Bidding 6NT on the hand partner usually holds

The problem

A small slam in notrump needs about 33 points between the two hands. Until now the app bid 6NT only when its own points plus the least partner’s bidding could hold reached 33. Partner seldom holds the least. A player who has heard partner open 1♣ and rebid 1♥ expects about 14 points opposite, not 12, and with 20 of their own would look for slam rather than stop in game.

What partner usually holds

This uses the same table as the keycard study: for every sequence of calls the app made often enough, the average strength of the hand behind it. The new rule adds that average to this hand’s high-card points at the moment the hand would otherwise settle in 3NT, in an auction the opponents have stayed out of.

Three lines tested

Each line was played on 200,000 deals and every changed deal was replayed 200 times with the unseen cards dealt afresh. “Points a changed deal” is what 6NT gained over 3NT on average, with its margin of error.

A higher line wins more on each deal it changes but changes far fewer deals. Over all deals, 31 gains the most: about 28,000 points per 100,000 deals, against 23,000 for 32 and 8,000 for 33.

Because the rule was chosen from these figures, it was then checked on a second, independent set of 200,000 deals:

On both sets 31 gains the most in total; the deals it adds beyond 32 average about 60 points each. With the owner’s own settings the results were the same in direction: +134 (±29) and +156 (±30) a changed deal at 31.

A correction after review

A review of the first version found that, after partner had bid notrump (a 1NT or 2NT rebid, or a natural 3NT), the rule judged partner’s maximum too high: it used a figure that adds a point for a suit contract, or no maximum at all after 3NT. So it could bid 6NT with one point less than the hand that makes the ordinary quantitative 4NT invitation. The rule now uses the top of partner’s notrump range itself (and 15 after a natural 3NT, which shows 13–15). Re-measured on both sets:

That keeps the total gain (about 29,000 and 32,000 points per 100,000 deals) and drops the bids that could not reach 33. Simply keeping the rule out of every auction where partner bid notrump was also tried; it gained less, because many of those slams are good ones.

Where the rule stays out

• After a strong 2♣ opening. Measured on its own, 6NT lost about 60 points a deal there: the 2♣ opener’s range is already known closely, and responder’s own slam invitations handle it.
• After a 1NT or 2NT opening. Those auctions have their own slam invitations based on the opener’s exact range.
• When the opponents have bid or doubled. The table was built from quiet auctions.
• When a setting changes what partner’s calls mean, as on the keycard study.
• When the hand lacks controls. As for any direct 6NT, it needs two aces, or an ace and a king, or three kings.
• When a major has been bid and raised. A known major fit goes through keycards in the major instead.

What BidMaestro does with this

After a one-of-a-suit opening, in a quiet auction, a hand about to settle in 3NT (or to pass partner’s 3NT) bids 6NT when its high-card points plus the strength partner usually holds after this auction come to 31 or more, and the top of partner’s range, counted for notrump, still allows 33 between the two hands. Dubois’ Bidding Notes puts the small-slam line for notrump at about 33 points; this rule reaches it by expectation instead of by guarantee.

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