"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.
You're right that they're incorrect to say RPS can't be understood in terms of the Nash Equilibration concept. Possibly they mistook RPS's lack of a Pure Equilibrium to mean NE is inapplicable. Instead, it has a Mixed Nash Equilibrium.
The advice in the article - bias towards previous opponent win is just an under-specification of how to play a no regret strategy (alter your distribution to match opponent play, which is more or less what your example describes). If you've already installed a random number generator in your brain then playing optimally (in the sense that it will exploit weakness and shift to random as necessary) can be very easily done via a no-regret algorithm such as randomized weighted majority.
This class of algorithm is proven to converge on the NE for zero-sum games while being much quicker than linear programming (this actually has practical consequences for poker bots - see counterfactual regret).
The only reason that sharks can pretend to be fish is that there is real fish out there, that make it an expected win to deviate from nash equilibrium. The fish are not a property of the game, but rather a property of the playerbase.
You can still use game theory to analyze the game though, if you "include" the player model into the game model.
"Rock-paper-fool goes like this. First a coin if flipped without you seeing If tails, you face a fool npc, who will play according to..., if head, you face a (homo economicus) player"
You could then try to analyze the equilibria of this game.
>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?
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.
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.
In my opinion, the parent example was rather oversimplified. If a player started playing more aggressively, that would be an obvious 'tell'. Most opponents would recognise that they should play more conservatively until they figure out what's going on.
However, this strategy really just needs one sucker: if it works, it works.
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).
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.
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 ;)
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.
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...
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.
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.
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 :)
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.
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.
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 :)
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.
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.
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.
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.
>> 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.
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.
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.