## Rock Paper Scissors experiment

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## See OP

Rock (vs)
63
12%
Paper (vs)
103
20%
Scissors (vs)
95
18%
Rock (co-op)
131
25%
Paper (co-op)
70
14%
Scissors (co-op)
55
11%

Total votes: 517

Blatm
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### Rock Paper Scissors experiment

Do not vote before reading!

This is designed to test competitive RPS vs. cooperative RPS.

Normally, I would include two distinct polls, but the forums don't seem to allow that, so instead I have to do this.

There are 6 options in the poll: Rock (vs), Paper (vs), Scissors (vs), Rock (co-op), Paper (co-op), Scissors (co-op), and you have 2 votes. Spend exactly 1 vote on the first three, and 1 vote on the second three.

Among the first three, you are trying to choose the option that will beat the most popular choice, i.e. standard RPS.

Among the second three options, you are trying to choose the most popular option.

I'm looking forward to seeing how this turns out.

Also, for those who might have missed it, I think my last experiment of the sort turned out well.

skeptical scientist
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### Re: Rock Paper Scissors experiment

Of 4 voters so far, 3 of them voted the same way I did!
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

greycloud
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### Re: Rock Paper Scissors experiment

Woah... everyones voting for that one?? That's really weird!

skeptical scientist
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### Re: Rock Paper Scissors experiment

greycloud wrote:Woah... everyones voting for that one?? That's really weird!

You forgot to vote cooperatively.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

greycloud
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### Re: Rock Paper Scissors experiment

I didn't forget, I just can't work out how to do it...

skeptical scientist
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### Re: Rock Paper Scissors experiment

So far, out of 6 people who voted in both categories, 5 voted in such a way that their coop vote beats their vs. vote.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

PatchMonster
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### Re: Rock Paper Scissors experiment

I always pick paper when playing RPS against a newbie. Reason being, when opponent is thinking about their options rock comes to their mind first. It actually works, a lot. If I know my opponent is sharp, I pick scissors to counter their paper.
The liberal media has a hidden agenda!

Zak
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### Re: Rock Paper Scissors experiment

I usually pick rock, just to counter people like you.

Also, for some reason almost everyone that I've played rock paper scissors with has chosen scissors first. Not sure why.
*waggles eyebrows*

PatchMonster
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### Re: Rock Paper Scissors experiment

Z.A.K wrote:I usually pick rock, just to counter people like you.

Also, for some reason almost everyone that I've played rock paper scissors with has chosen scissors first. Not sure why.

Well, sometimes I can sense if they know how I work, so I'll pick a counter. To me, RPS is just thinking one step ahead of the other person, which can be quite complicated if the other person is attempting the same thing. RPS is source of many headaches for me.
The liberal media has a hidden agenda!

Zak
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### Re: Rock Paper Scissors experiment

Have you ever played kongai?
*waggles eyebrows*

skeptical scientist
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### Re: Rock Paper Scissors experiment

For the moment, I seem to be winning.

Interesting observation: if everyone votes completely at random, then everyone has a better than 1/3 chance of winning the cooperative one, and a worse than 1/3 chance of winning the competitive one. This is true no matter how many people vote, but the probabilities tend to 1/3 in the limit as the number of voters tends to infinity.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

Blatm
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### Re: Rock Paper Scissors experiment

Spoiler:
At the moment, there are 99 votes as follows:
13
20
17
22
14
13

Assuming that people chose the throw they thought people would judge the most popular (for the most part, "Good ol' rock. Nothin' beats that.") in their co-op vote, and that the level of thinking was between 1 and 3 (1 being "Everyone picks rock, so I pick paper.", and 2 being "Everyone thinks with 1 level of thinking, so I pick scissors,"), the arithmetic mean of the level of thinking, given by: 0.44*(0.4 + 2*0.34 + 3*0.26) + 0.28*(0.34 + 2*0.26 + 3*0.4) + 0.26*(0.26 + 2*0.4 + 3*0.34) (I assumed 100 votes, here) is 1.936.

Though both those assumptions are probably a bit of a stretch, I think the result is pretty sensible, if not a bit more than I was expecting.

skeptical scientist
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### Re: Rock Paper Scissors experiment

Blatm wrote:Assuming that people chose the throw they thought people would judge the most popular in their co-op vote, and that the level of thinking was between 1 and 3, the arithmetic mean of the level of thinking...
...would be 2 if everyone chose completely at random. You are pigeonholing people into a framework that is completely invalid, since you can't account for the people choosing at random, or the people going with some rationalization other than the one you are assuming. In any case, the result is close enough to 2 that there's no significance.

I'm calling bull.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

crzftx
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Location: Rockford, IL

### Re: Rock Paper Scissors experiment

I'm winning
EDIT:
Spoiler:
No, I'm not. Haha, don't know what I was thinking when I first read them. I'm losing vs., and I don't know why. Keeping with rock being the most popular, I don't think there are any level 0 thinkers (that pick rock because it's the most popular). I thought most people would pick up on that and few people would remain a level 1 thinker (pick paper in order to beat the level 0 thinkers picking rock). I was a level 3 thinker, thinking most people would think most other people would be a level 1 thinker, thus becoming a level 2 thinker. So I picked rock, in case you don't follow, in order to beat the level 2 thinkers which pick scissors. It looks like most people were just level 1 thinkers... or (oh no) level 4 thinkers... I'd believe it, but I doubt it right now.
The second part was easy. There wasn't really any levels in my mind. You're trying to pick what everyone else picks. I'd think everyone would just know to pick rock, as it's the most popular in vs.

Dom
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### Re: Rock Paper Scissors experiment

PatchMonster wrote:I always pick paper when playing RPS against a newbie. Reason being, when opponent is thinking about their options rock comes to their mind first. It actually works, a lot. If I know my opponent is sharp, I pick scissors to counter their paper.

lol, so thats why the opening rock is so solid.
I'm alive

fjafjan
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### Re: Rock Paper Scissors experiment

I have played a fair bit of RPS with "noobs" and my experience is that people go with either rock, but more often scissors. Around 60% scissors really
//Yepp, THE fjafjan (who's THE fjafjan?)
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Blatm
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### Re: Rock Paper Scissors experiment

skeptical scientist wrote:
Blatm wrote:Assuming that people chose the throw they thought people would judge the most popular in their co-op vote, and that the level of thinking was between 1 and 3, the arithmetic mean of the level of thinking...
...would be 2 if everyone chose completely at random. You are pigeonholing people into a framework that is completely invalid, since you can't account for the people choosing at random, or the people going with some rationalization other than the one you are assuming. In any case, the result is close enough to 2 that there's no significance.

I'm calling bull.

As I said, my assumptions are a bit of a stretch, but I don't think that there is no significance to the result.

Yes, there will be people choosing randomly. Yes, there will be people thinking on the 4th level or higher, and yes, people will go with other rationalizations than the one I thought of, but I think that the majority of the people who play will fit into these assumptions, because RPS is a pretty straightforward game with which most people have a comparable amount of experience with.

Just because the result is close to what it would be if people were to choose randomly given my assumptions doesn't mean that that's what happened. It's conceivable, and I think more likely, that people simply think a bit less than 2 levels deep on average. As an analogy, in the 2000 US elections, the popular vote was split almost exactly 50/50 between Bush and Gore, bit that certainly doesn't imply that almost the entire population voted randomly. Though the small noise that is undoubtedly there will make the average tend towards 2, the fact that it is at the moment close to, but less than 2 still tells me "People think a bit less than 2 levels deep on average".

BoomFrog
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### Re: Rock Paper Scissors experiment

At the time of my vote I won both types. I will sleep happily tonight.
"Everything I need to know about parenting I learned from cooking. Don't be afraid to experiment, and eat your mistakes." - Cronos

greycloud
Posts: 103
Joined: Sun Nov 23, 2008 7:18 pm UTC

### Re: Rock Paper Scissors experiment

I'm pretty sure this isn't just random.

Spoiler:
I tried to use the chi-squared goodness of fit formulae, mostly because I'm bored and meant to be revising for my stats test...

At the moment, there's 165 votes, so each one should have an average of 27.5 votes. The sum of ((Expected - Observed)^2)/Expected made 8.35, which with 95% certainty we can see that the hypthesis that it's random doesn't fit.

... I think.

Puck
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### Re: Rock Paper Scissors experiment

At the time of my vote, I wasn't winning vs., but now I am. Here's how I think it breaks down (as I'm typing I realize that crzftx said the same thing):

Spoiler:
It's clear from the co-op results that Rock is the most popular choice. So, let's use this assumption in the vs. model - if you know that Rock is the most popular choice, then a level 1 thinker would choose paper to beat it. I guessed that most people would be level 2 thinkers, realizing this and choosing scissors to beat it. So, I took it one more level, choosing rock to beat that. Of course, a level 3 thinker is indistinguishable from a level 0 thinker... Whatever. I'm winning.
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sonickid01
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### Re: Rock Paper Scissors experiment

I think I just failed. I picked scissors on both. My first instinct said "paper and scissors," but I went against the instinct. :^P. I coulda won the first one, but meh.

Christopher
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### Re: Rock Paper Scissors experiment

This whole situation is poorly defined. Who are we playing against? Are we playing against a completely unknown opponent? In that case I think you would have to expect them to throw the most common choice (rock) and so you would throw paper. Some people I think are making this assumption. Others are making the assumption that their opponent knows as much about RPS as they do and so are trying to out think them by running some way around the RPS circle.

skeptical scientist
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### Re: Rock Paper Scissors experiment

Christopher wrote:This whole situation is poorly defined. Who are we playing against? Are we playing against a completely unknown opponent? In that case I think you would have to expect them to throw the most common choice (rock) and so you would throw paper. Some people I think are making this assumption. Others are making the assumption that their opponent knows as much about RPS as they do and so are trying to out think them by running some way around the RPS circle.

You are playing against the other players (or with them). It's a game. You win the first part if your vs. guess beats the most popular vs. guess, and you win the second part if your coop guess is the most popular coop guess.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

Christopher
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### Re: Rock Paper Scissors experiment

skeptical scientist wrote:
Christopher wrote:This whole situation is poorly defined. Who are we playing against? Are we playing against a completely unknown opponent? In that case I think you would have to expect them to throw the most common choice (rock) and so you would throw paper. Some people I think are making this assumption. Others are making the assumption that their opponent knows as much about RPS as they do and so are trying to out think them by running some way around the RPS circle.

You are playing against the other players (or with them). It's a game. You win the first part if your vs. guess beats the most popular vs. guess, and you win the second part if your coop guess is the most popular coop guess.

Ah, I understand now. That makes much more sense.

Sungura
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### Re: Rock Paper Scissors experiment

Wow, I happen to have picked paper for the first (I generally pick paper, again because it seems most people pick rock) and then I voted rock accordingly for the second set.

RPS is interesting...in the mafia subforum one of the games used RPS and it added an interesting twist and some debate about rps strategy.
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The_Duck
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### Re: Rock Paper Scissors experiment

I won!

Spoiler:
For vs. I figured "xkcdians will pick paper [to my mind the 'intelligence over brute force' strategy]" and so went with scissors, and luckily paper is just edging out scissors as most popular. For the co-op I figured "people have no experience playing this, and so will pick the first option" which looks to be correct.
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Game_boy
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### Re: Rock Paper Scissors experiment

I think it's impressive that everyone who has voted has voted twice, once in each category. With that many votes, any normal forum would have people who didn't get it, randomly picked two or something else like that.
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### Re: Rock Paper Scissors experiment

Game_boy wrote:I think it's impressive that everyone who has voted has voted twice, once in each category. With that many votes, any normal forum would have people who didn't get it, randomly picked two or something else like that.

That's not actually true. I know for a fact that someone voted in the versus category and not the co-op category. All we really know is that the total number of vs. votes is the same as the total number of co-op votes.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

greycloud
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### Re: Rock Paper Scissors experiment

True, I didn't vote for both. For some reason it wouldn't let me vote twice :S

crzftx
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### Re: Rock Paper Scissors experiment

The first option isn't clearly stated. I went with the one that I thought would beat the most picked option. An alternate method would be to go with the one that wins the most compared to all options.
Spoiler:
For this game, Paper and Scissors have about the same amount of votes. For the time, Scissors has more. So Rock beats the highest picked. But since rock has such a small number of people picking it, Paper loses a lot less. Paper recieves a better ratio, while Scissors wins the most. Noboody said which to prefer.

skeptical scientist
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### Re: Rock Paper Scissors experiment

crzftx wrote:The first option isn't clearly stated. I went with the one that I thought would beat the most picked option. An alternate method would be to go with the one that wins the most compared to all options.
Spoiler:
For this game, Paper and Scissors have about the same amount of votes. For the time, Scissors has more. So Rock beats the highest picked. But since rock has such a small number of people picking it, Paper loses a lot less. Paper recieves a better ratio, while Scissors wins the most. Noboody said which to prefer.

It said, "you are trying to choose the option that will beat the most popular choice." This is not ambiguous, and means that the goal is to get the most wins, not the best win/loss ratio.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

crzftx
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### Re: Rock Paper Scissors experiment

skeptical scientist wrote:
crzftx wrote:The first option isn't clearly stated. I went with the one that I thought would beat the most picked option. An alternate method would be to go with the one that wins the most compared to all options.
Spoiler:
For this game, Paper and Scissors have about the same amount of votes. For the time, Scissors has more. So Rock beats the highest picked. But since rock has such a small number of people picking it, Paper loses a lot less. Paper recieves a better ratio, while Scissors wins the most. Noboody said which to prefer.

It said, "you are trying to choose the option that will beat the most popular choice." This is not ambiguous, and means that the goal is to get the most wins, not the best win/loss ratio.

Ok, so you got me. I didn't read it since I first picked my choices.
Maybe I could say the first poll isn't as sensible as it could be. I think any player would prefer to have a better win/loss ratio than win/"not win" ratio.

Kaeyn
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### Re: Rock Paper Scissors experiment

I got the vs one right, but the co op one wrong. Why does hardly anybody like scissors??? Just because you can't run with them doesn't make them dangerous!

Moridin
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### Re: Rock Paper Scissors experiment

I think I did the first fairly well.

Spoiler:
first one:
i win 38.317%, tie 22.897%, lose 38.785%;
the ones who beat me win 22.897%, tie 38.317%, lose 38.785%;
the ones i beat win 38.785%, tie 38.317%, lose 22.897%

ok, maybe i was wrong. the last one seems to be optimal, as it it gives a better chance to proceed to a second round if you don't win
sadly, we are lacking data on a second round

TheManInTheHat
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### Re: Rock Paper Scissors experiment

Spoiler:
I chose rock for both because I thought that most people would assume that most people would know better than to choose rock, and would choose scissors to counter the paper that would be used by people to counter the most common rock. I was wrong, but only by a little bit.
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