Here is the advice from Annie Duke, professional poker player and the 2006 Champion of the World Series of Rock, Scissors, Paper:
The other little small piece of advice that I would give you is that people tend to throw rock on their first throw. Throwing paper is usually not a good strategy because they might throw scissors. You should throw rock as well.
The key is, and this is the best piece of advice that I can give you, if you do think that you recognize the pattern from your opponent, it’s good to try to throw a tie as opposed to a win. A tie will very often get you a tie or a win, whereas a win will get you a win or a loss. For example, if you think that someone might throw a rock, it’s good to throw rock back at them. You should be going for ties.
If at first it sounds dumb, think again. The idea is some combination of pattern learning and level-k thinking: If she thinks that I think that I have figured out her pattern and it dictates that she will play Rock next, then she expects me to play Paper and so in fact she will play Scissors. That means I should play Rock because either I have correctly guessed her pattern and she will indeed play Rock and I will tie, or she has guessed that I have guessed her pattern and she will play Scissors and I will win.
She is essentially saying that players are good at recognizing patterns and that most players are at most level 2
Research note: why are we wasting time analyzing penalty kicks? Can we get data on competitive RoShamBo? While we wait for that here is an exercise for the reader: find the minimax strategy in this game:
Cheap Talk 
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June 14, 2010 at 11:36 pm
twicker
Interesting.
As it happens, I played a game of RoShamBo just this weekend.
First round: I threw scissors, opponent threw rock. 1-0 oppo.
Second:
I assumed oppo wouldn’t expect scissors twice in a row (esp. since I’d lost the first time with it). Therefore:
I threw scissors, oppo threw paper. 1-1.
Third:
Obviously, I wouldn’t throw scissors *three* times in a row — *everyone* changes it up. Thus, obviously:
I threw scissors. Oppo threw paper. 1-2 me. Which stunned the heck out of my opponent.
Now, if I’d led w/rock, then we would’ve tied. And the next move would’ve been unpredictable. Meaning I would’ve lost, because I hadn’t given him a story for why I would *not* throw the same thing twice.
Note that this worked because # rounds = 3 (i.e., below the threshold for deciding that I’m likely to throw scissors yet again). For best 3 of 5 or 5 of 7, I’d likely need to do something else …
June 14, 2010 at 11:45 pm
twicker
Further thought: note that Annie Duke was playing against championship-level players. I suspect most opponents would be more likely to act like my opponent – which means both that they’re less likely to recognize a pattern (esp. in best 2 of 3 matches), and they’re less likely to be as strategic as either she or her opponents were — meaning going for a win may work better. In games like this, some advice from professionals will work well, while some may not since your fellow players aren’t the same caliber and, thus, have different training (just as, when driving down the interstate, you should *not* do what NASCAR drivers do and, thus, you should *not* try to draft off the car in front of you).
June 15, 2010 at 12:03 am
jclee
Interesting that they talked about rock, paper, scissors in this story also!
http://www.npr.org/templates/story/story.php?storyId=127772215
“…all men usually go rock first. Women usually go scissors. No person who isn’t a professional will repeat the same throw three times.”
June 15, 2010 at 12:10 pm
Federico
There used to be a RSP tournament, in which people would submit computer programs for playing RSP repeatedly, kind of like Axelrod’s Torunament. The winning program was one called Iocaine Powder:
http://www.ofb.net/~egnor/iocaine.html
June 15, 2010 at 12:19 pm
jeff
awesome!
June 17, 2010 at 8:26 pm
David Pinto
This reminds me of a Star Trek TNG episode where Data lost a game to a live player, and lost it quickly. At the end of the episode, Data figured he couldn’t beat him, so he played to prevent a win by his opponent. After a while, the opponent couldn’t go on and conceded.