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Flash
322016.  Tue Apr 22, 2008 12:13 pm Reply with quote

This topic was started during an e-mail correspondence about something else, but let's open it up. I thought it might be fun to do something about scissors/paper/stone in the Fingers show. There has evidently been some academic modelling of the game to come up with an optimum strategy. Fred thinks you just have to choose paper every time but he can't remember why and anyway he must be wrong, because if he does that I'm going to choose scissors every time.

Academic stuff is in 'Optimal Strategies for a Generalized "Scissors, Paper, and Stone" Game by David C. Fisher and Jennifer Ryan in The American Mathematical Monthly (Vol. 99, No. 10 (Dec., 1992), pp. 935-942) but we don't have that handy and we're waiting around for Will who will have memorised it.

Meanwhile, I call "scissors". Fred, what's yours?

 
Flash
322021.  Tue Apr 22, 2008 12:22 pm Reply with quote

Molly sends this:
Quote:
The RPS society have an article about how to win at RPS (? ! Rock, Paper Scissors obviously).

Secret 1 - Rock is for Rookies. see below.

It would be good if there is a more mathematical and succinct answer up Will's sleeve.

1 - Rock is for Rookies
In RPS circles a common mantra is "Rock is for Rookies" because males have a tendency to lead with Rock on their opening throw. It has a lot to do with idea that Rock is perceived as "strong" and forceful", so guys tend to fall back on it. Use this knowledge to take an easy first win by playing Paper. This tactic is best done in pedestrian matches against someone who doesn't play that much and generally won't work in tournament play.
http://www.worldrps.com/index.php?option=com_content&task=view&id=256&Itemid=37

 
eggshaped
322568.  Wed Apr 23, 2008 4:17 am Reply with quote

SQUIRE DUMP

Papers, Scissors, and Stone is a Far Eastern game originally played during Chinese New Year.

When the game first arrived in Japan it was an adult drinking game played in drinking places and red-light districts.

In Korea the game is called 'Kai bai bo', where kai is scissors, bai is rock, and bo is cloth or paper.

In Thailand it is the same and called 'Janjii'.

In India and Indonesia, and on Bali, the game is played with elephant, human and ant, where elephant beats human and human beats ant.

ALSO:

Sotheby's won a $20 million contract to sell The Maspro Denkoh electronics corporation's collection of Picassos and Van Goghs after a game of scissors, paper, stone.

It's tactic was to ask one of the director's daughters, who gave them the following advice:

1. Stone is the one that "feels" the strongest
2. Therefore a novice will expect their opponent to go for stone, and will go for paper to beat stone
3. Therefore go for scissors first

Sure enough, they played scissors and won the contract ahead of Christie's

 
Molly Cule
322581.  Wed Apr 23, 2008 4:36 am Reply with quote

I like that story. According to the NYC times,
Quote:
instead of the usual method of playing the game with the hands, the teams were given a form explaining the rules. They were then asked to write one word in Japanese - rock, paper or scissors - on the paper. After each house had entered its decision, a Maspro manager looked
at the choices. Christie's was the winner: scissors beat paper.
http://www.nytimes.com/2005/04/29/arts/design/29scis.html?_r=1&oref=slogin

 
Flash
322585.  Wed Apr 23, 2008 4:45 am Reply with quote

Nice - same story, just different in every respect.

Will sends this:
Quote:
I seem to remember that there was a 'game' that we looked at (in those dim distant maths days) which seems fair but isn't. Two players pick ODD or EVEN as their team. As in Scissors, Paper, Stone, on cue each player holds up either one or two fingers. If the sum of the two numbers is odd (i.e. 3) then EVEN pays ODD 3p. If the sum is even (2 or 4) then ODD pays EVEN 2p or 4p accordingly. One of the two players has a very small advantage if he plays his finger right.

 
Flash
322599.  Wed Apr 23, 2008 4:59 am Reply with quote

I suppose the point is this: the Even team wants to win 4p more often than he wins 2p, so if he was playing against a random choice he would always choose 2 fingers. But if he's playing against a human opponent he can't do that because the opponent will always choose 1, and win. Conversely, the Odd team wants to deny the Even guy the opportunity of winning 4p, so he will tend to play 1 finger, and his opponent will respond by playing 1 also. So it's a classic Game Theory optimisation problem - there's a mathematically optimal strategy for each side, though I have no idea how to calculate it.

Game Theory is rather a good topic if we're looking for mathematical subjects, as it can be applied to real-life decisions - military strategy, amongst other things.

 
Flash
322626.  Wed Apr 23, 2008 5:24 am Reply with quote

Von Neumann worked out the optimal strategy for a finger game called Morra. Each player holds up 1, 2 or 3 fingers and simultaneously calls out what he thinks his opponent is showing. If both are right or both wrong there's no pay-off, but if one player guesses right the other one pays him as many pennies as the total number of fingers extended by the two of them. The optimal strategy is to guess that 4 will be the combined total (ie if you are holding out one finger, you call "three" as your guess for the other guy) and out of each 12 games you show one finger 5 times, two fingers 4 times and three fingers 3 times.

This breaks even if the opponent is also following the same system, and wins if he isn't.

 
WB
322646.  Wed Apr 23, 2008 5:41 am Reply with quote

Flash wrote:
I suppose the point is this: the Even team wants to win 4p more often than he wins 2p, so if he was playing against a random choice he would always choose 2 fingers. But if he's playing against a human opponent he can't do that because the opponent will always choose 1, and win. Conversely, the Odd team wants to deny the Even guy the opportunity of winning 4p, so he will tend to play 1 finger, and his opponent will respond by playing 1 also. So it's a classic Game Theory optimisation problem - there's a mathematically optimal strategy for each side, though I have no idea how to calculate it.

Game Theory is rather a good topic if we're looking for mathematical subjects, as it can be applied to real-life decisions - military strategy, amongst other things.


Yes I think you've got the right idea. If x is the proportion of times ODD holds up one finger, then his strategy should be to equalise his winnings whatever EVEN does. If EVEN holds up one finger, then ODD wins 3(1-x)-2x. If EVEN holds up two fingers, ODD wins 3x-4(1-x)

3(1-x)-2x = 3x-4(1-x) gives x=7/12

So if ODD holds up one finger seven out of every twelve games he should win 1/12p per game on average.

For military strategy games, you might try Colonel Blotto at http://www.amsta.leeds.ac.uk/~pmt6jrp/personal/blotto.html

Sadly G is for Game!

 
Flash
322653.  Wed Apr 23, 2008 5:59 am Reply with quote

The Col Blotto site is v interesting. One snippet:
Quote:
This recalled to Ted Sohn an (illegal) strategy called 'fiddling the board order' in chess tournaments, where a team puts a weak player on the top board, in the hope of cleaning up by winning on the lower boards; rather than, as is supposed to happen, arranging the players in descending order of strength.

I didn't know that.

 
dr.bob
322851.  Wed Apr 23, 2008 8:58 am Reply with quote

Quote:
This tactic is best done in pedestrian matches against someone who doesn't play that much and generally won't work in tournament play.


Tournament play?!

<boggle>

Whilst some games, such as the ones mentioned by WB and Flash, can be analysed by game theory to provide the best strategy, I can't see that applying to RPS in any way. Unless there's some psychological aspect, as suggested by the Christies story, that people prefer rock. Mind you, that relied on assuming the opponent assumed people preferred rock and trying to beat that, so they were effectively double bluffing them. Once you start down that road, I'd've though it rapidly becomes a game of chance once again as you don't know how many levels of double bluff your opponent will indulge in.

My favourite was an episode of I'm Sorry I Haven't A Clue where they played Cow-Lake-Bomb: Cow drinks Lake, Lake puts out Bomb, Bomb blows up Cow. Fun to play on the radio with sound effects, less practical to play down the pub, I'd imagine.

 
eggshaped
324484.  Fri Apr 25, 2008 7:57 am Reply with quote

All the following facts come from the World RPS website:

http://www.worldrps.com (wrp)

The clenched fist movements that one makes before one thrusts out his choice are called "primes"

 
eggshaped
324487.  Fri Apr 25, 2008 7:59 am Reply with quote

Other names for RPS include:

Jenken, Jan Ken Pon (Japan), Roshambo (Southwestern U.S), Shnik Shnak Shnuk (Germany), Ching Chong Chow (South Africa), Stone Scissors Well (France), Hammer, Nail, Paper (Vietnam) or Farggling (US)

s: wrp


Last edited by eggshaped on Fri Apr 25, 2008 9:10 am; edited 1 time in total

 
eggshaped
324491.  Fri Apr 25, 2008 8:01 am Reply with quote

There is some debate as to whether a rock dulls scissors or crushes them.

s: wrp

 
eggshaped
324494.  Fri Apr 25, 2008 8:03 am Reply with quote

Quote:
The sympolic meaning of paper covering a rock dates back to ancient Chinese culture. When a petition was made to the Emperor, the petition was signified by a rock. Upon making a decision the Emperor would have his servants place a sheaf of paper either over or under the rock. If the sheaf was placed under the rock it would signify acceptance of the petition. If the sheaf was placed on top of the rock it signified denial of the petition. Over time the symbolic image of paper covering a rock became synonomous with defeat.


s: wrp

 
eggshaped
324501.  Fri Apr 25, 2008 8:11 am Reply with quote

The WRPS association claims that:

Quote:
An 1842 law stated that: "any decision reached by the use of the process known as Paper Scissors Stone between two gentleman acting in good faith shall constitute a binding contract"


That seems mighty unlikely to me.

Telegraph 11/06/05

 

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