Friday, April 29, 2005
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Rock, paper... Christie's
When it comes to changing diapers, Erika and I try to alternate when we are both home. Occasionally, however, we lose track of whose turn it is, in which case we resort to the time-honored tradition of rock, paper, scissors.
That was flashing through my head when I read this Caroline Vogel article in the New York Times (thanks to J.H. for the link):
After re-reading the article, however, what I found particularly interesting about this story is the contrast between these two paragraphs. There's this one:
This actually makes sense -- when the decision-making costs exceed the payoff differential between the two choices, this is a rational decision.
However, this leads to an interesting question -- is rock, paper, scissors a game of chance? While Hashiyama faced a minimal difference in payoffs between his choices, both Sotheby's and Christie's saw a whopping difference between getting nothing or getting some sizeable commissions from Hashiyama's business. Given this gap in payoffs between winning and losing, Christie's thought it was worth doing some strategic research:
Sotheby's thought of the game as a strict game of chance, and did no research.
Given that there are apparently rock paper scissors championships and rock-paper-scissors strategy guides (and please, someone tell me if these are hoax sites), who was right -- Christie's or Sotheby's?
[Christie's won, so isn't the answer obvious?--ed. In a one-shot game, it's not clear that Christie's won because of research; they might have won because of chance. A normal-form version of this game reveals that the only equilibrium strategy is to randomize equally among the three options. However, this might be a game where the designations of "rock, paper, scissors" alters how human beings feel about the choices, which subtly alters their expectations of what other players will do, which then alters their own strategies. In other words, a formal model of rock, paper, scissors might not carry the crucial piece of information to optimize on strategy. Now you're making my head hurt--ed. Aha! This is evidence to support the original claim; even if there might be a strategic element to this game, that element is so small that it's outweighed by the computational costs of figuring out the optimal strategy against a specified opponent!!]
"Good ol' rock. Nothing beats that. D'Oh!!" Bart Simpson.posted by Dan on 04.29.05 at 11:46 AM
Either person could of made it a game of a chance if they wanted to by rolling a die to determine their choice. But by using a human brain to make a choice consciously it becomes a game of pyschology.posted by: wml on 04.29.05 at 11:46 AM [permalink]
Those are joke (not really hoax) sites.
The strategy guide is intended to be humorous, like the website.posted by: MattJ on 04.29.05 at 11:46 AM [permalink]
This is a fun site, though it sheds no light on the psychology of the game:posted by: brent on 04.29.05 at 11:46 AM [permalink]
As the game is traditionally played, it's not a game of chance at all. A good RPS player can subtly delay her move until she sees what the other player does and act accordingly. If sufficiently smooth, this slight of hand is nearly undetectable.
Is this cheating? Well, of course.
Presumably, the Sotheby-Christie RPS smackdown was done via sealed bids, so the above does not apply.posted by: uh_clem on 04.29.05 at 11:46 AM [permalink]
Then there's Rock Paper Scissors Spock Lizard which I've never actually played, but seems like it would add quite a bit of complexity, and so probably unpredictability....posted by: Wiz on 04.29.05 at 11:46 AM [permalink]
Glad the UN hasn't adapted yet. Saddam was an old pro at it:posted by: MKL on 04.29.05 at 11:46 AM [permalink]
agree with wml "But by using a human brain to make a choice consciously it becomes a game of pyschology."
pyschology doesn't end only with the choice, one must consider the personalities involved and the subconscious inclinations towards rock, paper and scissors, what personaility types are more likely to select one item over the other (initially I wrote implement - what does that say?) and what unconscious cultural and social significance do the individual items bear and so bearing how does this influence outcome. Or does it? Oooo... You need control groups tested and grouped by personality type psychology battling against known and randomnly classifed combatants. Pupil dilation response testing to randomnly interspersed RPC elements within an overallly accessed emotinal null group of test images to suggest if predispostion is a subconscious or conscious filtering process ... who knows, Mr. Hashiyama may yet give us the world's first RPC PhD thesis.posted by: Jon on 04.29.05 at 11:46 AM [permalink]
Err... while those sites are someone tongue-in-cheek , I do believe they are legitimate. Here's a press release from the Rock-Paper-Scissors Society about the recent Collegiate Rock Paper Scissors Championship:posted by: Mark on 04.29.05 at 11:46 AM [permalink]
As a repeated game, it becomes fairly clear that RPS is not a randomized game. The traditional reasoning behind claiming it's purely random is that no deterministic strategy could outperform a random strategy when playing against another random strategy. This is true but trivial; people do not play random strategies, because they hope for a better than 50% chance of winning. Perhaps the best proof of this is that a computer program managed to win in a computer RPS tournament. See:
Anyone remember the old Far Side cartoon entitled "In the days before paper and scissors"?
Two cavemen playing, with the punchline "dang, tied again!"
Cracks me up just thinking about it.posted by: Barry P. on 04.29.05 at 11:46 AM [permalink]
Complicated, why not assign one "Heads", the other "Tails", and spin a coin?posted by: Ying-Yang on 04.29.05 at 11:46 AM [permalink]
Because then there is an element of uncertainty in the decision making process. With RPS the players are fully responsible themselves for the outcome. It shifts all responsibility to the players.posted by: One eyed Jack on 04.29.05 at 11:46 AM [permalink]
One interesting thing about Rock-paper-scissors is that it's not binary like flipping a coin or yes-no. I'm reminded of the famous "...one the one-hand, on the other-hand, ...yet on the gripping-hand..." of the Mote in God's Eye.posted by: Ted B. on 04.29.05 at 11:46 AM [permalink]
In Rock, Sissors, Paper, every strategy is rationalizable (by some conjecture, which is in turn rationalizable by another conjecture, etc.). Human psychology would become relevant if it helped a player to make a correct conjecture about the play of the other player. However, if both players used their knowledge of human psychology to form correct conjectures about the play of their opponents, and optimized in response to these conjectures, then it would follow that they play the unique equilibrium, which involves choosing each (pure) strategy with equal probability, making psychology irrelevant.posted by: ok on 04.29.05 at 11:46 AM [permalink]
I always preferred odds and evens.posted by: Jor on 04.29.05 at 11:46 AM [permalink]
bubble gum bubble gum in a dish is the better way to goposted by: Pkill on 04.29.05 at 11:46 AM [permalink]
Steve Mirsky had an interesting column in the June 1996, Scientific American, titled "Anti Gravity: The Lizard Kings". Apparently the male of the side-blotched lizard species, Uta stansburiana, comes in three types that are caught in a living version of RPS. In mating, the strategy of the orange-throated males beats that of blue-throats, which beats that of the yellow stripped-throats, which beats that of the orange throats. Apparently the cycle takes six years.posted by: Acad Ronin on 04.29.05 at 11:46 AM [permalink]
Upon further reflection, the answer to your question of who was right is obvious: Christie's was right (in the sense of choosing an optimal strategy). Since Sotheby's randomized, every strategy for Christie's was a best response (including the strategy that Christie's chose on the basis of research, although the research turned out to be irrelevant). Sotheby's on the other hand did not foresee Christie's reasoning about the problem. Christie's reasoning in fact made Christie's vulnerable to defeat. If Sotheby's had correctly anticipated Christie's reasning, Sotheby's would have won. On the other hand, in another sense, both players were wrong. Both had an erroneous view of the process generating the opponent's choice. In particular, Christie's consulted psychology, which turned out to be irrelevant, since Sotheby's randomized.posted by: ok on 04.29.05 at 11:46 AM [permalink]
The first time I saw this question considered tactically was in an Ian Fleming novel, of 1964 vintage.
If a percentage of the paintings turn out to be fakes, as has been shown to be the case on examination of some other Japanese stashes of French Impressionism, does Christie's still count as the winner?posted by: big dirigible on 04.29.05 at 11:46 AM [permalink]
This addresses the issue of decision-making when the available information is inadequate to make an informed selection.
"Complicated, why not assign one 'Heads', the other "Tails", and spin a coin?"
But because then another argument begins as to what constitutes "Head" or "Tails" when the design of a coin has no one's head stamped on it, as is the case with Japanese coins.
The psychological aspect is clearly spelled out in the article.
'"Everybody knows you always start with scissors,' she added. 'Rock is way too obvious, and scissors beats paper.' Flora piped in."
For children, the desire to avoid the faux pas of doing the obvious drives their choices toward scissors and paper, with a resulting bias toward scissors as the stronger of the two.
I live in Japan. My children and I use Jan-ken-pon (its Japanese name) to make decisions all the time. I always choose rock first. Even though my eldest is 10 years old now, the kids have still not figured out why Dad always wins.
If you believe my strategy preposterous, look at the example. Christie's, using children as consultants, went with scissors. Sotheby's would have won with rock.posted by: MTC on 04.29.05 at 11:46 AM [permalink]
It is not entirely chance. We have an elaborate system of picking which movie we will watch when we have people over. Part of The System involves rock, paper, scissors. The same two people almost always win. You just have to decide what the other guy is going to think and think one step ahead of him. The element of chance decreases with the number of throws; there's more "luck" involved in a one throw shot than if you're doing best two out of three.
There is also a part of The System that involves a coin toss. Obviously this is entirely chance.
I would say that rock, paper, scissors is about like black-jack. Chance is definitely involved, but you need strategy to win consistently.posted by: Freeman Hunt on 04.29.05 at 11:46 AM [permalink]
In one of his Phaze novels (Red Adept, maybe) Piers Anthony had his protagonist mulling the strategies of R-P-S -- viewing it as a game of skill.posted by: Mark L on 04.29.05 at 11:46 AM [permalink]
The RPS sites linked in your post (worldrps.com and rpschamps.com) are neither hoax sites or jokes. Doug and Graham Walker (the founders of the World RPS Society) take their Rock Paper Scissors quite seriously, and hold a yearly international tournament in Toronto. This past year, competitors came in from various parts around the US (NY, Michigan, DC), Australia, and Japan. It's been covered by CNN, the CBC, The NY Times, NHK Japan, and an hour-long special was aired on Fox Sports News.
Google for RPS Training Blog, and you'll find a couple of sites devoted to preparation for last years event.posted by: Ken Bromberg on 04.29.05 at 11:46 AM [permalink]
RPS is very much a game of skill. To convince youself of this, set up a tournament with some friends, playing to win a prize (or series of prizes) that you all care about and desire. If you do this often enough, you will quickly see that some folks are much, much 'luckier' than chance allows.
I can attest to how common RSP is in Japan and it is not confined to children. Here in Tokyo, just yesterday I was playing tennis with a group of 30 year old men and women and doubles pairings and playing order was all decided by a round of group RSP. If you spend more than a week in Japan, I can guarantee that you will witness RSP.
They don't call it "Rock, Scissors, Paper." It has it's own nonsense name ("jyan, kenn, poi") and song/cadence, kind of like eeney, meaney, miney, moe... It's so deeply ingrained in Japanese culture that many people are surprised to learn that the game exists in America.posted by: John in Tokyo on 04.29.05 at 11:46 AM [permalink]
Definitely a game of skill...
A surprisingly interesting discussion. How long has RPS been in America? Was it brought back from Japan by returning GI's after WW2 or has it been here longer? Where did it originate?posted by: rickl on 04.29.05 at 11:46 AM [permalink]
For a one-shot game, I'm not sure what to think -- but when you play the game multiple times in succession with real people, it is definitely a game of deduction. People are very bad at simulating random strings, and they have detectable regularities in their behavior.
Of course, a completely random strategy is guaranteed to win 1/3, lose 1/3 and tie 1/3 against any other strategy; but one can often do better. [And, my son and I have an eerie tendency to tie multiple times in a row, which suggests that SOMETHING predictable is going on -- but neither of us can out-meta-analyze the other...]
Incidentally, the quote about Sotheby's does NOT say that they chose paper randomly, only that they "thought of the game as a strict game of chance". Did they roll a die to pick paper, or did someone choose paper casually, assuming that it made no difference what they chose? If the latter, than Christie's research may have been valid.posted by: TMA on 04.29.05 at 11:46 AM [permalink]
In fact, reading the articule, the Sotheby's representative said:
Which is quite different from saying they chose randomly [in the strict, uniform sense]!posted by: TMA on 04.29.05 at 11:46 AM [permalink]
I am a PRS (in the South we say "Paper Rock Scissors) enthusiast, and use it frequently for medium stakes competitions - drinks, dinner, movies.
1st, delaying your throw so as to see what the other person is doing and then changing your throw accordingly is definitely cheating, and no honorable player would do that. You should KNOW before you throw what you are doing. You should be able to do it with your eyes closed or back turned and have the same result.
It can of course be a random game, but is only fun when both players have reasons for doing what they are doing. And even among players who don't take it seriously, there are definite tendencies, so the good PRS player can beat them - unless they are determinedly random. Almost noone opens with paper, it seems weak and is the biggest gesture so it feels very vulnerable. Thus rock is the best opening move. A lot of people open with scissors, but rock is most common (probably because it involves no movement from the clinched fist). So if you open with rock you will either smash scissors or tie another rock. That's why I think Sotheby's played paper, going for the kill.
Which is why the 11 year old twins are clearly rookies. The reason you play rock is because it's obvious and you can base your subsequent moves on what that person throws first and whether or not they seem like a double or triple throw type person. Trust me, paper first people are very rare and if you do find one and end up one hand down that's usually ok because you learn a lot based on the fact that they threw paper at you - assuming you actually have 3 hands to use not this one off garbage.
Christie's certainly deserved to have their scissors crushed by the strength of the mighty rock but Sotheby's tried to be too cute and met the fate of all un-seasoned paper firsters.posted by: Stress on 04.29.05 at 11:46 AM [permalink]
Classic game theory. Many video games are balanced on this idea, as well as the US government. Why do you think there are three branches of government?
posted by: bago on 04.29.05 at 11:46 AM [permalink]
As to whether RPS is a game of skill or not, I am reminded of Mark Twain's Science vs. Luck (it's there; scroll down). It's relevance to this conversation is strained, but a Twain reference is its own justification. :)posted by: Moe Lane on 04.29.05 at 11:46 AM [permalink]
In the Piers Anthony book described above, the winning strategy (in a repeated game) is to play the hand your opponent loses with.
I've tried this, and it actually works pretty well.posted by: Zak on 04.29.05 at 11:46 AM [permalink]
My brother used to invent new objects for the game. Dynamite - Make a rock but stick you thumb up for the wick. Dynamite beats rock and paper because it blows them up but scissors can cut the wick. Then there was rain. hold you hand palm down with fingers splayed. Rain rusts scissors, erodes rock, turns paper to mush and puts out the wick on dynamite. Good ol rain, nothin beat that.posted by: matt on 04.29.05 at 11:46 AM [permalink]
Bond-san lost to Tiger Tanaka in "You Only Live Twice" and Tiger was disapointed by Bonds poor showing.
Any conversation of RPS strategy must include a reference to Iocaine Powder from "Princess Bride". . . "What you do not smell is Iocaine powder. It is odorless, tasteless, and dissolves instantly in liquid and is among the more deadly poisons known to man."
Vizzini's strategy "All I have to do is divine it from what I know of you. Are you the sort of man who would put the poison into his own goblet or his enemies?" fails because both glasses are poisoned and the Man in Black is immune to Iocaine.
Clearly, this thread needs some input from Vizzini from "The Princess Bride":
"Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I am not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool, you would have counted on it, so I can clearly not choose the wine in front of me.
Your taste in movies is excellent!posted by: Erik on 04.29.05 at 11:46 AM [permalink]
the quote about Sotheby's does NOT say that they chose paper randomly, only that they "thought of the game as a strict game of chance"
Al Taubman leaves nothing to chance. Looks like this time Sotheby's couldn't find a way to fix the outcome.
Well, I just read 39 of these comments which begs the question, Who needs to get out more, the writer or the reader?posted by: Dr. Fager on 04.29.05 at 11:46 AM [permalink]
Extrapolating the tools into a real world survival fight: I'd take a rock every time. It can take down a scissors wielder from a safe distance, so long as the rock thrower is willing to chance a miss. The paper wielder is relegated to using his sole advantage to wiping the considerable sweat off his bilateraly doomed brow.
The survivor of the battle would then have all tools to choose from, but might still favor one for making a life with. Scissors serve as a knife and fork, magnifying mirror or striking tool for starting fires, razor, scalpel, spear, tweezers, measuring caliper, drill, drawing compass, and so on. The rock is crude and heavy, the paper is fragile and not of much use but for wrapping, without a pen made of blood dipped-scissorpoint.
In a battle of what legacy to leave? A scissors-equipped bard can scratch his brief screed into a tree, or a soft stone perhaps. A rock-writer can only manage a few words, but onto a large cliff. The paper-inscriber can wax the most eloquently and crown herself the most sought after by her successors, provided she can obtain enough ink or blood and penpoint.
So in summary, the rock is best for conquest. The scissors best for advancement. The paper best for posterity.
Reading the personality type of the player in a RPS game into one of these categories might thusly give you a predictive edge, factoring in their proclivity for intentional deceit.posted by: RufusLeeKing on 04.29.05 at 11:46 AM [permalink]
Like Matt's brother, in college we, too, added a new weapon -- the pencil (extended forefinger.) Scissors cut pencil, and pencil writes on paper. But rock and pencil tie (pencil can write on rock, but rock can crush pencil.) The winner of a pencil-rock throw was determined by who acted first, acting out the writing on the rock, or the crushing of the pencil. In this game, paper is a loser throw, and scissors strongest, but many a pencil was thrown for the sheer novelty of it.
In the tradtional game, I'm one of those "paper throwers" when playing novices, as the hand starts out in the rock position, and some never figure out how (or when) to change that.posted by: max on 04.29.05 at 11:46 AM [permalink]
Usually we (Chinese) play best 3 out of 5. I use strategy to "trap" the other by setting a "pattern" showing any one of the 3 choices TWICE in a row and then SWITCH to the kill. Because of the "pattern" set, the oponent will immediately counter with the "killer" for the third round. However, I will come up with the counter to that and win the fourth round.posted by: b on 04.29.05 at 11:46 AM [permalink]
In response to TMA,
I think that it is a reasonable reading of the article that Sotheby's randomized. Reasonable, but not necessary; so you make a fair point. However, it is worth pointing out that my reasoning holds if Sotheby's did randomize, which is consistent with (and I would argue, suggested by) the article.
Many of the posts here talk about the difficulty of actually randomizing in a repeated face to face interaction; none of these points are relevant here, since either Christie's or Sotheby's could have rolled a dice to decide.
I think an important point to make is that trying to second guess the opponent is only worthwhile if the opponent is not randomizing (i.e., playing each pure strategy with equal probability). Moreover, reasoning about the other's play can be worthwhile against some opponents, but not against all opponents. Namely for any chain of reasons arguing for some choice, there is some opponent who will reason one step further and beat you. So reasoning can only help you if (i) you are EXACTLY ONE STEP more sophisticated than your opponent (given that the first step of the reasoing is the same for both of you, i.e., both of you start off thinking that a totally unsophisticated player would start off with scissors), or (ii) it causes you to win by accident.
On the other hand if your opponent is drawn randomly from a population and the frequency of strategies within the population is known, then it is a simple caculation to determine the best strategy (on average against the population), and recommendations of how to play make sense.posted by: ok on 04.29.05 at 11:46 AM [permalink]
1. It’s not a game of psychology unless you're playing against an idiot or a little child. Get real. Neither is tic tac toe. The fact that one person often wins a few games in a row is no different from the fact that if you’re flippin’ a coin sooner or later you get a string of heads or a string of tails – ooooh! The laws of probability have been suspended!
If you really think it's just a child's game, I suggest you look at the old tournaments of RPS computer programs at:
The task was to write programs that could play each other many times (with access to the history of the match) -- the "obvious" programs that just did everything completely randomly finished in the middle, as you'd expect, and did equally well against all opposition. But some programs did substantially better, overall, beating up very seriously on some programs while not doing too badly against any others. Again, this depends on a set of opponents who play each other many times and who use the information of their previous games as input in making their current decision.
Getting 6 ties in a row should happen -- well, once in every 729 times you try the game 6 times. I haven't kept careful records, but I can tell you that my son and I have tied 6 in a row several times -- and we can't have played more than maybe 200 times total.posted by: TMA on 04.29.05 at 11:46 AM [permalink]
We used to add two tools: fire and water. Fire beats rock, paper and scissors but loses to water, which loses to the other three.
It would appear that fire is the superior and water the inferior choice. However, because everyone recognizes this and is more likely to choose fire, water becomes a much better choice.posted by: I'llbeyou on 04.29.05 at 11:46 AM [permalink]
Well, I don't see why fire is superior -- this is just a larger game of rock-paper-scissors (fire-rpg-water) with an automatic tie-break built in when both players choose rpg...posted by: TMA on 04.29.05 at 11:46 AM [permalink]
"If you really think it's just a child's game, I suggest you look at the old tournaments of RPS computer programs at:"
Yeah and this is what I see:
/* Index of RoShamBo Player Algorithms:
Rank Dummy Bot Open BoB Leng -max level history use
27 * Random (Optimal) 32 19 1 [-0] L0 h0
with the word 'random' right next to the word 'optimal'. Now, a clever programmer could actually exploit the fact that a computer cannot really generate random numbers, just like a 'random number's table containts numbers that are deterministic (otherwise they wouldn't be in a table).posted by: radek on 04.29.05 at 11:46 AM [permalink]
The random method is "optimal" in a very precise mathematical sense -- it maximizes the minimum return against any other strategy. And in this symmetric game, that return is exactly 0. But you know that.
That's not at all the same thing as saying that people (or other programs) don't have exploitable patterns of behavior -- sure, if you attempt to exploit them, you are vulnerable to someone else whose past behavior was a ruse to set you up for a kill -- but it's an empirical question just how many levels of this there are in a real life house of games.
In the "overall" standings from the second competition, "Random (Optimal)" came in 41st out of 64.
I doubt that any program attempted to explicitly hack the random number generator, though if there is a detectable and explotable pattern in the sequence of choices, that counts -- do you think people's internal random number generators are any better?posted by: TMA on 04.29.05 at 11:46 AM [permalink]
Put it this way, a computer program which randomizes over the three strategies is gonna win half the time against ANY other program, no matter how sophisticated. Now yeah, if you're playing a child or an idiot, who plays rock every time say, then you can do better. But what's the point of that?
If I was Mr. Hashiyama and I had learned beforehand that Christie's was "researching" the game, I'd have immiediatly called off the game and given my business to Sotheby's. Why would you hire a naive idiot to be your broker? The fact that Christie's got lucky doesn't change that fact.posted by: radek on 04.29.05 at 11:46 AM [permalink]
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