Bob Mackinnon

Vulnerable Grand Slams and Games

The two situations in which the expected action of the opponents plays a major part in constructive bidding have to do with vulnerable games and grand slams, the first being common and the second being rare. The game situation engenders reckless abandon, the grand slam situation, extreme caution. One would think that holding hands that have the combined assets to make 13 tricks would be a pleasurable and momentous occasion for any pair, but many nervously anticipate the event more with apprehension than joy. Some come ill-prepared. Alan Truscott in his book, Grand Slams, suggested that grand slams that at worst depend on a finesse should be bid, yet it is common enough to hear veteran players advice novices not to bid a grand slam unless they can count 14 tricks. Larry Cohen has commented on BBO to the effect that grand slams are overvalued in IMPs, as a single board can produce a disproportionate swing that may determine the match winners. In effect, there is wide-spread feeling that bridge would be better if grand slams didn’t exist, and many bid as if they don’t. That shortcoming influences one’s strategy.

Standard bidding methods are poorly suited to exploring grand slam possibilities. If one starts the bidding at 2-level, worst at 2NT, one has eaten up valuable bidding space, so it becomes difficult to obtain sufficient information on which to base a critical decision, especially with regard to the minor suits. It so happens that this week we received further evidence on this point. In the Bridge Canada Magazine Michael Yuen reported this success in the 2010 Canadian Seniors Team Championship where he and partner, Maurice De La Salle, reached a contract of 7 when their opponents bid to 6NT and stayed there.


De La Salle Yuen
AQ 98 2NT 3 * (relay, minor suit slam try)
A432 KQ 3NT* 4♣* ( 5♣, 4 )
A53 KQJ10 4 * 4NT* (KC ask, 1 KC in clubs)
♣ AQ75 ♣ K10432 5 * 7♣ (asks for outside kings)
20 HCP 14 HCP Pass


The sequence has some odd features in that the one who holds the stronger hand and makes the asking bids does not get to decide the final contract and does not get to play it. Some players like this approach as it allows the responder to make the final decision on the basis of undisclosed features. It is like the old burlesque fan dance, where the performer flutters about seductively promising much while revealing little that can’t be guessed. Over the limited 2NT, Yuen begins by describing a powerful hand with the minor suits. Opener can ask concerning the quality of the club suit, and would be very surprised if partner couldn’t show the K. 5 is another asking bid, but like Blackwood 5NT it is also descriptive, here showing all the key cards in clubs are held. Yuen decides enough is enough and executes a grand leap to what he thinks he can make, as the lights go out. The strong hand is left in the dark, unable to bid a confident 7NT. Nonetheless, the effort was worthy of applause and 9 IMPs.

2NT is an especially badly designed part of popular systems. It’s easy to imagine the bidding going: 2NT – 6NT. Responder with just 14 HCP might very well doubt that a grand slam will be bid or that it can make without that a hoped-for favorable lead. Thus players are condemned by their own reluctance to disclose specific features, so remain unsure as to how good a grand slam might turn out to be on the lie of the cards.

Playing a Big Club system I could open 2NT based on the high-card content, but my preference when holding 8 controls is to open with 1 . Responder bids 2 to show minor suit orientation with at least 5 clubs and 4 diamonds with honors distributed in the minors. One sees that the 2 response is fully 9 steps below 4 , the point where Yuen can impart a similar description. This saving in space is a great advantage to the Big Clubber.

This example demonstrates why grand slam decisions are based partly on the perceived capabilities of the opposition. This is expressed mathematically by PB, the probability the grand slam will be bid. If I held a hand like De La Salle’s I would be aware that against standard bidders I have a great advantage. As the bidding progressed I would be encouraged to move towards a grand slam as my superior methods can land me in a good contract others are unlikely to pursue. On the other hand, against expert Big Clubbers I would bid the grand slam in a close decision expecting to tie the board. The theoretical point of neutrality is where it is 50-50 that the opposition will bid the grand slam (PB=½), and the probability of making it, PM, equals 17/30 (a 57% chance.)

Vulnerable Game Strategy

Grand slams are the nectar of the bridge gods, whereas vulnerable games are the ham sandwiches of the masses. Sometimes they survive on baloney alone. The neutral point is at PM=3/8, PB=½, a point far removed from the point of maximum uncertainty, PB=½ and PM=½. The dice are heavily loaded in favor of bidding the game. One doesn’t need much hope when bidding on, especially when many will be bidding the game as well, poor as it is. The gain if successful is 10 IMPs, the loss if not is 6 IMPs. The optimal rule is to bid the game if PM>3/8 (37.5%). Above that threshold on aggregate the expected score is greater for bidding the game. Plainly put, one should bid game on any excuse, the quicker the better. That is not the whole story, as there is a downside. The risk is minimized under the prevailing rule of not doubling mutually agreed contracts at IMPs. So one can hope to enjoy the benefit of making the contract without fearing unduly about the consequences of arriving in a hopeless one. This leads to loose action which provides thrills, suspense, anguish, and rapture – exactly what wise mothers warn against.

The Full Picture

Below is shown the full map of the critical decision zone over a range of PB and PM. The numbers given are the expected scores in IMPs for the game on the left and the partial on the right. The aggregate for each contract is given below the line. This is the pattern:


Game Partial
S1 S4 (expected gain)
S2 S3 (expected loss)
S1 + S2 S3 + S4 (aggregate)


PM PB = 3/8 PB = 4/9 PB = 1/2 PB = 5/9 PB = 3/5
2/7 1.79 1.61 1.59 1.90 1.43 2.14 1.27 2.38 1.44 2.57
-2.68 -1.07 -2.38 -1.27 -2.14 -1.43 -1.90 -1.59 -1.71 -1.71
-0.89 0.54 -0.79 0.63 -0.71 0.71 -0.63 0.79 -0.57 0.86
1/3 2.08 1.50 1.85 1.78 1.67 2.00 1.48 2.22 1.33 2.40
-2.50 -1.25 -2.22 -1.48 -2.00 -1.67 -1.78 -1.85 -1.60 -2.00
-0.42 0.25 -0.37 0.30 -0.33 0.33 -0.30 0.37 -0.27 0.40
3/8 2.34 1.41 2.08 1.67 1.88 1.88 1.67 2.08 1.50 2.25
-2.34 -1.41 -2.08 -1.67 -1.88 -1.88 -1.67 -2.08 -1.50 -2.25
0 0 0 0 0 0 0 0 0 0
4/9 2.78 1.25 2.47 1.48 2.22 1.67 1.98 1.85 1.78 2.00
-2.08 -1.67 -1.85 -1.98 -1.67 -2.22 -1.48 -2.49 -1.33 -2.67
0.69 -0.42 0.62 -0.49 0.55 -0.55 0.49 -0.62 0.44 -0.67
1/2 3.12 1.13 2.78 1.33 2.50 1.50 2.22 1.67 2.00 1.80
-1.88 -1.88 -1.67 -2.22 -1.50 -2.50 -1.33 -2.78 -1.20 -3.00
1.24 -0.73 1.11 -0.89 1.00 -1.00 0.88 -1.11 0.80 -1.20


The comfort zone, wherein the criteria to maximize the gain and minimize the loss both require that the higher contract be bid, consists of the boxes below the critical boundary line at PM=3/8. Two exceptions are highlighted in blue. On the left one minimizes the loss by staying in the part score, but the gain is 0.41 IMPs against a potential loss of 1.53 IMPs, so even if the opposition is not bidding this game, the odds favor doing so at IMP scoring. On the right one maximizes the gain by staying in a part score when most will be bidding the game. One gains 0.22 IMPs, gambling a potential loss of 1.33 IMPs. Clearly one should go with the opposition on this one in order to minimize the potential loss. This is entirely consistent with the optimal rule.

What if in their enthusiasm the opposition has bid a filthy game, represented by the line PM=1/3? If the probability of their doing so lies between PB =4/9 and PB=5/9, there is less than one-tenth of an IMP to be lost on average by bidding on. This reduces the penalty for being foolish. The effect is to degrade the game of bridge in such a way that good judgment based on hand evaluation is not well rewarded – boldness is.

Defensive Action versus a Vulnerable Game

If the opponents are vulnerable and you are not, there is good reason to expect them to strive to bid game. On the assumption they will bid game most of the time, the task at hand is to prevent them from making it. Every decision should taken with that in mind.


One sure way to help the opposition is to make a lazy overcall on a bad heart suit in a mediocre hand. Lately this was demonstrated to me yet again when I opened a standard 1 on: A87 Q6 AKJ86 A83. LHO overcalled 1 and partner bid 1NT which I unhesitatingly raised to 3NT. RHO led a heart and partner easily racked up game after losing the finesse in diamonds. Game would have been in danger if the RHO had made his natural lead of a spade from KJxxx, and LHO had switched to a club upon winning the Q. Automatic nonvulnerable overcalls have become for some a bad habit.

On the other hand I love overcalling 1 even on a bad suit. In the same session I overcalled 1 /1 on: K8763 A3 AK 9874, not an especially brave action. The LHO raised to 2 , partner raised me to 2 , and the RHO went directly to 4 . Obviously, I had a plan. I led an unusual K, and found QJT4 in dummy. The K was wasted paper, but my holding it made it more likely partner held the A. The A, a low spade to the A and a diamond ruff ensured a 2-trick set. My overcall and partner’s raise actually set up the defence for us before I made the opening lead. If my LHO had bid 1NT instead of raising hearts on 3-small, our prospects would not have been so bright. Support with support, yes, but trump support on 3-small should mean there is hope of a ruff to be had in the short-trump hand, especially when raising an opening bid.

The lead-directing aspect is a very important when partner will be on lead against a vulnerable game. That increases the attractiveness of overcalls of a minor on a good 4-card major, preferably spades. Such overcalls may prevent the opponents bidding a thin 3NT and making it on a favorable lead. The less you hold in HCPs, the tougher will be partner’s decision if you don’t bid, as he may hold scattered values in 2 other unbid suits.

The Victory Point Distortion

The worst form of team play is the 4-round Victory Point Swiss. It is not duplicate bridge as around the room teams are playing different boards. One needs must maximize the gains against teams in the early rounds, as a pair of small margin victories puts one’s team well behind the leaders. The need to maximize the gains distorts priorities so that one is inclined to gamble on risky vulnerable games and slams that require a misdefence.

Last month going into the last 7-board match our team was behind the leading team by 4 VP’s as a result of a well deserved loss to them. In order to overtake our rivals and win the event we had to outscore our final opponents by a large margin, that is, we had to maximize our gains on the big hands if such opportunities arose. We bid a vulnerable game the opponents missed, a gain of 11 IMPs, and partner boldly proceeded to a slam making 12 tricks when the opposition stayed in game making just 11 tricks. As a result of these swinging actions, we emerged with 20 VPs and won the event by the slimmest of margins, as the leaders could manage only a highly respectable 15 VPs on their last round. I consider this unjust, as we were playing a different set of boards. Playing good, steady bridge and scoring honorably flat boards against a good team in the last match leaves one at the mercy of the deals being played by the third place team. Often at Swiss Teams there is a psychological advantage to be had for coming up from behind, and at Victory Points this advantage can be amplified by a swinging set of boards. This offers hope to the lowly trailers, which may account for the immense popularity of the event.


Slim JimSeptember 12th, 2010 at 9:37 am

My recent experience playing Swiss teams events in the Uk is that where possible all rounds are played with duplimated boards. In more local events without the resources to duplimate all rounds the last half of the event uses duplimated boards. This removes the injustice mentioned in your final paragraph, although it does retain the injustice of the opponents having a better day than you.

Bob MSeptember 12th, 2010 at 6:19 pm

Thanks for the info. That approach is sensible. Even if organizers would duplicate the top tables it would help. Our game has 26 tables. Coincidentally on Thursday the same thing happened again. Well behind the leaders going into the last round, we scored 20 VPs against one of the lesser lights and ended in a tie for top. It’s not fair, but if we got only what we deserve the world would be in a sorry state.

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