The Figure 33

I said in my series 15 years ago that of the 3 figures, the most important by far is 26, and I'm not going to retract that here. Just by its sheer frequency vis-à-vis the times 33 is important, it has to be given pride of place. Nevertheless, I suppose largely because 26 is so well known and indeed built into bidding systems, I seem to have many more illustrations of how ignorance of or indifference to number 33 proves costly than I do of misuse of 26.
The first illustration I believe will indicate this. I don't have the hand here, though I'm sure I do in my archives somewhere. It was in either the second or the third Epson tournament, 19 hcp's facing an opening bid, at my table bid by two Life Masters who'd been partners for years and now decided to be opponents for a hand. The bidding went like this: one club, one diamond, one heart, one spade, one no. Then 4 no trump, 6 no trump, 7 no trump, double by my partner looking at the ace of hearts and knowing he's on opening lead. I don't think they couldn't have gotten screwed up if it'd been 13 or 14 points facing that opening bid or perhaps 8 points facing 19 with a bid and then a jump rebid of 2 no.
Wait! Nineteen facing and opening bid! That's not 33, is it? No, 19 plus 13 is 32, of course. Nevertheless, it's awfully difficult for an opening bidder to distinguish between holding 13 or 14 points, and putting a little sport into the hand, I would not quibble with the person who drove to little slam on that holding. And as far as I'm concerned, the sixth bid should have been a leap to six no. (I have said in my opening thoughts on bidding, Keep away from ambiguous bids!) I also might mention that there's a difference between 32 pts, maybe 33, and 32, maybe 31 with no chance of 33. With the former, I'd be predisposed to bidding the slam, but would play it safe with the latter.
The post-mortem recriminations went like this: "Why on earth couldn't you tell me how many aces you held?" "I took 4 no as quantitative," (a rather curious assertion in itself, since she held a minimum 13 hcp's, and if that bid was quantitative, she should be passing!). And finding an uninformative response to her Blackwood, the 19-point hand should have known -- the opening bidder had made 3 bids at the one level! -- that if anything, they just might be overbid a trick. There simply should have been no vector toward 7 no, with or without knowledge of aces. I'll even go a step further: give 'em the ace of hearts if we can extract any 4 hcp's in compensation and you're still not going to make 7 no (probably -- I don't say it is impossible on 32 hcp's).
Four aces and four kings add up to 8 tricks! Not even enough for game in themselves. You must have the infrastucture for 12 or 13 tricks. Sometimes one partner holds a long, solid suit and then only needs to know how many aces and kings his partner holds. But when the hands are balanced and full of tenaces, Blackwood and Gerber can't tell you what you need to know. In that situation, there's no more reliable indicator than this lovely figure 33.
Here's a hand from OKbridge.
A 10 7 4
A 7
Q J
Q 9 7 6 3
9 8 6 5 3 2
Q 9 8 6 3 J 4
10 6 5 8 7 2
10 4 K J 8 6 2
K Q J
K 10 5 2
A K 9 4 3
A

This has become one of my favorite hands, and certainly my favorite for illustrating this figure 33. For this hand alone offers any number of lessons on that figure for those who would take a few minutes to ponder it. Let me go through its handling by about 84 pairs and then recapitulate the lessons offered.
Twenty points opposite an opening club bid. I bid a diamond and when my partner rebid a spade, indicating a minimum opener and no major suit fit, I bid six no -- and was condescendingly told later that I was lucky! The final contracts ranged all over the place from four partials and 6 game bids to 9 grand slams, seven in no trump. Three people had an opportunity for a clear top out of 84 pairs and blew it. One pair was in seven spades, another in seven diamonds, each of which makes with a ruff in the short trump holding, but each declarer proceeded to play the hand as if in no trump, cashing out 12 top tricks for down one. (One declarer did make 13 tricks in diamonds, but he was in 2 diamonds! The bidding at his table went one club, two diamonds, passed out! Evidently one partner thought they were playing weak jump shifts and the other didn't.)
Those are matters involving play and here I'm more interested in the blown chance strictly on the bidding vis-âvis 33 points. This was the pair that got doubled in five no and elected to play it there, with an overtrick, for a below average board, where a redouble would have given them a top. Here are the lessons this hand and a modicum of trust in the figure 33 have to offer.
(1) Let me start with the pair in 5 no doubled. Now, if 33 points indicates a little slam, this pair should certainly have felt confident of making 11 tricks. So it now becomes a matter of keeping score. Do you make more on a doubled 5 contract with an overtrick than bidding slam? No, you do not. Do you make more on a redoubled five contract with an overtrick than in a little slam. Yes, you do. You can go through what you make in the former situation. Let me go through the redoubled score. You don't need to figure out one total score versus the other. It'll be easier and quicker I believe just to balance the differences, to wit:
The slam bonus not vul is 500 points, period. On a redoubled five no bid, the trick score alone is increased threefold, which is 540 points right there! (The trick score of 180 is quadrupled, of course, to 720, but here I'm referring to the difference.) 'Nuff said? You'll now get also 170 more for an overtrick (i.e., 200 less 30 the undoubled people get), plus 100 for making a redoubled contract. But vulnerable? Okay. The bonus is 750. The trick score is still raised only 540 points, you still get 100 for making a redoubled contract, which brings us to 640, and now add 370 for the overtrick (400 minus 30), and you don't have to be a rocket scientist to know that 640 plus 370 is greater than 750. And further, if the hand only offers 11 tricks, you're obviously going to be way ahead of those bidding slam. Indeed, as just shown, if you're not vul, you can throw away a 12th trick and still beat the people in slam, though vulnerable, that won't work. In any event, you can't afford to be faked out of your natural slam by a 5-level double.
(2) The seven no bidders. The figure 33 should have warned those foolhardy souls away from the grand. Well, couldn't we have more than 33, or even for that matter make grand on 33? Oh, yes, of course. I'm going to get to that in just a minute. But the point of the figure 33 isn't that it will necessarily bring a little slam or absolutely precludes a grand but that it's the figure that will by and large put you in good stead for picking up 12 tricks. Period. I didn't check out the bidding of everyone in 7 no,but of the 2 or 3 I did check, all had used Blackwood. Some of these people had five or six rounds of bidding and took 13 or 14 minutes the play the hand only to pick up a bad score. But the problem with Blackwood (and Gerber) on balanced hands is that they don't tell you what you need to know. All the aces and all the kings add up to 8 tricks! You don't have slam if you don't have the infrastructure, and the figure 33 is going to tell you a lot more about the infrastructure than aces-asking bids.
(3) I wuz lucky. So sez a self-appointed mentor. Well, I dunno. I was following a figure handed down by Charles Goren, following it not blindly but after making my own observations and finding that there's a lot to be said for it. When people act as if they're, well, a little more sophisticated than Goren -- after all, his stuff is 40 years old, isn't it? -- I hafta wince. I find it more than a little presumptuous in the first place, and beyond that, I wonder if they've spent 1% of the time examining the cards for what various permutations offer that he spent.
My detractor went on to say, "Your partner could have 18 points." Well, yes, and a meteor might hit Arizona tomorrow. Oh, I suppose it's possible my partner had 18 points with that one spade rebid, but balance that against people getting screwed up on whether 4 no is Blackwood or quantitative, 4 clubs is a suit bid or Gerber. Add on the question of just how this partner, after a minimum rebid, is going to convey those 18 points, not to mention the sheer improbability of it, and I'm very comfortable settling in 6 no. Actually, I could also point out that I'm bidding my 20 points, and that's what bidding is all about. My partner has only promised me 13 points, and I said I wanna be in little slam, indicating 20 points. If she has 18 points, she can then go to the grand, no?
Now I want to change the hand a little without changing either the point count or the distribution:
A 10 7 4
A 7
Q 5
K 9 7 6 3
9 8 6 5 3 2
Q 9 8 6 3 J 4
J 10 6 8 7 2
Q 4 J 10 8 6 2
K Q J
K 10 5 2
A K 9 4 3
A

And do you see what I see? Yes, of course. Now it does make grand slam in no trump (as well as for the spade and diamond bidders). It makes grand slam by not just one but two pieces of luck: diamonds break 3-3, which you need without the jack, and every blooming point card is pulling its weight. Nothing is wasted. The grand slam bidders would have been cockahoop and doubtless would have felt their bidding methods were clearly superior to those who followed an old-hat principle like trusting the figure 33. But their bidding style wouldn't have been vindicated. It would have been a lucky stab here, and in the long run, they're going to lose more points to hands like .. well, like the hand that existed! Those who bid 7 no didn't come out smelling like a rose. Well, here another change (from the original).

A 10 7 4
A Q
J 5
Q 9 7 6 3
9 8 6 5 3 2
9 8 7 6 3 J 4
Q 10 6 8 7 2
10 4 K J 8 6 2
K Q J
K 10 5 2
A K 9 4 3
A

Now do you see what I see? When I exchange the red queens, keeping the point count and the distribution constant, you can't even make slam on an opening club lead. And even without a club lead, you can make slam only on a bit of luck. The 3-3 diamonds will still turn the trick, or with the queen in the long holding on a 4-2 split, the queen must lie with West. And you have to play it right. Now I suppose the underbidders would be rather satisfied with their bidding style. But they too will miss in the long run. They too will miss hands like the one that existed.
I hope these two emendations will lend some insight into just what this figure means. It's not a perfect indicator. But it's a helluva lot better than anything else on balanced hands.

The figure also serves or should serve a negative function too, i.e., of warning people off slam when they're not even close:

J 5
Q J 7
K Q J 10 5
K 5 4
Q 8 6
9
A 8 5
A Q J 8 6 3

I was kibitzing this table of experts, as they identified themselves on OKbridge. To do them justice, they played rather well up to this table. Now North opened a diamond, South bid two clubs, North bid three clubs and South was off to the races to 6 clubs! As a kibitzer, I could see that they had three quick losers in clubs and that the only makable game was actually three no, as the defense could do no better than run their 4 major suit winners (the top heart honors were split). Of course it's a virtually impossible game to find and I wouldn't have blamed the experts for being in a down one game. But I didn't understand the drive toward slam.
South only has 13 hcp's opposite an opening bid. He can add a couple of points for a heart singleton, but even at that, some would tell you that's rather skimpy for a minor suit game! What on earth triggered the thought of slam? Further, this is one case where a check for aces would have served the purpose of at least keeping them out of slam. Over 3 clubs, South bid 4 clubs, alerted and North bid 4 diamonds! I took that to be Gerber, with a response showing no aces. And if it wasn't Gerber, why didn't South use Blackwood, where with two aces, he would be safe if they had slam potential in the first place, and where here he would pass a 5 club (no aces) response?
I don't know the answer to those questions. Nor do I mean he should have gone to Blackwood. The recognition of slam potential should precede your aces-asking bids. That's just a checkup. Here South just doesn't have the tickets to think slam after his partner's rebid. But he did solve the mishap in the usual way among bridge players by blaming his partner: "I would have rebid 2 diamonds on that garbage," said he.. . the first player in memory to complain about a partner showing a fit in his suit!
Three clubs is a minimum rebid. It's not a new suit. It establishes a fit, and establishing a fit early is something I would strongly advise. South would doubtless say 3 clubs is not a minimum rebid, judging by his bidding and later comment. Okay. I can understand different bidding styles. But how he can go from reading his partner for 13 points on the opening bid to about the 20 points needed for slam on the 3 club rebid is beyond me.
But that's the ol' spirit. Just blame your partner and make sure you don't learn anything, eh? I think a look at the figure 33 would have saved one level in the bidding anyway.
A few weeks later I was unfortunately the partner of a player who didn't pay heed to what a clear indication of a shortfall from 33 should have told him. I opened a weak two spades and to skip over a few bids, found myself in six spades a few rounds later. The opponents took the first two diamond tricks, but that wasn't all. They didn't even need to lead diamonds. Had they led any other suit, I would still have had to get out trump and claim 11 tricks. There was no suit I could build, no way of throwing someone in for a sluff-and-ruff (if trump split 2-2) or a favorable lead. Nothing.
Later I counted his points and saw he had 19 hcp's on a flat 4-3-3-3 hand. Now, I have earlier referred to a player with 19 points opposite an opening bid and suggested that she should simply have jumped to 6 no when it was apparent that her partner had a minimum opening. So I'm certainly not holding out for iron-clad proof that you've 33 points between you. You have to take some chances, and I personally am in favor of those where you may very well have 33 points. A five-card suit may serve you well or a defensive error or skillful play or whatnot. I'm willing to take my chances and think it makes for a more exciting game.
But here we were both on a shortfall from the desideratum of 20 points opposite 13. A weak two is by definition less than an opening bid, and my partner was short of 20 even if by only one. So we'd have done well to face reality and steer clear. But there are any number of people who are simply uncomfortable being close to slam. They've just gotta bid it.

So . . the figure 33 doesn't give you any guarantees. Keep your eyes peeled. Don't trust Goren if that is your bent. Make your own observations about little slams. Go to hands on Okbridge and check out those that make on any defense and count the points. Check out those that could have been held to 11 tricks, regardless of the bidding and regardless of the defense. I think you're going to find that the ol' guy knew pretty much what he was talking about. It's up to you.