Note: Not at the old Poker1 site. A version of this entry was first published in Card Player. This entry in the "Aunt Sophie" series covers pan (or panguingue), which is a multi-player form of rummy, often played for money.
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Michael Wiesenberg
Aunt Sophie learns about infinity
“How many plucks does it take to go out?” asked Aunt Sophie as she rolled out on a floured board the dough for hamentashen.
“That, my dear,” I responded, “depends on far too many variables for me to answer without further explanation on your part.”
“I knew,” she shot back, “you’d have some smott answer.”
“Now please,” I begged, “don’t get upset. I can answer your questions if they’re more specific. You didn’t tell me what kind of hand, how many players, and so on. Tell me the situation, and maybe I can do a better job of answering.”
Patsy for twelve
She cut the dough into circles with an inverted floured glass. She added to some a mixture of large, ground, pitted prunes, white raisins, walnuts, apricots, cherry jam, and sugar, into others a filling made of poppy seeds scalded four times with boiling water, honey, well-beaten eggs, black raisins, and ground almonds, and into still others a cheese mixture consisting of cottage cheese, egg, grated lemon rind, sugar, cinnamon, and sour cream. She drew up three sides of each to form a triangle and pinched the edges together, brushed each with a beaten egg yolk to give a nice shine, and left them to rise. “I had the best pan hand I’ve ever had,” she finally replied; “three threes of spades, three sevens of spades, and four kings of spades. Can you believe it? A patsy for twelve I’m dealt, and five others playing!”
“Yes,” I interrupted, “I can see it coming. Pat for twelve, and not one hit. Some idiot hit a garbage hand ten times, and finally went out for two while you just waited for cards that never came.”
“So,” she pressed on, “Mr. Smotty, how many plucks does it take to go out?”
“Well,” I hedged, “that’s a little hard to say. Oh sure, you can work out mathematically the precise odds for any hand, how many hits it should take. That’s not a very straightforward calculation, however. It would require knowing precisely what cards the other players held. Failing that, though, you could still work out on the average how many hits any particular hand ought to require. And of course that would be worth little. It would not tell you in the short run how many hits you’re going to need to get on the board. It’s worth something only as predicter of the long run. Nevertheless, I can say with some assurance that you got robbed this time. I can also say that if you play pan long enough, it’s not the last time that will happen to you. All you can do is play your best, and in the long run you’ll do okay.”
“Long run, schmong run,” she grumbled. “Either I’m supposed to put that hand out, or I’m not. If I’m supposed to put it out, I should play it; if I’m not, I shouldn’t.”
No guarantees
“Unfortunately,” I explained, “it’s not quite that simple. Most of the time you’ll get a hit and make money on such a hand. In fact, most of the time you’ll put the hand out and make a lot. But there are no guarantees. You could be running bad, and in one session, or even several sessions, never put out a hand, good or bad. Probabilities don’t mean anything until extended out for a long time, sometimes practically until infinity.”
“Infinity!” Aunt Sophie exploded. “What does infinity have to do with it? I’m talking about playing pan, not the physics courses you took in your fancy Stanford education.”
“Actually,” I gently corrected, “that’s more the province of mathematics, in particular statistics courses. I won’t tell you how many plucks it should take to put that particular hand out, because for one thing it depends on the constitution of the hands of the other players, and, for another thing, it doesn’t matter. As to the constitution of the other hands, it’s entirely possible — not very likely, mind you, but well within what mathematicians like to call “the realm of possibility” — that your hand was impossible to put out.”
“Impossible?” she demanded. “Whaddya mean?”
“Well,” I continued, “I won’t go into great detail, but suppose the other players also had threes, sevens, and kings. Since there are no cutoffs there, you have to hit specifically one of those cards. If all of them were accounted for among your hands, it’s possible that no cards remained in the deck for you to hit. You would all sit there gnashing your teeth while some other player put out a pisser after a multitude of hits. Be thankful another player was in the hand. You might never have gone out; you might all still be sitting there. I’m not going into more detail about this because Mr. Griggs explained such a situation nicely in his column in the PAN PLAYER+ of February 9. What I’m trying to get at, though, is that in pan everything is possible, and if you play long enough, you’ll see everything eventually. Even including not putting out such beautiful hands once in a while.”
“And that,” she quested, “is what you meant by infinity?”
Anything can happen
“In a way,” I went on. “Maybe you’ve heard it said that if you sat fifty monkeys at typewriters in a room, each pecking away randomly at the keys, eventually the monkeys would type every book in the British Museum. This is not to say anything about the smartness of the monkeys; it is merely a definition of infinity. In reality, the monkeys would likely all be dead before even one intelligible sentence was randomly typed. They’re just saying that somewhere in an infinitude of randomly typed letters all the great works have to sometime be reproduced. But that was only meant to be an analogy, their comment on infinity. Most people don’t understand the point of that story. And what I’m saying is, that if you play long enough, anything will happen. Including just by chance all of the players getting dealt perfect hands that none can put out because each holds the other’s cards. That’s not to say it’s likely; just that in the long run anything can happen. And in the long run, things also tend to even out. If you keep playing good hands like that, in the long run you’ll do well.”
“But what,” she requested, “do I do about the short run?”
“Just grin and bear it,” I answered. “And let me tell you the denouement of that story about the monkeys. It was a Bob Newhart routine, but I also read it long before he started telling jokes in public in a collection of Jewish humor about some scientists actually conducting the experiment. They put fifty monkeys in a room with typewriters. One of them came into the room to see how the monkeys were progressing. “‘Hey, Joe,’ said the researcher in the room, `come in here a minute. I believe one of these monkeys has something. Listen to this: “To be or not to be, that is the xgztshrbtfsplk.’” Anyway, that’s infinity and the short run.”