Apparently, the ancient game of Rock, Paper, Scissors is flourishing these days, at least to the extent that there are championships.(?!!) I suppose this shouldn’t come as a surprise insofar as many combat systems essentially use an RPS system but with more elements and more ways in which those elements are structured. Still, I couldn’t help but chuckle at first, and immediately IM’d the link to a friend. Then, I started reading more about the strategy of the game and it got me thinking.
What makes RPS fun for these guys? It’s clearly not the whopping three total moves or even the dynamic, larger-than-life personalities that dominate the sport and keep it in the headlines (Who can forget the controversy over Pete “The Hand” Gimmens after he lopped off the first joint of his first two fingers to make throwing the scissors slightly easier? I thought EPSN was never going to stop talking about it.). It certainly can’t be that the theoretically optimal strategy is simply to throw out random moves. Instead, just like poker, this game is all about reading the play patterns of your opponents and taking advantage of their lack of true randomness. In fact, typically, tournaments of the past have been invitational only so that all participants have information about their play styles out there for their opponents to take advantage of. It is -hard- to throw randomly, and because the three different throws differ in how easy it is for the human body to form them (rock being easiest, paper second, scissors third, I’m told), it becomes even harder.
To compensate for this, serious players memorize three move gambits, just like a chess player might memorize opening gambits. There are gambits like the ‘Avalanche’ (three rocks in a row), Paper Dolls (scissors, then two papers), and so on. The idea is that by practicing these gambits one both commits them to muscular memory (no last split-second hesitation over what to throw). Presumably, they’ve also been optimized to take advantage of typical human reaction patterns as well.
This all got me thinking a little about combat systems and trigger systems (or auto-reaction systems or whatever you want to call them in MUDs/MMOs). In RPS, the optimal strategy is randomizing what you do. People can’t randomize, and my understanding is that computers can’t either (they can provide a convincing simulation of randomization, but not true randomization, at least with anything that is going to make it to someone’s desktop anytime soon). For the sake of argument, let’s pretend that the simulation of randomization provided by random number generators is functionally random insofar as while it may not be truly random, for 99.9% of people, it may as well be. (I’m aware that many random number generators are considered gameable.)
What’s depressing about that is that it makes it somewhat pointless to do in an electronic tournament where one can’t verify that someone isn’t using some sort of randomization program to help. We have the same problem in the Iron Realms games, which all have ascii-graphical chess sets for people to play with: I’d love to be able to do things like hold chess tournaments, but there’s just no way to do it and ensure there’s no cheating. We’ve even considered modifying the chess rules slightly to invalidate the strategy used by all chess programs, but with RPS, half the point of the game is to stay as simple as possible and thus to make manipulating your opponent or taking advantage of his or her weakness in pattern the whole point of the game.
Here’s a question for someone who has math skills: In a game of a purely random strategy against a human who isn’t random, is it equally likely that the random strategy will win as the human will win? It seems to me that in the long run, it’d be a draw just as much as if the human used the random strategy but that there is a chance to actually be better if one is using a non-random strategy vs. another human. If you use a random strategy, you’re basically playing a ‘perfect defence’: There is no weakness in your play for the opponent to take advantage of, and you cannot be misled. On the other hand, you also can’t take advantage of your opponent’s strengths. Does that actually mean, then, that in the long run, because a completely random (or functionally random) strategy can only draw (on average), it wouldn’t have a good chance of winning a tournament with humans who played both it and other humans?
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June 13th, 2006 at 9:45 pm
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June 14th, 2006 at 8:41 pm
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June 10th, 2006 at 7:53 am
damijin
I have my own issues with RPS. It’s overused in a simplified form as a video game “balance” crutch, and that’s a shame, considering it ends up being about as entertaining as watching 2 computers play each other.
The game itself is pretty evil. Some people look at it as the ultimate form of balance, but it’s not that obviously. It has a very small margin of opportunity for advantages (imbalance) which are the direct result of any fun that can be had. If you remove the aspect of player psychology in an RPS implementation, it’s nothing more than pure randomness, static, noise… unfun. I really wish people would stop using it like that
June 10th, 2006 at 8:01 am
Matt
I don’t disagree. Without the added imbalances introduced by playing face to face, the opportunity for meaningful choice is pretty much gone.
June 10th, 2006 at 11:25 am
Austin
In RPS the mixed-strategy Nash equilibrium is for each player to play each move with probability 1/3. When we say that a strategy profile is Nash equilibrium, we mean that if one player deviates from that profile, then he or she cannot improve their score. So, if one player is playing {1/3, 1/3, 1/3}, the other player can do no better than a 50% win rate, by the definition of Nash equilibrium.
Establishing a lower bound on the odds is a little harder, but I believe it is still 50%. Consider any given round of play; the random player’s move will obviously not depend on the history, so no matter what move the human player makes, he only has a 1/3 chance of winning and a 1/3 chance of tieing. His strategy is irrelevent.
So, in the presence of a purely random player, each player will have a 50% chance of winning.
June 10th, 2006 at 2:30 pm
DonathinFrye
Check out the free-form matrix dueling system of the RDI Days(now almost 20 years old). It originated as the FFGF on the original AOL and its predecessors, and has moved to the open net since then.
www.ringsofhonor.org
This gaming/roleplaying environment has created three “sports” that are, more or less, matrix-base dueling. RPS is also matrix-based dueling. The difference in these matrices is the purposeful design of each choice/move not being equally useful to others, as well as some more advanced rules.
They’ve created a Duel of Swords(larger playerbase over the past 18 years than any MUD besides Simutronics’ headliners), and nearly as popular variants Duel of Magic and Duel of Fists. All three of these sports utilize, at minimum(DoS being the smallest matrix), 15 different moves, and at Maximum, 28. Like RPS, the scoring is broken down to rounds, with more specific scoring rules for each game. The games then also have very complex ranking, challenge, and political systems infused in the background.
These “sports” are perfectly suited to the roleplaying environment, and each is very unique from the other two. My point is that they have taken the concept of matrix dueling and created something that requires both more use of strategy, and a heavy reliance on psychology. Just as with professional RPS players, the top DoS/F/M players in the world are a master of their opponents psychology and understand all of the different gambits and patterns of that matrix.
I’ve used this system to create an identical mini-game on a MUD(with their permission). Clandestine MUD utilizes Duel of Swords as a mini-game, and while the PvP itself is not focused on this matrix/RPS style of combat, it has made for an extremely popular mini-game that allows the results of each round to be customizably roleplayed out by the duelists. While the results of a Thrust versus Stophit round will always yield the same result, this has allowed many of our roleplayers who do not like the crunch/hack’nslash elements of our PvP system to still be competitive in a variant on PvP that allows them to roleplay each round out entirely to their own personal liking.
So, as a longtime member of the Rings of Honor community, a top-ranking duelist in all three Games, and a game designer who has implemented this successfully, I would say there is definitely merit in a matrix combat-system.
Also, many have attempted to create complex bots that use A.I. to study opponents, learn from them, randomize at the right times and “scout”(use the opponent’s studied patterns against them) at the right time. Even with some amazing coders in the community, the best bots have not been able to defeat the best players. Bots that are completely dice-roll/randomized-based tend to do very poorly. The key seems to be in weighing the matrix so that it is not as flush as RPS.
June 12th, 2006 at 8:16 am
Tiax
Regarding the question at the end:
I would think that you are correct, because we should view the competition not in terms of randomness of the players, but in randomness of the match. In other words, as long as one of the players in a given match is throwing pure random, then the match itself is randomized. It is only when neither player is throwing random that the match is non-random and the chance arises to do consistently better than 50-50.
Note the implication that pure randomness can only be the sole optimal strategy against a non-random opponent. Against a random opponent, the match is randomized no matter what you do, so any strategy is equally optimal. Against a non-random opponent, there is either an optimal non-random strategy - which occurs when the player is better than the opponent, or the optimal strategy is pure randomness, when the player is worse than the opponent, and any hint of non-randomness could be exploited.
Also, I like the blog.
June 13th, 2006 at 6:41 am
moo
When I look at Rock-Paper-Scissors, what I see is PvP boiled down to its ultimate essence. It’s theoretically fair (both players have an equal chance to win) but whichever player understands the psychology of their opponent better and can predict their actions better will win in the long run.
Actually, it might be worth looking at ways we can make our PvP systems more Rock-Paper-Scissors-like.
June 13th, 2006 at 6:56 am
moo
Oops.. about your math question… taking RPS as the example, if one player is perfectly random then the three outcomes (win, loss, draw) are equally probable for them no matter what the opponent does. Since its a zero-sum game, the three outcomes are equally probable for the opponent too.
In order to have a higher probability of winning, a player must be able to predict (at least some of the time) which of the opponent’s actions is the most probable. In this sense, non-perfectly-random players could be said to “leak information” to the opponent about their future moves; the opponent is trying to “get inside their head” and model their decision making, to predict their most probable choice. (The similarity with predictive models for information compression is striking).
June 13th, 2006 at 1:14 pm
Mageman
I can’t comment much with the maths of the whole thing as my own are almost non exhistant, but when I play chess, both in the real world and ingame, I just usually take every situation as they come. Whenever someone makes a move, I take a look at the board with “new eyes” for lack of a better term and tend to play like that.
June 14th, 2006 at 5:56 pm
ML
maybe your math question could be related to the Prisoners Dilemma, in that if both players choose to play non-random they both have a higher chance of winning… or?
June 15th, 2006 at 1:10 pm
J.
Unless RPS is played best out of three, it has no meaning, and more importantly, that lack of meaning should be obvious to the player. I find it lots more interesting to work in psychology and player attempts to “read” opponents — that scenario is far more likely in my mind to lead to players enjoying the experience of playing aside from any outcomes. And that’s the goal, right?
Right?
Related story: A Florida federal judge this week ordered two bickering attorneys to play RPS to settle their argument, but unfortunately, it was only one round. And only one attorney (so far) is planning to comply with the order to play.
http://money.cnn.com/2006/06/07/magazines/fortune/rps_fortune/
June 15th, 2006 at 1:19 pm
Matt
RPS has to be played more than best out of 3 to really be meaningful, I think. The edge you can gain on your opponent isn’t that large.
Thanks for the story link.
–matt