Research
A study of 100,550 deals. At a slam decision, count the hand partner’s bidding usually holds instead of the least it could hold: with a major agreed, ask for keycards at 30 expected points and 12 or fewer expected losers between the two hands.
Until now every slam decision in the app added its own hand to the fewest points partner could hold for the calls made. A partner who opens 1♠ promises 12 points, so a 17-count opposite that opening counted 29 and no more, and the app moved towards slam only when partner was guaranteed to hold the values. A player does not bid that way. Opposite an opening bid a player assumes partner holds about 13 or 14, because that is what an opening bid usually is, and bids on when the expected total is enough.
The app bid every deal in the sample, so the sample shows exactly which hands lie behind each sequence of calls. For every sequence seen 30 times or more (920 of them), the average strength of the hand that made the last call was recorded. A few examples:
| The calls so far | Hands | Average points | Average losers |
|---|---|---|---|
| 1♠ | 7,558 | 13.4 | 6.1 |
| 1♠ – 3♠ (the limit raise) | 354 | 9.7 | 7.9 |
| 1♠ – 4♠ (the weak jump raise) | 78 | 5.6 | 8.5 |
| 1♦ – 1♥ – 1♠ – 4♠ | 55 | 11.7 | 6.7 |
| 3♥ (a pre-empt) | 384 | 8.2 | 6.6 |
| 2♣ – 2♦ – 2♥ – 3♣ – 4♥ | 34 | 21.2 | 3.4 |
The 1♠ opening is the plainest case: the minimum it promises is 12, and the hands behind it average 13.4.
The rule tested was “my own points plus the points partner’s calls suggest reach the line”. It was scored at every point where a player made the side’s last bid, or passed partner’s last bid out, against what the app actually did. “Slam is sound” is the share of those decisions where the small slam made on at least three-quarters of the redeals, and “points a deal” is what bidding the slam gained over the contract the app reached.
| Rule | Applies | Slam is sound | Points a deal | App bid slam |
|---|---|---|---|---|
| 29 points | 668 | 46% | +162 | 6% |
| 30 points | 327 | 58% | +253 | 8% |
| 31 points | 166 | 66% | +289 | 13% |
| 32 points | 82 | 82% | +348 | 21% |
| 30 points and 12 or fewer expected losers between the hands | 175 | 66% | +313 | 11% |
| The slams the app already bid at these points | 100 | 44% | — | 100% |
Thirty points with twelve or fewer expected losers between the two hands is as reliable as the slams the app already bids, and it applies on deals where the app bid slam only one time in nine.
With a major agreed and the opponents silent, a hand about to settle for game asks for keycards when its own points plus the points partner’s calls suggest reach 30, and the expected losers between the two hands are 12 or fewer, provided it can stand any reply at the five level. The keycard count then decides the slam, exactly as it does when partner’s promised minimum reaches the line.
On the sample this changed 18 auctions: nine small slams, all of which made, and nine stops at the five level after a reply showed a keycard missing, seven of them a trick short. That is 168 points a changed deal, with a margin of error of 81.
The table of averages is built from the app’s default settings. Where a setting changes what a call means, as a Bergen raise or Reverse Drury does, or where switching a convention off changes the strength a call promises, as happens to a two-over-one when Jacoby 2NT or splinter bids are off, the rule stays out of the auction and partner’s promised minimum decides as before.
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