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eggshaped
324570.  Fri Apr 25, 2008 9:56 am Reply with quote

Question: What is the best thing to play in a game of Scissor-Paper-Stone?

Answer: The answer is scissors. Because rock is the most common opening, and many people know that fact, paper is a common ploy, so it's best to play scissors. But now we've told the world that, the best thing to play is probably now rock. However...

 
WB
324599.  Fri Apr 25, 2008 10:36 am Reply with quote

eggshaped wrote:
Will mentioned in an e-mail that in an ideal world there can be no strategy in RPS, as if the choice is random, there is no statistical advantage of any throw.


Actually what I said was:

Quote:
The Value of the game is zero and the best strategy is to choose each of the options randomly one third of the time (pretty much as you'd expect.)


There very definitely is a best strategy. (I think Piers pointed out that there are some pretty stupid strategies - e.g. always choosing Rock). As you say, for a human to achieve the randomness may be difficult - but if you could, then this strategy would defeat all the other strategies you have been talking about in the long run. The best possible strategy for your opponent is to adopt the same thing (randomly each one third of the time) and then you should come out evens.

 
Flash
324611.  Fri Apr 25, 2008 10:47 am Reply with quote

This is definitely a runner, isn't it? I think we need to use it as a bit of business - eg, if you get a forfeit you can challenge Stephen to double or quits using RPS. Any other angles we can think of?

I wonder whether we could between us predict what each panellist would call, then write down our prediction on the back of their notepad, which they can then reveal. If we happen to get it right it'll look like pure magic, and if we don't, we stay schtum.

 
MatC
324629.  Fri Apr 25, 2008 11:03 am Reply with quote

Many years ago, there was an American bloke used to drink in my local, who was a games theorist - a job none of us had heard of at the time - who would get you to play noughts and crosses with him, by which means he would demonstrate a sure-fire method of ending war. His name was Arnold Arnold, and I believe he was quite famous in his field. He was quite famous in the pub, too, mainly for having an odd name.

 
Jenny
324684.  Fri Apr 25, 2008 11:53 am Reply with quote

He seems to have written a book:

Winners And other losers in war and peace, by Arnold Arnold. London: Grafton Books, 1990, 431 pp

However, I can't find it on Amazon new, though it turns up on a second hand site: http://www.biblio.com/details.php?dcx=71422203&aid=frg

 
eggshaped
324708.  Fri Apr 25, 2008 12:30 pm Reply with quote

If that's what you said Will, then I agree with this:

Quote:
As you say, for a human to achieve the randomness may be difficult - but if you could, then this strategy would defeat all the other strategies you have been talking about in the long run.


But I think the most important phrase is "if you could". The fact is that humans are not able to pick randomly, and perhaps more importantly, people who play RPS believe that there are optimal strategies - so they don't ever pick randomly. So I don't agree with this:

Quote:
the best strategy is to choose each of the options randomly one third of the time


However, I never studied game theory - not even to a basic level - so I'm not claiming to be right. Maybe this subject would be a good one to get a bit of maths into, if there is something to be said?

 
WB
324711.  Fri Apr 25, 2008 12:32 pm Reply with quote

John Nash (of "A Beautiful Mind") is the game theorist that most people will have heard of. He leaves the legacy of the 'Nash Equilibrium' a strategy set adopted by all the players where no player can do better by unilaterally changing theirs.

The father of game theory is John von Neumann.

 
Flash
324759.  Fri Apr 25, 2008 1:20 pm Reply with quote

Egg, it's part of game theory that everyone is assumed to be playing optimally, ie they've outguessed each other to the point of bafflement and now it's all about the maths.

 
WB
324766.  Fri Apr 25, 2008 1:27 pm Reply with quote

Flash wrote:
I wonder whether we could between us predict what each panellist would call, then write down our prediction on the back of their notepad, which they can then reveal. If we happen to get it right it'll look like pure magic, and if we don't, we stay schtum.


Prestidigitation comes under fingers in my book.

If you really want to look smart, prepare three pads with "Alan says X will play Rock/Scissors/Paper" (different on each pad). Give one pad to Alan, one to guest X and one to Stephen. You get Stephen to say that Alan is pretty good a predicting the outcome. He then asks one of the guests (X) to play their hand. Stephen (who knows who has which pad)then either asks X or Alan to raise their pad (or does it himself) depending on the outcome.

Didn't that Alan play Jonathan Creek............

 
Flash
324807.  Fri Apr 25, 2008 2:31 pm Reply with quote

I think we're getting some insights into the Derren Brown show here, folks. Production credits for Something Wicked This Way Comes:

Quote:
By:
Derren Brown, Andy Nyman, Peter Clifford
Management:
Objective Productions
Director:
Andy Nyman, Peter Clifford
Design:
Will Bowen

http://www.thestage.co.uk/reviews/review.php/8199

 
WB
325186.  Sat Apr 26, 2008 4:39 am Reply with quote

DAMN!

Now I've got to kill you.

 
eggshaped
325352.  Sat Apr 26, 2008 9:31 am Reply with quote

Quote:
Egg, it's part of game theory that everyone is assumed to be playing optimally, ie they've outguessed each other to the point of bafflement and now it's all about the maths.


Hm, what an unsatisfactory simplification. Do we have to assume that the players are all perfect spheres and that they're playing in a vacuum as well?

 
MatC
325369.  Sat Apr 26, 2008 10:01 am Reply with quote

Quote:
Egg, it's part of game theory that everyone is assumed to be playing optimally, ie they've outguessed each other to the point of bafflement and now it's all about the maths.


It's not going to replace snooker, is it, from that description ... ?

 
Flash
325384.  Sat Apr 26, 2008 10:49 am Reply with quote

<sigh> Such short attention spans these day. OK then, here's a more exciting game situation that von Neumann and his mate Oskar Morgenstern used as a model.

Sherlock Holmes is being pursued by Moriarty, who will kill him if he catches him. Holmes catches the train from London to Dover, in order to flee to the Continent. Moriarty, rather stylishly, charters another train and follows him. There is only one stop before Dover: Canterbury.

Each of them now has to decide where to leave the train. If they choose the same station, Moriarty catches Holmes and kills him. If Holmes gets off at Canterbury and Moriarty goes on to Dover then it's a draw as Holmes hasn't made good his escape from England.

As the railways have been starved of funding, each of them has plenty of time to try to figure out what the other will do (He'll think that I'll think that ... etc). In Games Theory, though, both of them are (rightly) assumed to be geniuses of equal stature, so they can't out-reason each other. What is needed is an unforeseeable or random strategy.

To reduce it to numbers, if they get off at the same station Moriarty scores 100. If Holmes goes to Dover and Moriarty to Canterbury, Holmes scores 100. If the other way round, Holmes only scores 50, as he could still be caught later. On this basis, Holmes' best strategy is to make Canterbury a 60% probability choice - eg by putting 10 bits of paper in a hat, 6 of them nominating Canterbury. Similarly, Moriarty should make Dover his 60% choice.

The most likely single outcome is therefore Canterbury for Holmes and Dover for Moriarty, which is indeed the outcome that Conan Doyle selects. This is a draw. But although it is the most likely, it is only a 36% probability (60% x 60%) and it's actually more likely (48%) that they will match at one station or the other and Holmes will be killed.

Better?

 
MatC
325385.  Sat Apr 26, 2008 10:51 am Reply with quote

Oh, Sir, that's not a game! That's maaaaths!

 

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