Showing a control after partner’s splinter

The question

With a splinter, opener shows four-card support for partner’s major, a singleton or void in the suit bid, and a strong hand: for example 1♦–1♠–4♣. Responder can sign off in four of the major, ask for keycards, or show a control below game (an ace, king, singleton or void) as a slam try. The sources say to show a control “as long as slam is possible”, but give no strength for it. How strong should responder be?

The deals

The app dealt 960,000 deals at random and bid them on three settings: the default, every convention switched on, and one club player’s own settings. Opener splintered on 2,825 of them. Each deal that any of the rules below bid differently was played 200 times, with the opponents’ cards redealt each time and all four hands visible. The three settings gave almost identical results; the figures below are for the default settings.

The results

Each row is compared with never showing a control. Every rule gains, because a control bid finds slams that a sign-off misses. Comparing each rule with its neighbour, on the deals where the two bid differently (the “±” figure is the margin of error; a difference smaller than it counts as no difference):

• 13 against 15: 13 is better by 125 ± 36 points a deal, on 89 deals. It does better on 36 of them and worse on 51, but its gains are the larger ones.
• 12 against 13: no difference. 12 is ahead by 22 ± 30 points a deal on 99 deals, which is within the margin of error, and 13 does better on more of them (65 against 28, with 6 the same).
• 10 against 12: 10 is worse by 137 ± 27 points a deal, on 137 deals.
• Any hand against 12: worse by 156 ± 20 points a deal, on 202 deals.

The control bid itself costs nothing below game. The loss with lighter hands comes afterwards: opener, hearing a control bid, asks for keycards and reaches the five level or a slam that the combined hands cannot make.

Counting the control bid

A control bid at 13 or more support points also tells opener something: that responder holds at least 13. Counting it that way when opener places the contract after a keycard reply made the 13 line better again: +49,381 points on the 2,825 deals, against +45,995 without the counting. Against the old rule (15 or more), this version gains 153 ± 35 points a deal on the 95 deals where the two bid differently. With the control bid counted, 12 against 13 is still no difference (39 ± 35 points a deal on 99 deals).

What BidMaestro does with this

After opener’s splinter, responder asks for keycards when it can do so safely. Otherwise, with a top trump honour and 13 or more support points, it shows its cheapest control below game; with fewer it signs off in four of the major.

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