Player's Stories

"Conundrum"
By Dave Hench
(All Rights Reserved)

A while back I was playing in an Omaha game at Caesars Indiana and another player at the table, who I didn't know, passed me a little note across the table. It was a scrap cut out of a magazine, and contained a quote about the odds on the sequence of cards in a 52-card deck ever repeating itself. It attributed the quote to a woman named Virginia Postrel. Now this seemed a long shot to me, on two counts.

First of all, the name quoted seemed familiar to me. I thought I recognized it as one in the same as the editor of "Reason" magazine, but I couldn't be sure. The second thing was just how incredible the statistic it quoted seemed to me. The statistic was something like this: In the history of the universe or in it's foreseeable future, no two decks of cards have ever been or will ever be in the same sequence (unless artificially so arranged ). In other words, the sequence of cards in any deck would never match the sequence of cards in any other deck either past, present, or future, in the life of our universe.

I got to tell you, having been around a deck of cards at least my fair share of time and having a pretty sporty intuitive grasp of probabilities, this seemed to me an impossibly absurd claim. But, again, I thought I recognized the name that cited the statistic (Virginia Postrel), and I knew she wouldn't be capriciously throwing around inaccurate material. Just the opposite was her style. So I didn't know what to think. It really was a conundrum for me. I recognized it as a great betting proposition opportunity, but needed to find out for sure first if I had the name identified correctly, and second if the claim itself was statistically accurate.

I emailed Virginia Postrel at "Reason" to check on the first part. She confirmed it indeed was her name associated with the quote, and further, gave me a link to the lecture where she had originally come across it. Satisfied with that part of it, it was time to check on the statistical accuracy of the claim. I must admit it was one of those things that struck me as so impossible and so counterintuitive that, at first, I didn't bother to focus on how to actually figure it out. Stunned by it, I just kept saying "No way, that's impossible."

So I submitted it for independent objective analysis. Fearing Mike Caro might still be mad at me over a similar query I pestered him about a few years ago, I farmed this one out to my brother, Rob Cinch. (He's legit, in the mathematics world, and thinks he knows how to play poker, which is a whole 'nother story.) He crunched the numbers and came up with some staggering probabilities. If it turns out wrong, call him. I'm a poker expert here, not a mathematician. Who do I look like John Nash (see "A Beautiful Mind")?

Anyway, he sent it back to me saying there are so many possible sequences in a deck of 52 cards that you're getting up there into numbers such as how many atoms are in the galaxy. Now I was ready to go off. The whole thing just kept getting more unbelievable to me. I quit playing for a month or so, thinking something might be going on. I've been around poker enough to know when something sounds fishy, so I pulled up. I admit I got a little paranoid.

After all, I had long since been the proud originator of the saying "There are no long shots in poker. There are only 52 cards in the deck. There is nothing truly unlikely that can happen." I was quite fond of this saying, and recited it frequently. But, of course, it was meant in regard to the play of hands, and particularly, to the odds of catching a particular card or cards to win a particular hand. For instance, if you have the infamous one-outer hand - you're holding set under set with no other outs - it's only about 40 something-to-one against you to hit it. That isn't a long shot at all, though when it happens, people act like it was a million-to-one or something. It isn't, it's (about) 40-to-1. And 40-to-1 shots are not the least bit unlikely or remote; they happen continuously in every walk and sphere of life, all day every day. They happen about 1/40th as often as even money shots, if that puts it in better perspective. For every 100 even money shots, there are 2 ½ 40-to-1 shots. IT HAPPENS ALL THE TIME, and it is supposed to.

Realizing all this and having incorporated it neatly into my poker philosophy, I was wholly unprepared for the ungodly statistic quoted in the magazine article. It hit me like a ton of bricks. It shook my philosophy.

The straightforward math says the total amount of possible sequences in a 52 card deck is 52 factorial (denoted "52!"). It turns out that this number is so big that you just can't believe it. There are 8 x 10e+67 (that's ten to the 67th power) possible sequences in a 52 card deck. In other words, you would run out of atoms in the galaxy before you run out of different sequences in a deck of cards. You could shuffle a billion different decks once a second and it would take 20,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 centuries, minimum, for all the possible sequences to come out. Put that in your stack. But I can't believe that and I won't believe it. "There are no long shots in poker" - or so I'm fond of saying - but apparently, every time a dealer shuffles the deck a vigintillion-to-one shot jumps out of it (vigintillion is a ridiculously large number). What in the hell is going on?

And if you put the 53rd card in the deck - the joker - you won't even believe what kind of astronomical numbers you get. More tears than Phil Hellmuth would cry if he got outdrawn in the WSOP main event final table 1000 years in a row; more hairs than Max Shapiro has lost since he first introduced Big Denny to his loyal readers; more tales than Amarillo Slim has ever spun; more nightcaps, chasers, and women than the Rat Pack ever bottomed up; more passes than Archie Karras ever made at the dice table; more points than Bugsy Siegel sold to the unsuspecting investors of the Flamingo Hotel; MORE MONEY THAN WAS EVER SKIMMED OUT OF SIN CITY; etc. We're talking big, truly astronomical numbers.

A Final Word
There are more possible sequences of cards in a 52-card deck than there are atoms in the Milky Way. I don't want to joke around too much and draw attention away from that fact. Because that's the damnedest thing I've ever heard in my life. When somebody passed that stat across the table to me, written on a scrap of paper, it rocked my world. I commenced researching it. Why? Because who else would do it? I'll tell you, if somebody had tried to bet me on this proposition - that a deck of cards would never randomly repeat its sequence, say, just in my lifetime - Howard Hughes couldn't have bankrolled my action! Neither could Kirk Kerkorian, Sheldon Adelson, Kerry Packer, or any of the other moguls cavorting around Sin City.

But I don't care if every mathematician in the world is on the other side of this proposition; I don't buy it. I'm betting against it. I say there are more atoms in the Milky Way than there are permutations in a simple 52-card deck. Way more. And I'm taking bets. Maybe I've met my match on proposition bets with this one. So be it. Just bust me.

Addendum
If you like kickers, here's a bizarre one for you. Rob Cinch of the Georgia Institute of Technology reports back to me the following: there has long been a consensus in astronomy that there are approximately (1 x 10e+79) atoms in the universe. Hubble Telescope estimates the number of galaxies in the universe to 125 billion. Therefore, simply dividing the two numbers, there are 8 x 10e+67 atoms in an average size galaxy such as the Milky Way. That's the exact same number as 52 factorial - the amount of possible sequences in a 52-card deck. There are exactly the same amount of atoms in the Milky Way that there are possible sequences of cards in a 52-card deck. You can look it all up. It's a scientific fact. The whole thing is an astronomical dead heat.

I had a premonition this statistic was going to turn out weird the whole time I was looking into it. That's why I kept at it. But men of science stick to their guns when they discover the impossible. Like Copernicus and Galileo before us, Rob and (yours truly) Dave Cinch have stumbled upon one of the great mysteries of the universe. I wouldn't even be surprised if this number (8 x 10e+67) turned out like pi or something, one of the mysterious numbers that makes the universe work. The "Cinch Constant" I'll call it, revealed for the first time in this paper.

It goes to show you: never underestimate a lowly poker writer. We're not all just guys that can't play. Some of us are heavy-duty theorists. Maybe I'll take the Cinch Constant anomaly - my new discovery - on the RGP forum and see if anybody can shoot it down. Famous though they are for their vitriolic flame-throwing attacks on all things suspect and fallacious, I doubt if anybody would even try to discredit this. Once you start invoking names like Copernicus, Galileo, Hubble et al., the posters there will probably clam up real quick, and kind of lose their voice - if you know what I mean. Science like this is tough to overcome. I'm all for the school of hard knocks - I gradjeeated from there myself along with most of my fellow gamblers - but this is pure science I'm talking now. This is academia. I invoked the Hubble deep field in my proof, for goodness sakes. That's as strong a science as you're ever gonna see in a poker article. You usually don't see stuff like that except in scientific journals. No, I suspect the naysayers on RGP will get behind my work on the Cinch Constant. They know the nuts when they see it. 8 x 10e+67 is the number of atoms in the Milky Way and it is also the number of possible sequences of cards in a 52-card deck. Remember who told you. It's a strange one.