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You and your opponent each simultaneously choose rock, scissors, paper.  If you choose the same, play again.  Otherwise, the winner is determined by:  rock blunts scissors; scissors cut paper; paper wraps rock.

It's obviously a game of pure luck. 
...Or is it?  What if you notice your opponent always plays Scissors?  What if they play Rock 50% of the time?  What if there's a pattern to when they'll play Paper, but you haven't quite worked it out yet?

This is where GameTheory? comes in, although you do have to decide whether you want to play a strategy which is optimal, averaged over all possible strategies your opponents could take, or want to assume that your opponent must have some deep pattern, and you'll get enough plays that it's worth playing suboptimally initially in the hope of figuring them out and then beating them. The problem with the latter approach is that they'll notice, and change their strategy...

RockScissorsPaper is actually the basis, conceptually, for many modern games. Take a classic slash-em-up; you will probably find three attack styles and three defences with a RockScissorsPaper set-up. Oh, and some candy for the eyes, plus the ability for bonkers reflexes on 13-year-olds to defeat anything you do.

How could you POSSIBLY suggest that it's just luck?
[The world society of Rock, Paper and Scissors]

I wasn't suggesting it.  Quite the reverse - I was giving some FoodForThought? for those who view RPS as just a game of luck. --AlexChurchill

My response was twofold there, but never mind.
This is actually an instance of a very interesting class of games - one which can be forcibly reduced to 'just luck' by your opponent.  But an opponent may wish to try a strategy which (if YOU are not going for 'forced just luck') may do better than just luck would.
And so you choose a strategy which would beat that strategy and so on.
'Just Luck' (in this, and most examples of this class, you force it by playing totally randomly yourself) becomes a defensive strategy.  And not-coincidentally annoys the hell out of your opponent.  (Psycho-analyse randomness, sucker)

Personally I like such games, for the challenge of trying to be TrulyRandom? rather than ApparentlyRandom?.
It would be interesting to see if, over a run of 200 or more RSP games, a computer program (or sufficiently skilled player) is able to detect the variation from TrulyRandom? in their human opponent who's trying to play Random, and get a significantly higher number of wins than losses because of it... It ought to be theoretically possible, but I'd imagine quite hard... --AlexChurchill
Mmmm... it'd be easy to create something that LOSES more often against truly random.  Create something that wins well unless the opponent chooses an unlikely sequence - for example, play rock rock rock paper paper paper (repeat).  A truly random sequence will match it perfectly occasionally (How often is left as an ExerciseForTheReader) whereas a human trying to be random will shy away from such a repeating sequence.  Of course, a human excercising any iota of other skills will whup you (which random would not)  In fact, I'd lay money that a computer playing truly randomly would be able to give very good detection of human-random, simply by playing lots of tests and checking that their final score is (substantially) non-zero.  --Vitenka

I presume that such games have a special name - but my knowledge of GameTheory? peters out somewhere just short of knowing it.
'such games' - ones where you win by being truly random?

I'd be slightly nicer and say "Games where there is no strategy that does BETTER than acting truly randomly, if that is the strategy your opponent is using" - but again, I've run out of textbook knowledge here and don't know what the OfficiallyAccepted? definition is.  Not that I stick too hard to such definitions anyway.
Just a side-note.  NetRunner is almost, but not quite, such a game - and benefits from the association.
-- Vitenka

<snip discussion on random strategies - see Revision 25> - in summary, there is disagreement about whether it makes sense to talk of a strategy for a game with an infinite number of choices which involves random decisions for each choice with weights based on play so far,  but there is agreement that it is an interesting property of such a game whether or not the optimal strategy has weights which are independent of the number of turns played and the play so far.

Avid experimenters can join in the game below. We have to decide on when we reveal our choices, BTW.
(moved from ToothyWikiInternals/SignatureServer)

So, anyone for a game of scissors,paper,stone? :-) -- Emperor

Kazuhiko chooses: 959107380873c380cd7bffaba16cf548
MoonShadow chooses: 03a619cdae589d132fadea79c6c8ec94
Senji chooses: b16b717b28317bc04e88f3cc57fd66b3

PeterTaylor asks how one plays multi-player RSP.

Easy. Everyone chooses stone, paper or scissors. The server administrator then tweaks the secret key until he can show that his scissors beats everyone else's paper. ;) - MoonShadow

Hmm... Actually mine was paper (I completely forgot about revealing :/)  I think it was 'paper 186681', but I think I've mis-remembered the code...  I made a note of at home. - Kazuhiko

Nope, ah well.  Of course, I could be bluffing :)  Sorry if I brought this to a premature end, we could always have another round.  What happens if we have one of each? - Kazuhiko

I signed "MoonShadow chooses stone. Muhahaha!!" (not including the double quotes) - so I lose to you. If we have one of each, we just have to play again.. :P

Mine was 'aardwolf:paper' (similarly without quotes) -- Senji

I'm pretty sure that Aardwolf? is a nonstandard throw.

Found it... My original move was 'paper 185581' so Senji and I are tied... - Kazuhiko

Kazuhiko: e897313ee6eeca1bb17299829bf81561
Senji: b1f19e8952ed0baf438f18d97a2cd775

Kazuhiko reveals: "jin ken po... rock"
Senji reveals: "Minerva:stone" - draw again...

Senji: 3420e7202c549994f1b08ba38fa9ca05
Kazuhiko: 02356e8a8adf4d8332ac3347d2a71b05

Kazuhiko then realises that hiding his submission was thoroughly pointless and reveals: "This is paper such as has never been seen before!"

Bah, that beats my 'rock-stone'... -- Senji -- ...you win.

PeterTaylor: 3a02740af7c967d
Garbled: c6ea00281bb1a0c36a40af4b5b0f0b0e5f18958988cf35bbb

AlexChurchill wants to join in:  02c3bd3580d2fa701ee862605d45667e
MoonShadow:  7d22e0cf66527e88160a0499998fa453
MoonShadow idly wonders why PeterTaylor and Garbled both got signatures of weird lengths that the signature server shouldn't be capable of producing.
PeterTaylor has no longer got a clue what his entry was.
Garbled reveals S1t7o34n897 (roughly translated stone with random numbers and no E's
MoonShadow forgot to write down what his random number was. *sheepish* It was scissors anyway, so he's lost.
S1t7o34n897 produces a [signature] of 390cfd2ecf7344db6f9343afe09b89ee! Where did you get the long number above from, Garbled?
AlexChurchill loses as well with "It has to be SCISSORS".
But - do we really lose at this point, or do we disqualify the match because the alleged winner's signature was invalid? Alternatively, if we *just* disqualify the people with the obviously invalid signatures, we need a play-off.. Clearly, this is a question of vital importance :) - MoonShadow
We wait for Garbled to justify himself >:-) And if he doesn't come up with a convincing explanation then we disqualify his entry, and hold a playoff between the winners of the remainder if appropriate. --AC
Garbled acted in accordance with his name, and probably missed some numbers
Ahh, I see what happened.  Look at Revision 31 vs Revision 32 - Garbled inserted his signature into the middle of PeterTaylor's.  In suitably Garbled fashion.  However, his signature doesn't match with what he says his throw was.  Unless he produces something which matches c6ea00281bb1a0c36a40af4b5b0f0b0e, we have to disqualify his entry, and have a playoff between me and MoonShadow...  --AlexChurchill
Ah, thankyou Alex, S1t7o34n897e was my original text. --Garbled-san

MoonShadow's new entry: cd36dc39c0ebce213e02ce33155fe831 (this time MoonShadow's emailed it to himself, so he definitely knows he'll remember it..)
AlexChurchill also enters, with: 3c1026535a5ebfa91ef6983bd5296ffd
M-A says f7d1dd771b17e4e66a054a1370931d18.
PeterTaylor reckons e7dbb1bda84ffe52450dfceb8a69f90b and hopes this time he won't have to remember his entry for 4 months.
Garbled says 2ec45753f1a62732cf7c0f6c41f5b044 Muha Muha MuHaHaHaHa

PeterTaylor reveals "high on cannabis | s/$/d/". WhyAreYouAllLookingAtMeLikeThat?
Garbled reveals "Enter the text to be signed paper."
MoonShadow reveals "Scissors. 491792". MuHaHa!
PeterTaylor realises the text he _should_ have submitted is "high on cannabis | s/d//".
In order to avoid submitting "stonedd", you mean? Yes, one would imagine so ;)
AlexChurchill reveals "Will PAPER win this time?" and discovers the answer is "Not yet".

Why not yet?  If I can point out you now have 1 stone, 2 papers and a scissors.  The only possibly way I can think of of declaring a winner to this would be to go for majority win so you will be one of them, regardless of M-A's vote... - Kazuhiko
On declaring a winner, see [rev 10].

M-A reveals "How about paper?"

[Signature server]

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Last edited April 13, 2005 8:51 pm (viewing revision 59, which is the newest) (diff)