5 ms·

How to win at rock-paper-scissors

32 points by GvS 12y ago

ars 12y ago
Or in other words "Humans are really bad at random."
- yeukhon 12y ago
  The question is, are you sure that true random is always the best move? I say some random strategy, but totally random, like perfect random? I am not sure that actually has a big improvement...
  - ars 12y ago
    If it's anything other than perfect random your opponent can figure out your pattern and use it against you. The only time to differ from true random is if you figured out your opponent's pattern. Which can lead to some interesting strategy of making your opponent think he figured out your pattern. Then use your knowledge of what he thinks you will do to win.
oliwary 12y ago
Interesting how the pattern "rock-paper-scissors" is followed. If this is because of the name, Swedish people, for example, would follow another patterns as they call the game "rock-scissors-paper" (Sten-sax-påse).
- thomasahle 12y ago
  I wonder if it has less to do with the name and more to do with which hand beats which. That is, if you lose with a rock, you have lost to a paper, hence a paper might start looking like a better option.
  - jmilloy 12y ago
    That's what I remember from looking into this a few years back.
  - oliwary 12y ago
    Ah, that makes sense. It would lead to a lot of rock-rock etc., as the winner stays and the loser moves to the winner hand. I wonder what the players pick then? If both move up one it would lead to an even larger number of same-hand encounters.
- flux_w42 12y ago
  I never thought of that actually. In Dutch we say paper-rock-scissors (blad-steen-schaar).
  - rix0r 12y ago
    I would have said "steen schaar papier" (rock scissors paper). I guess, taken all over the world, most permutations show up.
- brusch64 12y ago
  in German it is "scissors-rock-paper" (Schere Stein Papier). I guess all combinations are possible...
  - madeofpalk 12y ago
    And in Australia it's scissors-paper-rock.
  - ximeng 12y ago
    Same in Chinese: 剪刀石头布: scissors stone cloth
    - franzwong 12y ago
      in Cantonese, it is called 包剪揼, cover-scissors-hammer
- TazeTSchnitzel 12y ago
  The order is presumably the same in Chinese as in English, given the conclusion.
- tawan 12y ago
  I have this strategy to rearrange the order when I ask someone to play. For example I'd say "Hey, to settle our discussion, let's play scissor rock paper!" While pronouncing a little bit the last option. My opponent still caught off guard will more likely play the last option, in this example "Paper". The next time I will say "ok let's play rock paper scissors". And then I'll play Rock, haha. I don't know if it really works, but I was always good in this game. At least I think so ;)
JazCE 12y ago
"The only winning move is not to play."
jakobe 12y ago
TLDR: Players are more likely to pick the move that just won. To exploit that, the best strategy would probably be to always pick the move that wasn't played. Should give you an edge until your opponent notices your pattern :)
- yeukhon 12y ago
  But now everyone starts picking the move that wasn't played. I am not saying I am very good at this game (well who can claim that...), but I mostly win well by observing opponent's reaction and their habit. I try to exploit them by giving them some false sense of my next move. Too abstract? Random pattern. And honestly, the best strategy is don't get frustrated and enjoy the game :)
- jerf 12y ago
  My wife and I play RPS to determine who does things like change a diaper when we're out and about and stuff. We tie a lot. Far, far more than chance would dictate. We can tie for 10 in a row, quite easily, and before you jump up about how this can happen by chance, we tie in sequences a lot, not just 1/3^10 times. We're trying to second guess each other. Since humans are bad at random, "just play randomly" doesn't really work; humans don't have access to "random" to play that way. So you often do get into the sorts of strategies you mention, to compensate for this. Besides, it's more fun this way.
  - bradleysmith 12y ago
    I played for years with a close friend in high school to decide who was driving or whatever, or just pass time. The better we knew each other (ie the longer we were playing) the more ties. I believe there's a natural intuition for reading the expected movements of the other player, and have seen this reproduced (if anecdotally by only testing between myself and her, and not recording results) hundreds of times. Like you, 10-12 streaks of ties were not uncommon, certainly less common than statistics would seem to dictate. somewhat relevant, there's a competitive league: http://www.usarps.com/ http://www.usarps.com/ I always wanted to see it in vegas: https://www.youtube.com/watch?v=htX4T20t6lU https://www.youtube.com/watch?v=htX4T20t6lU EDIT: clarity
valdiorn 12y ago
"The game of rock-paper-scissors exhibits collective cyclic motions which cannot be understood by the Nash equilibrium concept." This is complete bullshit. It is well understood that if your opponent is not playing an optimum strategy, you can gain an advantage by shifting away from the Nash equillibrium yourself. Example: Image a player that always picks "Paper". By shifting away from a random choice (Nash optimum) to just always selecting "Scissors" will net you a 100% win rate. This is a common trick utilized in poker, where good players will apply a certain playing style, while placing smaller bets, let their opponent adjust to your style and then suddenly change to a more aggressive style. You can take advantage of the fact that your opponent is trying to capitalize on your previous strategy. He has now introduced a sub-optimal element into his game, which you in turn can capitalize on. As in the previous example, imagine we wager $1 on rock paper scissors. I pick paper for the first 100 rounds, you always pick scissors and you always win. Now we suddenly change the bet to one million dollars a hand. I change my selection to "Rock", while you play scissors, as that has given you a perfect win rate so far, and I win the money.
- vishnugupta 12y ago
  >This is a common trick utilized in poker, where good players will apply a certain playing style, while placing smaller bets, let their opponent adjust to your style and then suddenly change to a more aggressive style. Pardon my ignorance of poker, but won't the opponent notice that you have suddenly raised the stake and that something could be afoot?
  - ghshephard 12y ago
    Playing aggressively in poker usually means betting more than your hand would otherwise dictate - but your opponent doesn't know what your hand is. So - you play for 4-5 hours, folding on weak hands, and always raising on strong hands, and then, once people think you are a grinder, you start betting on weak hands; other players fold because they were used to you betting high stakes only on strong hands, you take their money.
    - throwaway13qf85 12y ago
cyborgx7 12y ago
I hope to see some replication of this. It sounds like they just looked through the numbers for patterns, instead of making a prediction beforehand and then trying to falsify it. That's fine but there needs to be replication for that kind of conclusions.
alextingle 12y ago
If winners tend to stick with their last winning move, then shifting forward after losing is the correct strategy. Only the winners are playing irrationally here.
- oliwary 12y ago
  Wouldn't shifting backward make more sense? That way you beat the other instead of playing equal.
namuol 12y ago
How to actually win at RPS: Memorize a long, truly random sequence. That is, assuming your opponent also does. Er... now I've gone cross-eyed.
- vorg 12y ago
  > Memorize a long, truly random sequence > Humans are really bad at random You could use the digits of some transcendental number, say, pi. Skip zeros, then each digit yields two moves. For the first move, lows(1,2,3) gives stone, mids(4,5,6) gives paper, and highs(7,8,9) gives scissors. For the second move use mod 3, so 0 gives stone, 1 gives paper, and 2 gives scissors.
avaku 12y ago
>> What are your odds of winning rock-paper-scissors? Simple - one in three. At least, that's what chance predicts. I thought the chance of winning with no prior is 1/2... Otherwise, okay, you win with 1/3, your opponent wins with 1/3, and where is the other 1/3? :) I know what the article means, but they phrase is wrongly.
- throwaway13qf85 12y ago
  I don't think there's anything wrong with what they say. Your chance of winning one round of RPS is 1/3. Out of three games you win once, lose once and draw once on average. If you replay when a draw occurs, then of course you have a 1/2 chance of winning.
- ville 12y ago
  >> okay, you win with 1/3, your opponent wins with 1/3, and where is the other 1/3? :) Wouldn't that remaining 1/3 be the odds for it being a draw?
- danieltillett 12y ago
  The odds are 1/3 win, 1/3 loss, 1/3 tie :)
  - avaku 12y ago
    Sorry I didn't know the rules properly :) Which combination is a tie? In my version someone always wins :) ha ha
kingrolo 12y ago
This article reminded me of a Rock-Paper-Scissors AI from a while back (requires Flash I think). http://www.nytimes.com/interactive/science/rock-paper-scissors.html?_r=0 http://www.nytimes.com/interactive/science/rock-paper-scisso... It uses data gathered from other players. I remember playing it at the time and it was creepy how good it was at beating me. Oddly it didn't do so well this time. Maybe because I've just read that article.
- thomasahle 12y ago
  AFAIR it works by storing the most likely human move for every 3 move sequence e.g. "St Pa, St Sc, St St". If we assume most players play similarly, and don't remember much more than the last three results, this works really well.
mseepgood 12y ago
You just have to be fast enough: http://www.youtube.com/watch?v=ZVNnoOcohaU http://www.youtube.com/watch?v=ZVNnoOcohaU
hrktb 12y ago
There is a 'variant' in Japan where every players start with rock, and the game starts after this first move. It's a small variation (I think it was originally aimed to synchronize more easily), but it nills the effect described in the Article for each session.
hrktb 12y ago
There is a 'variant' in Japan where every players start with rock, and the game starts after this first move. It's a small variation (I think it was originally aimed to synchronize more easily), but it nills the effect described in the Article for each session.
andyhmltn 12y ago
Is it actually a 1/3 chance of winning though? Is that including a draw as a win? I've tried coding it up here: https://gist.github.com/andyhmltn/5c8c5734fe894db5aa02 https://gist.github.com/andyhmltn/5c8c5734fe894db5aa02 Baring in mind it was a rushed 5 minute bodge-job so it could be wrong but there seems to be a massive skew towards draws After more tests with this code it seems there's an 11% chance of winning if it's random. Baring in mind javascripts RNG
- Monkeyget 12y ago
  There is an equiprobability of winning/losing/draw. Your code is erroneous. You do a +1 to the random number you generate giving you 1, 2, 3. You then use that number to access an array with indexes [0, 1, 2]. You end with an undefined which screws your results.
  - andyhmltn 12y ago
    Well if that was the case, then one result would always have 0. The indexes are used to find what something wins against

32 points by GvS 12y ago

ars 12y ago

Or in other words "Humans are really bad at random."

yeukhon 12y ago
The question is, are you sure that true random is always the best move? I say some random strategy, but totally random, like perfect random? I am not sure that actually has a big improvement...
- ars 12y ago
  If it's anything other than perfect random your opponent can figure out your pattern and use it against you. The only time to differ from true random is if you figured out your opponent's pattern. Which can lead to some interesting strategy of making your opponent think he figured out your pattern. Then use your knowledge of what he thinks you will do to win.

oliwary 12y ago

Interesting how the pattern "rock-paper-scissors" is followed. If this is because of the name, Swedish people, for example, would follow another patterns as they call the game "rock-scissors-paper" (Sten-sax-påse).

thomasahle 12y ago
I wonder if it has less to do with the name and more to do with which hand beats which. That is, if you lose with a rock, you have lost to a paper, hence a paper might start looking like a better option.
- jmilloy 12y ago
  That's what I remember from looking into this a few years back.
- oliwary 12y ago
  Ah, that makes sense. It would lead to a lot of rock-rock etc., as the winner stays and the loser moves to the winner hand. I wonder what the players pick then? If both move up one it would lead to an even larger number of same-hand encounters.
flux_w42 12y ago
I never thought of that actually. In Dutch we say paper-rock-scissors (blad-steen-schaar).
- rix0r 12y ago
  I would have said "steen schaar papier" (rock scissors paper). I guess, taken all over the world, most permutations show up.
brusch64 12y ago
in German it is "scissors-rock-paper" (Schere Stein Papier). I guess all combinations are possible...
- madeofpalk 12y ago
  And in Australia it's scissors-paper-rock.
- ximeng 12y ago
  Same in Chinese: 剪刀石头布: scissors stone cloth
  - franzwong 12y ago
    in Cantonese, it is called 包剪揼, cover-scissors-hammer
TazeTSchnitzel 12y ago
The order is presumably the same in Chinese as in English, given the conclusion.
tawan 12y ago
I have this strategy to rearrange the order when I ask someone to play. For example I'd say "Hey, to settle our discussion, let's play scissor rock paper!" While pronouncing a little bit the last option. My opponent still caught off guard will more likely play the last option, in this example "Paper". The next time I will say "ok let's play rock paper scissors". And then I'll play Rock, haha. I don't know if it really works, but I was always good in this game. At least I think so ;)

JazCE 12y ago

"The only winning move is not to play."

jakobe 12y ago

TLDR: Players are more likely to pick the move that just won. To exploit that, the best strategy would probably be to always pick the move that wasn't played. Should give you an edge until your opponent notices your pattern :)

yeukhon 12y ago
But now everyone starts picking the move that wasn't played. I am not saying I am very good at this game (well who can claim that...), but I mostly win well by observing opponent's reaction and their habit. I try to exploit them by giving them some false sense of my next move. Too abstract? Random pattern. And honestly, the best strategy is don't get frustrated and enjoy the game :)
jerf 12y ago
My wife and I play RPS to determine who does things like change a diaper when we're out and about and stuff. We tie a lot. Far, far more than chance would dictate. We can tie for 10 in a row, quite easily, and before you jump up about how this can happen by chance, we tie in sequences a lot, not just 1/3^10 times. We're trying to second guess each other. Since humans are bad at random, "just play randomly" doesn't really work; humans don't have access to "random" to play that way. So you often do get into the sorts of strategies you mention, to compensate for this. Besides, it's more fun this way.
- bradleysmith 12y ago
  I played for years with a close friend in high school to decide who was driving or whatever, or just pass time. The better we knew each other (ie the longer we were playing) the more ties. I believe there's a natural intuition for reading the expected movements of the other player, and have seen this reproduced (if anecdotally by only testing between myself and her, and not recording results) hundreds of times. Like you, 10-12 streaks of ties were not uncommon, certainly less common than statistics would seem to dictate. somewhat relevant, there's a competitive league: http://www.usarps.com/ http://www.usarps.com/ I always wanted to see it in vegas: https://www.youtube.com/watch?v=htX4T20t6lU https://www.youtube.com/watch?v=htX4T20t6lU EDIT: clarity

valdiorn 12y ago

"The game of rock-paper-scissors exhibits collective cyclic motions which cannot be understood by the Nash equilibrium concept." This is complete bullshit. It is well understood that if your opponent is not playing an optimum strategy, you can gain an advantage by shifting away from the Nash equillibrium yourself. Example: Image a player that always picks "Paper". By shifting away from a random choice (Nash optimum) to just always selecting "Scissors" will net you a 100% win rate. This is a common trick utilized in poker, where good players will apply a certain playing style, while placing smaller bets, let their opponent adjust to your style and then suddenly change to a more aggressive style. You can take advantage of the fact that your opponent is trying to capitalize on your previous strategy. He has now introduced a sub-optimal element into his game, which you in turn can capitalize on. As in the previous example, imagine we wager $1 on rock paper scissors. I pick paper for the first 100 rounds, you always pick scissors and you always win. Now we suddenly change the bet to one million dollars a hand. I change my selection to "Rock", while you play scissors, as that has given you a perfect win rate so far, and I win the money.

vishnugupta 12y ago
>This is a common trick utilized in poker, where good players will apply a certain playing style, while placing smaller bets, let their opponent adjust to your style and then suddenly change to a more aggressive style. Pardon my ignorance of poker, but won't the opponent notice that you have suddenly raised the stake and that something could be afoot?
- ghshephard 12y ago
  Playing aggressively in poker usually means betting more than your hand would otherwise dictate - but your opponent doesn't know what your hand is. So - you play for 4-5 hours, folding on weak hands, and always raising on strong hands, and then, once people think you are a grinder, you start betting on weak hands; other players fold because they were used to you betting high stakes only on strong hands, you take their money.
  - throwaway13qf85 12y ago

cyborgx7 12y ago

I hope to see some replication of this. It sounds like they just looked through the numbers for patterns, instead of making a prediction beforehand and then trying to falsify it. That's fine but there needs to be replication for that kind of conclusions.

alextingle 12y ago

If winners tend to stick with their last winning move, then shifting forward after losing is the correct strategy. Only the winners are playing irrationally here.

oliwary 12y ago
Wouldn't shifting backward make more sense? That way you beat the other instead of playing equal.

namuol 12y ago

How to actually win at RPS: Memorize a long, truly random sequence. That is, assuming your opponent also does. Er... now I've gone cross-eyed.

vorg 12y ago
> Memorize a long, truly random sequence > Humans are really bad at random You could use the digits of some transcendental number, say, pi. Skip zeros, then each digit yields two moves. For the first move, lows(1,2,3) gives stone, mids(4,5,6) gives paper, and highs(7,8,9) gives scissors. For the second move use mod 3, so 0 gives stone, 1 gives paper, and 2 gives scissors.

avaku 12y ago

>> What are your odds of winning rock-paper-scissors? Simple - one in three. At least, that's what chance predicts. I thought the chance of winning with no prior is 1/2... Otherwise, okay, you win with 1/3, your opponent wins with 1/3, and where is the other 1/3? :) I know what the article means, but they phrase is wrongly.

throwaway13qf85 12y ago
I don't think there's anything wrong with what they say. Your chance of winning one round of RPS is 1/3. Out of three games you win once, lose once and draw once on average. If you replay when a draw occurs, then of course you have a 1/2 chance of winning.
ville 12y ago
>> okay, you win with 1/3, your opponent wins with 1/3, and where is the other 1/3? :) Wouldn't that remaining 1/3 be the odds for it being a draw?
danieltillett 12y ago
The odds are 1/3 win, 1/3 loss, 1/3 tie :)
- avaku 12y ago
  Sorry I didn't know the rules properly :) Which combination is a tie? In my version someone always wins :) ha ha

kingrolo 12y ago

This article reminded me of a Rock-Paper-Scissors AI from a while back (requires Flash I think). http://www.nytimes.com/interactive/science/rock-paper-scissors.html?_r=0 http://www.nytimes.com/interactive/science/rock-paper-scisso... It uses data gathered from other players. I remember playing it at the time and it was creepy how good it was at beating me. Oddly it didn't do so well this time. Maybe because I've just read that article.

thomasahle 12y ago
AFAIR it works by storing the most likely human move for every 3 move sequence e.g. "St Pa, St Sc, St St". If we assume most players play similarly, and don't remember much more than the last three results, this works really well.

mseepgood 12y ago

You just have to be fast enough: http://www.youtube.com/watch?v=ZVNnoOcohaU http://www.youtube.com/watch?v=ZVNnoOcohaU

hrktb 12y ago

There is a 'variant' in Japan where every players start with rock, and the game starts after this first move. It's a small variation (I think it was originally aimed to synchronize more easily), but it nills the effect described in the Article for each session.

hrktb 12y ago

andyhmltn 12y ago

Is it actually a 1/3 chance of winning though? Is that including a draw as a win? I've tried coding it up here: https://gist.github.com/andyhmltn/5c8c5734fe894db5aa02 https://gist.github.com/andyhmltn/5c8c5734fe894db5aa02 Baring in mind it was a rushed 5 minute bodge-job so it could be wrong but there seems to be a massive skew towards draws After more tests with this code it seems there's an 11% chance of winning if it's random. Baring in mind javascripts RNG

Monkeyget 12y ago
There is an equiprobability of winning/losing/draw. Your code is erroneous. You do a +1 to the random number you generate giving you 1, 2, 3. You then use that number to access an array with indexes [0, 1, 2]. You end with an undefined which screws your results.
- andyhmltn 12y ago
  Well if that was the case, then one result would always have 0. The indexes are used to find what something wins against