Clarity at the High End
On the squintillions of possible auctions
Note: This article was originally published in slightly modified form in the January 2022 issue of Bridge Bulletin. The most noticeable edit removed the reference to the rotating display of taquitos and hot dogs, leaving the reader to wonder what “meats” the two characters were contemplating during their highway pit stop. Egad!
Inspired by an article by Ted Muller.
The auction went 6NT->(DBL)->7C->(DBL)->7NT->(DBL). I won’t bother describing the deal or the play of the hand or the ugly smirks of our opponents. If you know my partner, Delbert, you know that he is prone to opening 6NT with a “strong” hand. Strong as in 20 points. I used to simply pass, but lately I try to put us in my longest suit just for the heck of it. No matter—I am just a speed bump on Delbert’s route to 7NT. Given the rarity of legitimate grand slam hands, and the fact that Delbert puts us in 7NT at least three times per session, you can imagine our opponents’ delight upon seeing us at their table.
In between tournaments I do try to interest Delbert in the ways of 1-level openers with fewer than 22 points, or 2 clubs with more than 21 points, but he laughs at the idea. “Why waste time with jibber-jabber down in the muck when you have the points?” he demands. He adds sagely, “There’s clarity at the high end.” By that he means that if you skip the part where you work your way up to slam, there’s only a few possible bids available to anyone else. Perhaps it was unwise of me to grant him that point, for he took it as approval; but early on I did try to tell him that the main clarity at the high end is that we have vastly overbid our hands.
While Delbert may have bid exuberantly long before our partnership, I may have made it worse some years ago when we were driving to a tournament. With the right partner, those road trips are half the fun of playing in tournaments, or I should say 80 percent of the fun given the carnage we experience at the tables. My masterpoint total has not budged upward since I started playing with Delbert, and in fact I have heard directors mutter something about subtracting points when they collect our scoresheets.
On that fateful road trip Delbert said from behind the wheel of his Cadillac DeVille, “I reckon we should make us a chart with all the possible auctions. Then we mark up the chart after each session. Over time, we would have a list of the most likely auctions. That can be our convention.” You see, Delbert is not process-oriented, so he is forever trying to come up with ways to just use brute force memorization instead of natural and conventional bids.
I laughed and said, “You do know, don’t you, that there are more possible auctions than there are atoms in the universe?”
The car swerved then straightened out and Delbert said, “This universe?”
I said, “No other.”
He said, “How do you figure that?”
I said, “It’s math. You start with the lowest possible opening bid. Well, actually you start with three passes followed by the lowest possible bid. So pass, pass, pass, 1 club.”
Delbert said, “OK. That’s one auction. I only see what, thirty-something more?”
I said, “No, that’s not one auction. That’s just the first round. In the second round you imagine all possible responses to the 1 club opener. Remember, once there’s a bid, the auction only ends after three passes. You have to count those passes when you are listing your possible auctions. But assume you keep having just two passes after each suit or no-trump bid, for round after round, until you get to 7NT. Many steps. That’s one auction.”
Delbert was shaking his head the whole time. When I got done he said, “What a monumental waste of time! What kind of hand would you bid like that?”
I said, “You probably wouldn’t see one like that, except maybe in Bridge Bulletin every now and then. But I was explaining the math that leads to more auctions than there are atoms in the universe. Because, see, you go back to the start and make up another auction that starts off the same way, but say instead of 1 club the fourth bid is 1 diamond. And you go along with every possible variation and every possible length of auction.”
Delbert said, “And it’s how many, total?”
I said, “Gosh, I don’t know that the number has a name. You get high enough they start writing it in exponential notation.”
Delbert said, “Well how about this. Could some of those auctions start up at the high end? Like 6NT?”
I said, “Of course! All opening bids are possible.”
Delbert said, “And I suppose with a 6NT opener, you don’t get eleven squintillion possibilities?”
I laughed and said, “That’s right! What with combinations of passes and 7-level responses there’s still a lot of possibilities, but nothing like your squintillion. But you know, a hand that justifies a 6NT opener is pretty rare.”
We drove in silence for a while after that, then we pulled into a gas station for a pit stop. Inside the store as we loaded taquitos and sausages from the roller grill onto our plates, Delbert turned to me with a mysterious grin and said for the first time, “There’s clarity at the high end.” I had forgotten about our conversation and I honestly thought he was making an admiring reference to the rotating meats before us. How I wish it were so. The next day, Delbert unleashed his clarifying 6NT bid for the first time.
People have asked me why I keep partnering with Delbert. They tell me I could easily be a Silver Life Master by now if I played with a reasonably competent partner. I reply with a soliloquy about the value of friendship and loyalty. Delbert is my best friend. You don’t break up a partnership with your best friend just because he routinely drags you into the bridge equivalent of burning buildings. People admire me for sticking with the guy. What I don’t tell them is that I actually enjoy the notoriety. Yes, I could be a Silver Life Master—one among many. Honestly, no one fears or even notices the Silver Life Masters, who are pretty thick on the ground at every tournament. But you’d better believe they notice the “Six No-trump Guys”. Not only do they notice us, but they are darn glad to see us. I was not going to be the reincarnation of Charles Goren or Omar Sharif anyway, so I’ll gladly settle for the notoriety that comes with being Delbert’s partner.
Along with the notoriety comes some actual tangible benefits of the non-masterpoint variety. Neither Delbert nor I are big drinkers, or we didn’t used to be, but our generosity at the tables has led to us receiving a steady stream of free drinks when we hang out by the hotel pool in between sessions. Our prospective opponents want us—or Delbert, anyway—lubed and loosened up. They could save their money if they understood, as I do, that once Delbert latches onto an idea he will not turn it loose. He would open 6NT with 20+ points stone cold sober.
The drinks do lead to some rather wild conversations, which I enjoy because I match Delbert drink for drink. Speaking of persistent ideas, a recurring topic is Delbert’s idea of listing all the possible auctions and turning that list into a formal bidding convention. Even knowing how many such auctions there could be, he views making the list as a simple logistical problem. One time, out by the pool after a few free drinks, when he brought it up again I told him that I had read in an article by Ted Muller that if you had seven billion people with seven billion computers each, with each computer producing seven billion auctions per second, it would take over a trillion years to list all the auctions.
Delbert burped at that and said, “So, it’s doable. Urp.”
I burped in return and said, “Urp. That is not. Hic. That is not the conclusion to which I…something. Hic. I say no. No. It is not doable.”
Delbert said, “Suppose we get the monkeys on the case?”
I said, “What monkeys?”
He said, “The Shakespeare monkeys.” You see, on another long drive I had made the mistake of telling him about the idea that if you set a million monkeys to typing on typewriters, over some vast amount of time there was a statistical certainty that one of them would produce the entire works of William Shakespeare, right down to the Olde English phrasing. Naturally, Delbert had missed the math and statistics element and had focused on monkeys with a predilection for writing Olde English plays and verse.
I said, “What, you think they are going to out-type seven billion times seven billion computers for a trillion years? Need I remind you…hic…squintillions.”
Delbert pondered that for a while, then said, “I’ve got it. You have them going at it randomly, just monkey-pounding on the keyboard, right?”
I conceded, “Yes. Slapping away like monkeys. Because they are monkeys.”
Delbert said, “So what say we get some more-organized animals involved? Someone to guide the work and collate the results? Maybe post charts so the monkeys aren’t just being totally random. Don’t type up any duplicate auctions. Make it more of a cooperative effort. Your billions of computers are just going at it randomly, are they not? Our team can do it better.” I began to understand why Delbert was the best managerial consultant in the painting and drywall industry east of the Mississippi.
If not for the drinks I would have changed the subject, but with my intelligence impaired I could not resist asking, “And what animal would be organized enough to do that job?”
Delbert answered so quickly that I realized he had anticipated my question: “Beavers, obviously.” He fell back unconscious and commenced snoring loudly.
I said, “Obviously,” and then I too fell back to dream of millions of monkeys wearing Elizabethan collars and typing out bridge auctions, supervised by a stern cadre of very organized beavers. Maybe Delbert was right. I didn’t think you could list all the auctions, but I know for sure that if you don’t get started, using whatever computers or animals you have handy, you’ll never finish.