

How to win at rock-paper-scissors - GvS
http://www.bbc.com/news/science-environment-27228416

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valdiorn
"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
>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
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
To clarify for the poster who asked you the question, playing aggressively
might mean better _more_ than your hand otherwise dictates, but it might also
mean betting _more often_ even if you don't change your bet size.

For example, you might always fold low pairs 22-66 initially (and perhaps
conspicuously reveal that you folded them) but then start raising with them
later. If your opponents were paying attention, then (a) they will think you
have a good hand, and may be scared into folding right now, but (b) even if
they don't, they won't suspect you of having a low pair, so that if e.g. a 2-6
comes up on the board and gives you three of a kind, you have an advantage
because your opponents won't consider that you have this hand.

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oliwary
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
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.

~~~
oliwary
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.

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andyhmltn
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
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
Well if that was the case, then one result would always have 0. The indexes
are used to find what something wins against

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mseepgood
You just have to be fast enough:
[http://www.youtube.com/watch?v=ZVNnoOcohaU](http://www.youtube.com/watch?v=ZVNnoOcohaU)

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

~~~
yeukhon
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
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.

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cyborgx7
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.

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jakobe
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 :)

~~~
jerf
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
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

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kingrolo
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-scisso...](http://www.nytimes.com/interactive/science/rock-paper-
scissors.html?_r=0)

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
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.

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

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hrktb
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.

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namuol
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
> 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.

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avaku
>> 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.

~~~
danieltillett
The odds are 1/3 win, 1/3 loss, 1/3 tie :)

~~~
avaku
Sorry I didn't know the rules properly :) Which combination is a tie? In my
version someone always wins :) ha ha

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JazCE
"The only winning move is not to play."

