## Rock, Paper, Scissors

If you haven’t seen it yet, you’ve got to play the interactive Rock, Paper, Scissors (RPS) game that appears in the Science section of the New York Times. Go ahead, indulge yourself in a few games before you continue… when you’re ready to come back, we’ll still be here.

Ah, good. Welcome back.

In the New York Times simulation, the computer is armed with over 200,000 pieces of data regarding the choices that humans have made when playing RPS. What the computer does is rather simple — it looks at your last four throws; it considers its last four throws; it searches its database to determine what other folks have chosen following the same string of throws; and then it makes its choice based on that information. It’s rather simple AI, but it’s very effective.

Said another way: You won’t win. Your ability to mingle at cocktail parties might imply that you’re as socially awkward as a computer, but it doesn’t mean that you’re as smart as one.

To have a chance to win, you have to stop thinking like a human. I was able to beat the computer using a simple method: I used the sequence of triangular numbers, and I divided each term by 3.

• If the remainder was 0, I chose Rock.
• If the remainder was 1, I chose Paper.
• If the remainder was 2, I chose Scissors.

Using that strategy, I prevailed, but barely: 8 wins, 6 losses, 6 ties.

You might notice, though, that it was a come-from-behind victory. I was down 5‑4 before winning 4 of the last 7. Using a random strategy only ensured that I wouldn’t play like a typical human. But doing so only gave me even odds, given that RPS is a zero‑sum game. In no way did it give me a major advantage, and my victory was merely a result of good luck.

All this talk of RPS makes me think about Demetri Martin’s take on the game:

I like rock, paper, scissors — 2/3. Rock breaks scissors: these scissors are bent, they’re destroyed, I can’t cut stuff — I lose. Scissor cuts paper: this is strips, this is not even paper, it will take me forever to put this back together — you got me. Paper covers rock: rock is fine, no structural damage to rock. Rock can break through paper at any point, just say the word. Paper sucks. It should be “Rock, Dynamite with a Cuttable Wick, Scissors.”

As it turns out, I’m a card-carrying member of the World RPS Society. My title is Senior Investigator, Theoretical Throws Bureau.  I got in on the ground floor. When I joined in 1996, my lifetime membership cost me a mere \$7. It’s now \$45 + S&H. Of course, you now get a DVD, an RPS strategy book, and a t‑shirt. Back when I joined all I got was a laminated card with my name, title, and membership number. But I joined primarily for one reason, the note on the back of the card:

By authority of the World RPS Society (through the authority granted by the World RPS Steering Committee), the bearer of this card is hereby entitled* to determine the number of rounds in a match of RPS before a decision is considered to be binding (i.e., best of 3, best of 5, best of 57, etc.).

Card must be shown prior to play.
* Not valid at officially sanctioned World RPS tournaments or in Myers County, Alaska.

I have no idea what that bit about Myers County is all about, but I love this kind of power. At a party, when my buddy and I both reached for the last Dogfish Head 90 Minute India Pale Ale, he said, “Let’s RPS for it.” I agreed, but first I reached for my wallet, showed him my World RPS membership card, and said, “Okay, but we have to play a ‘Best of 193’ match.” He shot me a look, asked if I was joking, and when I told him I wasn’t, he said, “You’re a _____. Take the beer.” Admittedly, pulling rank wasn’t as gratifying as if I had actually beaten him 97‑96 in a Best of 193 series — but the reward was drinking that last Dogfish Head instead of having to settle for a Pabst or Miller Lite.

RPS is full of inside jokes. A gambit is a series of three throws, and each one has a name. My favorites are:

• Paper, Paper, Paper – The Bureaucrat﻿
• Rock, Rock, Rock – The Avalanche
• Paper, Scissors, Scissors – Paper Dolls

What a great game…

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• 1. xander  |  March 9, 2011 at 11:02 pm

Abusing your power for a beer? Tsk tsk!

Which, of course, isn’t to say that I wouldn’t have done exactly the same thing. However, according to the card I carry in my wallet, I am a member of the Beer Drinkers of America—and have been since I was only 6—and I must respect the lure of Dogfish Head

• 2. venneblock  |  March 10, 2011 at 8:17 pm

I knew I liked something about you, Xander! Anyone who likes Dogfish Head is a friend of mine. I’m envious of your long-standing membership in BDA.

• 3. Veky  |  March 10, 2011 at 12:54 am

Computer is so bad it is not even funny. The biggest disadvantage in RPS is showing your opponent exactly how you think, and computer does that willingly. All I have to do is think of moves as usual, assume computer will play the move to beat me, and then beat that move. The version with Spock and lizard would be harder to beat that way.

Also, there is even an easier way. Just find some self-perpetuating pattern (I found paper-rock-paper-rock) of 4 moves such that the computer always guesses wrong, and you win some 6 times before computer “learns” what you’re doing. :-]

• 4. Brent  |  March 10, 2011 at 11:35 am

I am surprised you won. Taking the triangular numbers mod 3 means you will just endlessly repeat the pattern Paper, Rock, Rock. =)

• 5. venneblock  |  March 10, 2011 at 8:14 pm

Yeah, but humans don’t normally play using such regular patterns. I guess I would have gotten beaten if the computer tried to analyze the patterns in my play.

• 6. Veky  |  March 13, 2011 at 1:44 am

Computer does that (otherwise my play would give me an infinite advantage), but only after 30 moves or so. Enough to win, especially when you have The Card. 😉

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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