stand--

**With 8HCP at matchpoints**, the best results were to **pass with 4333; with 4342, 4144, or 4252, use Stayman, but if you find a 4-4 fit, always pass 2M**, never raise to 3M to invite game in the major. **At IMPs**, the best results were **with 4333 or 4342, use Stayman and pass 2M if you find a fit; with 4144 or 4252, use Stayman and jump to 4M if you find a fit.** In both cases, most profitable results after 1NT-2-2any-2NT were those using acceptance rule "D", raise to 3NT with any 16 or 17.

**With 9HCP at matchpoints**, the surprising result was to always **use Stayman, and leap to 3NT if you don't find a fit, but pass 2M if you do.** At IMPs, use Stayman, leap to 3NT if you don't find a fit; if you do find a fit, **pass 2M with 4333 or 4342 shape, leap to 4M with 4144 or 4252 shape.**

**With 7HCP**, Stayman showed a nice profit if a major fit was found, but the loss in 2NT/3NT was always too large for "bidding as if you had 8HCP" to ever be profitable. (Stayman followed by passing any rebid, however, is profitable with 4342 shape.)

Notice that, unlike 1NT-2NT, the invitational 1NT-2-2any-2NT sequence is actually correct with some 8HCP hands, and gains vs. the alternative of having to choose between 1 and 3 (about 10% at matchpoints, 0.5 IMPs NV, 1 IMP vul.) This is not proof that this is the *best* meaning for 1NT-2-2any-2NT, just that it isn't a completely idle bid.

Reproducing all the calculations that produced the above rules would take a lot of space. To illustrate the method, we show full results of the analysis of the case when responder has 4-2-4-3 shape. We simulated 10,000 deals where a major fit was found, and 10,000 deals where it was not:

Fit? | Acceptance rule: | MP net | IMP NV net | IMP Vul net |
---|---|---|---|---|

No | A | -0.26 | -0.90 | -1.17 |

No | B | -0.21 | -0.49 | -0.31 |

No | C | -0.21 | -0.51 | -0.33 |

No | D | -0.22 | -0.50 | -0.04 |

No | E | -0.30 | -0.96 | -0.49 |

Yes | A | 0.64 | 1.51 | 1.65 |

Yes | B | 0.37 | 1.06 | 1.42 |

Yes | C | 0.39 | 1.06 | 1.38 |

Yes | D | 0.21 | 1.11 | 1.76 |

Yes | E | -0.11 | 0.47 | 1.18 |

Having separately determined that we will find a fit 32% of the time, we take a weighted average of the fit and no-fit cases to decide whether responding 2 is better than passing 1NT or not. We see by inspection that responder should pass 2M if he finds a fit -- "Rule A" is far better than the alternatives, except vulnerable at IMPs -- but if 1NT-2-2any-2NT is going to be invitational, in the no-fit case, we have to consider which acceptance rule our partner is likely to use. Fortunately rules B, C, and D do not have wildly different expectations. As noted above, D is closest to current expert practice. So, using Rule D in no-fit situations and passing 2M in fit situations, bidding 2 with a 4-2-4-3 8-count...

- .32 x (+.64) + .68 x (-.26) = +.028: gains matchpoints 2.8% more often than it loses matchpoints vs. someone passing 1NT
- .32 x (1.51) + .68 x (-0.50) = +.14: gains 0.14 IMPS vs. someone passing 1NT not vulnerable
- .32 x (1.65) + .68 x (-0.04) = +.50: gains 0.50 IMPs vs. someone passing 1NT vulnerable

When responder is 4-4-4-1 or 4-4-3-2, the same method as above is used, except that we now have a 56% chance of finding a fit and a 44% chance of returning to 2NT or 3NT.

This, as it turns out, makes no difference to our strategic recommendations for 8 and 9HCP hands above: we already recommended using Stayman on all the 8-point hands with two 4-card majors, and our advice about raising vs. signing off in partscores will also remain the same. All that has changed is the expected size of our profit, given the increased probability of a fit. For a 4-4-2-3 8-count, for instance, .56 x (+.64) + .44 x (-.26) = +.24, making this a clear winner at matchpoints, compared to the 4-2-4-3 hand which was barely better than breakeven.

The increased chance of finding a 4-4 major fit means that it *is* profitable to use Stayman on a 7-HCP hand with two 4-card majors, and with 7HCP, returning to 2NT is better than passing 1NT-2-2 unless you also have 4 diamonds (4-4-1-4, 4-4-2-3, and 4-4-3-2 hands rebid 2NT while 4-4-4-1 and 4-4-5-0 should pass 2.) The same is true with 6 HCP and 4-4-1-4 or 4-4-2-3 shape -- but beware that you are making this bid *expecting* to suffer a large loss if you play notrump - just not quite as large of a loss as if you played in a five- or six-card diamond fit.

*If* you choose to use Stayman on those 6- and 7-HCP hands with two 4-card majors, you might also agree to define 1NT-2-2-2NT as "not invitational, opener must pass" to minimize your loss on the notrump hands. (You will wish opener was using "Rule D" when you hold 8 points, but not when you hold 6 or 7. 1NT-2-2M-2NT will always be 8, so you might still play that as invitational, but 1NT-2-2-2NT will more often be weak.) A better alternative is "Garbage Stayman," agreeing that 1NT-2-2-2 is a weak hand with both majors scrambling to play a 4-3 fit. This is another nonstandard but profitable agreement: as we've seen, there isn't much value in devoting a special bid to show the invitational-strength hands, and there is a *lot* of value in playing even a 4-3 major fit when responder is very weak.

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This page last updated 05.01.10

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