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        riddles >> general problem-solving / chatting / whatever >> rock paper scissors
        
(Message started by: temporary on Mar 25th, 2008, 6:31pm)
Title: rock paper scissors
Post by temporary on Mar 25th, 2008, 6:31pm
Optimal strategy, anyone? Keep in mind that a human mind can never be truely random, but if it was, would that help or hurt.
Title: Re: rock paper scissors
Post by BenVitale on Mar 25th, 2008, 8:53pm
Situation:

Suppose, for instance, that scissors scores 1 point against paper, paper scores 2 against rock, and rock scores 3 against scissors.

In this situation, would you automatically form a rock and hope to score 3, or would you expect your opponent to form a rock, which you could beat by forming paper?
Title: Re: rock paper scissors
Post by temporary on Mar 26th, 2008, 12:22am
If most people would then use rock or paper based on what you just said, paper would become picked up by professionals. I would take advantage of that and use scissors. Or possibly paper on the ameteurs who would probably use rock. Is it best 2/3 or just 1?
Title: Re: rock paper scissors
Post by BenVitale on Mar 27th, 2008, 11:07pm
Actually, making the same choice every time doesn't work. What seems to make sense, again, is to mix the three choices randomly, forming each of scissors, paper, and rock with a certain probability. The scoring system determines what these probabilities ought to be to achieve an optimal result. In the example given, you can calculate that the probability should be 1/3 for scissors, 1/2 for paper, and 1/6 for rock. Other scoring schemes give different probabilities.

Any deviation from a random mixing strategy gives your opponent an opportunity to profit from your actions. At the same time, by sticking strictly to these probabilities, you forgo any chance of taking advantage of bad play on the part of your opponent. When both players adopt exactly the same strategy, no one wins -- or loses -- in the long run.
Title: Re: rock paper scissors
Post by temporary on Mar 28th, 2008, 9:58am
Except that a human mind cannot be random, nor can it pick something with a probability, it decides whether or not to pick it. However, there might be a way...
Title: Re: rock paper scissors
Post by BenVitale on Mar 28th, 2008, 10:23am
How? I'm curious to hear your perspective.

I see it as a game theory problem where you would have 2 or more rational people.
Title: Re: rock paper scissors
Post by Grimbal on Mar 30th, 2008, 12:22pm
Unfortunately, game theory won't tell you how to win, it only tells you how not to loose.  What they call an "optimal strategy" is actually only a "balanced strategy".  Playing that strategy zeroes the expected winning for both players.  So it is a protection against any strategy, however devilish your opponent is, but at the same time prevents any possibility of winning, however stupid your opponent's strategy is.

To actually win against a stupid opponent, you have to depart from the "optimal strategy".  If he always plays rock, you can always play paper.  But you risk to be outsmarted.  He might play 3 times rock to show a trend and then switch to scissor.  Hehe...

But I have heard of a program that is successful at it.  It starts with a balanced strategy for some time and record what the player does.  It will assume that the player will react in the same way after winning or loosing in some way.  It will record for each sequence of 3 games or so, what was his next move.  When the same situation arrives, it will play in a way to beat what the player did previously.

The problem is to find how fast to do the transition.  
It should be gradual, departing from neutral play only in situations where a trend is quite visible (statistically significant) and return to neutral play whenever the trend proves wrong.  Or it could just adjust the probabilities of what it plays more or less depending on how significant the trend is.

Of course, there will always be a way to outsmart the program.  Just look at the source, write a program that does the same evaluations, see what the program would play and play that which beats it.
Title: Re: rock paper scissors
Post by temporary on Mar 30th, 2008, 11:43pm
Although mind tricks can also work on non-computer opponents. Like, "I think I should choose paper since you always choose that lame old rock. How predictable." Then expect scissors and play rock. The closest thing to being random a human can do is base decisions on randomness like, "I will flip 2 coins. If 0 are heads, rock, if 1 is heads, paper, if all are heads, scissors, which is 1/4 rock, 1/2 paper, and 1/4 scissors, decided randomly, but you wouldn't do that on every rock paper scissors game. Too inconvenient.
Title: Re: rock paper scissors
Post by BenVitale on Mar 31st, 2008, 8:58am
Nash showed that in any competitive situation—war, chess, even picking up a date at a bar—if the participants are rational, and they know that their
opponents are rational, there can be only one optimal strategy.

However, people aren't rational. And rational people can be predictably irrational.

Nash's theorem says that it is always possible for a player to choose a strategy that is best for him or her when all the other players are also following their best strategies. In this "equilibrium", no player can improve his or her prospects by choosing an alternative strategy.

Couldn't we apply this theorem in this rock paper scissors problem?
Title: Re: rock paper scissors
Post by towr on Mar 31st, 2008, 9:52am

on 03/31/08 at 08:58:36, BenVitale wrote:
Nash showed that in any competitive situation—war, chess, even picking up a date at a bar—if the participants are rational, and they know that their opponents are rational, there can be only one optimal strategy.
That doesn't sound right; surely there are plenty of games where there are multiple equivalent strategies, all equally optimal.


Quote:
Nash's theorem says that it is always possible for a player to choose a strategy that is best for him or her when all the other players are also following their best strategies. In this "equilibrium", no player can improve his or her prospects by choosing an alternative strategy.  
Not all games have a Nash equilibrium. There is no equilibrium for rock-paper-scissors, for example. Because each strategy (picking either rock, paper or scissors) is beaten by the next.
Title: Re: rock paper scissors
Post by pex on Mar 31st, 2008, 10:52am
What Nash proved is that any game with finitely many pure strategies, there exists at least one equilibrium - but possibly in "mixed" strategies, that is, randomizing over pure strategies.

In rock-paper-scissors, the equilibrium would have both players choosing any of the three pure strategies, each with probability 1/3.
Title: Re: rock paper scissors
Post by BenVitale on Mar 31st, 2008, 1:11pm
Generally speaking,
What if it looks like you just can't win, what's the most rational thing to do? What if neither you nor your opponent can improve your score by unilaterally changing your mind?

You can either decline playing the game or adopt a non-rational strategy. Wouldn't a rational strategy be to be completely irrational?

The thing is Classic game theory supposes, of course, that everyone is acting rationally. But what if they are not? I heard that a small group of mathematicians think they have found a way to boost the power of game theory. They have included the irrational" influences of emotion, they call it drama theory.  
Title: Re: rock paper scissors
Post by pex on Mar 31st, 2008, 2:02pm
Well, either way, rock-paper-scissors is a zero-sum game (one wins, the other loses). Thus, in the long run, nothing (rational or irrational) will work as a winning strategy, unless the other player is too stupid to imitate you...
Title: Re: rock paper scissors
Post by BenVitale on Mar 31st, 2008, 4:00pm
I've just come across an article on the web that says:

Scientists believe they have worked out the secret to winning at paper, scissors, stone.While most people are aware that stone blunts scissors, scissors cut paper and paper covers stone, there is a psychological element to the game which many players may have missed.

NewScientist http://www.newscientist.com/channel/being-human/mg19626352.700-how-to-win-at-rock-paper-or-scissors.html

I don't have access to read the complete article.

According to New Scientist magazine, the way to win is to start with scissors.

Research shows that stone, also called rock, is the most popular of the three possible moves in the game.

That means that your opponent is likely to choose paper, because they will expect to you to start the game with stone.

By going with scissors, you achieve an early victory.The scissors strategy has proven very successful in the past
Title: Re: rock paper scissors
Post by JiNbOtAk on Mar 31st, 2008, 7:54pm

on 03/31/08 at 16:00:37, BenVitale wrote:
By going with scissors, you achieve an early victory.The scissors strategy has proven very successful in the past


Which, most people would do once they read this article. But if you know your opponent had read this, and is probably going to use scissors, are you going to choose scissors as well ? Or choose rock ?
Title: Re: rock paper scissors
Post by temporary on Apr 1st, 2008, 4:38pm
Not only is there optimal strategy on what people usually start with and what you should start with to beat that, but also how to be unpredictable or predict your opponent. For example, choosing the same thing twice is supposedly unexpected, but the third time is it obvious, or unexpected for that reason?
Title: Re: rock paper scissors
Post by BenVitale on Apr 1st, 2008, 10:59pm
Have you tried to play this game with friends?
Well, I have tried with a match of 50 rounds. I've found out that the number of wins is equal to the number of losses and more than the number of ties.

I find that there are two contributing factors in predicting your opponent's moves: Past Performance (Pattern) and Human Psychology (Mental).
Title: Re: rock paper scissors
Post by temporary on Apr 5th, 2008, 7:38pm
But there is some overlapping between the two. For example, you choose scissors twice in best 3 of 5 and your opponent chooses paper twice. Say"You know what's coming next" and choose paper. Also, since you  people mentioned nash equilibrium, I thought I should mention e-card. emperor>citizen>slave>emperor. The emperor side(4 citizens and an emperor) plays their card (face down) first. Then the slave side(4 citizens and a slave) plays their card and they both reveal them. In the second round(assuming it is not already over), the slave side plays their card first then the emperor side plays theirs, etc until someone wins. And you cannot choose randomly. Discuss that nash equilibrium.
Title: Re: rock paper scissors
Post by ChrisPBacon on Jun 20th, 2008, 12:19pm
PAPER!! ;D lol


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