Research
A study of 100,550 deals on how strong a partnership must know it is before asking for keycards, and before bidding a slam with one keycard missing: 29 and 27.
In this article, the partnership’s known strength is your own points plus the fewest points partner’s bids have promised. Your own points are high cards plus shortness in the side suits, with the shortness capped by your number of trumps. Partner’s bids count at their lowest: a weak two as 7, a one-level opening as 12, a 1NT opening as 15 and a limit raise as 10, although partner will often hold more.
Asking for keycards commits you to the five level. If partner shows too few, you must stop in five of your suit, and five never scores more than four: it can only go down where four would have made. So an ask needs three things: an agreed fit, a safe stop at five whatever the reply, and a real chance of slam.
Whether five is safe depends on points. Our sources give the five level “around 29 points”. BidMaestro tested 27, 28, 29 and 30 as the known total needed to ask. How each result was scored is described at the end of this article.
| Ask when known is at least | Deals where the bidding changed | Per deal, actual cards | Per deal, re-dealt hands | Sign-offs in five that went down |
|---|---|---|---|---|
| 27 | 1,530 | −95 ±13 | −9 ±13 | 43% |
| 28 | 881 | −37 ±18 | +33 ±17 | 42% of the extra asks |
| 29 | 416 | +64 ±27 | +107 ±24 | 22% |
| 30 | 238 | +126 ±37 | +152 ±33 | 24% |
The “±” figure is the margin of error. At 27 and 28 the slams reached made a little over half the time, which about breaks even for a small slam. But the sign-offs in five went down more than four times in ten, so asking lost overall. At 29 the slams gained clearly and fewer sign-offs went down, so asking gained overall. At 30 the app asked on fewer deals for about the same total gain, within the margin of error.
Taking each point separately, the extra asks made at 27 that would not be made at 28 lose 171 points per deal on the actual cards. The extra asks at 28 lose 120, and those at 29 show no difference within the margin of error. Asking stops losing at 29, so BidMaestro asks at 29, the figure our sources give.
After the reply, a different figure applies. With all five keycards and the trump queen, BidMaestro bids the small slam whatever the total, and the results support that. Those slams made 61% of the time when the known total was only 27, and 87% of the time at 30 or more. The open question is a reply showing one keycard missing with the trump queen held. For that reply the app bids the slam when the known total is 27 or more, a figure set by an earlier study of 164,200 deals.
With the ask held at 29, the slam figure was tested at 28, 29 and 30 in the current version of the app. No higher figure gained. Stopping in five with a known total of 28 made no clear difference. At 29 it lost about 106 points per deal, and at 30 it lost 82 per deal on the actual cards and 64 on the re-dealt hands, both beyond the margin of error.
| Bid the slam with one keycard missing when known is at least | Slams stopped in five instead | Per deal, actual cards | Per deal, re-dealt hands |
|---|---|---|---|
| 27 (current rule) | — | — | — |
| 28 | 42 | −44 ±88 | −64 ±70 |
| 29 | 87 | −106 ±61 | −89 ±56 |
| 30 | 231 | −82 ±39 | −64 ±33 |
One reply is worth taking on its own: partner shows two keycards and denies the trump queen, and your own hand holds the other three. Every keycard is now accounted for and the trump queen is the only card missing. Is that a reason to stop in five?
It depends almost entirely on how many trumps the partnership is known to hold. In 723 of these decisions, solved by re-dealing the unseen hands 200 times each, the small slam made 62% of the time on a known six-card fit, 75% on seven, 85% on eight and 95% on nine. Counted by the trumps actually held rather than the trumps the asker could count, the pattern is the same: 47% on seven, 75% on eight, 91% on nine and 96% on ten.
| Trumps the asker can count | Decisions | Average tricks | Small slam makes |
|---|---|---|---|
| Six | 191 | 11.70 | 62% |
| Seven | 181 | 12.01 | 75% |
| Eight | 134 | 12.33 | 85% |
| Nine | 47 | 12.57 | 95% |
| Ten | 16 | 12.55 | 94% |
The reason is familiar to any player: with nine trumps the missing queen drops under the top two honours about half the time, and can be finessed the rest of the time, so it is worth at most one trick — and with every ace and the trump king held there is no second loser for it to join.
A quantitative 4NT asks partner to bid 6NT with a maximum. In Dubois’ Bidding Notes, opener accepts with a good 16 or 17 opposite a 15–17 notrump; in Timm’s book, opener passes with a minimum and bids 6NT with good values. BidMaestro accepted only at the very top of the range, so a 16 opposite 1NT, a 26 opposite a 2♣ opener's 25–27 rebid, or a 20 from a jump-shifter's 18–21 always passed.
Measured on 100,550 deals, every uncontested quantitative 4NT that was passed, by how far the passer sat below the top of the range its bidding had shown, re-dealing the unseen hands 200 times:
| The passer's points | Decisions | 6NT makes on at least 75% of redeals | 6NT instead of 4NT, per deal | Better / worse |
|---|---|---|---|---|
| One below the top | 107 | 69% | +348 | 92 / 15 |
| Two below the top | 114 | 51% | +176 | 75 / 39 |
One below the top, nothing else separates the makers: a five-card suit, tens and nines, the number of controls and the losing-trick count all leave the make rate between 59% and 74%. The reason is the same as everywhere in slam bidding: the hand that bids 4NT holds more, on average, than the least it needed to bid it. So BidMaestro now accepts a quantitative 4NT one point below the top of its range as well as at the top; two below it still passes. In the app this changed 164 auctions in the sample, every one from 4NT to 6NT: 133 better and 31 worse on the redeals, +299 a changed deal.
The same idea applies before the queen ask is made. When the hand asking for keycards can count ten trumps between the two hands (its own plus the number partner's bidding promised), the queen does not matter, and asking for it only invites a denial that stops the auction at the five level. Dubois’ Bidding Notes already gives the replying hand this rule: two keycards "and enough trump to guarantee a 10 card fit" count as holding the queen. BidMaestro's replier followed it; its asker did not, and asked for a queen it did not need.
Measured on 100,550 deals, taking every uncontested auction where the asker stopped at five of the major over a missing or denied queen and re-dealing the unseen hands 200 times:
| Trumps the asker can count | Decisions (one keycard missing) | Small slam makes on at least 75% of redeals | Six instead of five, per deal |
|---|---|---|---|
| Eight | 120 | 15% | −66 |
| Nine | 83 | 37% | +169 |
| Ten or more | 22 | 73% | +413 |
So with ten trumps the asker now bids the small slam directly over a reply that leaves one keycard missing, instead of asking for the queen; with nine or fewer it still asks. The queen-ask denial itself is unchanged: on that path, with eight or nine trumps, the slam made on 23% and 64% of the decisions, not enough to bid on. In the app this changed 17 auctions in the sample: 16 small slams instead of five-level stops, eleven better and six worse on the redeals, +242 a changed deal.
The point total made no difference within this group. Among the decisions with a known nine-card fit, the slam made 95% of the time with a known total of 27 to 29 (7 decisions), 90% at 30 or 31 (14) and 97% at 32 or more (40). Below 27 there were only 3 decisions, making 80%, so that corner is too thin to draw on. Every one of those figures clears the level at which the app treats a slam as worth bidding, so BidMaestro bids the small slam on this reply whenever the partnership is known to hold eight trumps or more, whatever the point total. That matters because the earlier rule needed 32 points and was turning down good slams below it.
Eight is a deliberate choice rather than a safe one. Of the decisions where the app previously stopped in five and now bids the slam, the nine-trump ones made 93% of the time (9 solved) and the eight-trump ones 75% (24 solved). Three quarters is comfortably worth bidding at either form of scoring, but it is not the near-certainty that nine trumps gives, and the difference is worth knowing when you are the one holding the hand.
One limit on all of these figures: every decision measured is one where the app itself chose to ask for keycards, and it only asks with the strength to stand the answer. So the results describe hands within that asking range, not every hand that could reach the same reply.
This applies only when every keycard is present. The same study covered 908 decisions with one keycard missing as well as the queen: on a known nine-card fit those made 67% of the time, below the level worth bidding, so there the point total still governs and the nine-trump requirement stays.
The ten-trump rule can look wrong when the missing keycard is the trump king. Take 1♠ – 2NT (Jacoby) – 3♣ – 4♣ – 4♦ – 4♥ – 4NT, where North holds ♠J9643 ♥A9 ♦72 ♣AQ64 and replies 5♠, “two keycards and the queen”, without the spade queen. The opponents hold the spade king, so North–South will lose a trick to it whatever they hold in queens.
That is true, but the trick lost is the one missing keycard, and a small slam can afford one loser. With ten trumps the queen adds nothing: if the king is missing, one trump trick is lost with or without the queen; if an ace is missing instead, the queen usually falls under the ace and king, and the ace is the only loser.
We tested two stricter rules against the one the app plays. The first allowed ten trumps to stand in for the queen only when the partnership holds the ace and king of trumps. The second, simpler rule allowed it only when all five keycards are held; otherwise the reply shows the queen only when the hand holds it. Each version of the app bid the same deals, and every deal whose final contract changed was solved by re-dealing the unseen hands 200 times:
| Deals | Ace and king required | All keycards required |
|---|---|---|
| 8,260 Jacoby 2NT auctions | −126 a changed deal (95 deals) | −123 a changed deal (120 deals; 44 better, 76 worse) |
| 25,380 control-bid auctions | −316 (121) | −286 (166; 33 better, 133 worse) |
| 8,260 new Jacoby 2NT auctions | −275 (81) | −260 (110; 26 better, 83 worse) |
Both stricter rules lost on every sample and at every setting tested, mostly by stopping in five when the slam would have made. So BidMaestro keeps the rule as Dubois’ Bidding Notes gives it: with two keycards and enough trumps between the two hands to be sure of a ten-card fit, give the reply that shows the queen even without holding it.
An earlier study of the same deals suggested that bidding slam at 27 was causing the losses. Slams bid with one keycard missing, after asking at a known total of 27 or 28, made only a third of the time. The cause was asking too early, not the slam level. A player who asks as soon as the known total reaches 27 usually finds partner holding no more than partner’s bids promised, so a slam bid on that total goes down. When the ask waits until 29, the partnerships that go on to slam with one keycard missing hold more, so the slam figure of 27 stays.
The study used 100,550 deals from the app’s stored deal library. For each candidate figure the app was rebuilt with only that number changed, and every deal was bid again by all four players. A deal counts only if its final contract changed. Each deal was scored two ways. The actual-cards score compares the contract reached with the contract the app’s previous rule reached, both played with all four hands visible (Double Dummy). The re-dealt score keeps the asking player’s cards, re-deals partner’s cards 200 times to fit every call made, and averages the results, so that one favourable or unfavourable layout does not decide the result. The margin of error is one standard error of the average over the changed deals. Each figure was measured once and not adjusted afterwards.
