This discussion inspired this thread:
http://www.smogon.com/forums/showthread.php?p=959509#post959509
http://www.smogon.com/forums/showthread.php?p=959509#post959509
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Skill Level
- Thread starter JesiahTEG
- Start date
Ahem, fancy genetic algorithm AI that somehow got stuck at a local minimum aside... my calculations point at:
Rock: 1/14 times (~7%)
Scissors: 3/14 times (~21%)
Paper: 10/14 times. (~71%)
Scissors @ 100% == Opponent wins 10 points, Scissors wins 10 points.
Paper @ 100% == Opponent wins 3 points, Paper wins 3 point
Rock @ 100% == Paper wins 10 points, Rock wins 10 points.
Clearly, no matter what ratio the opponent sets his weights to be, he'll never break even.
That said, what becomes interesting with the Metagame is when people for some reason start at 100% Rock. However, I can simply predict that very quickly, Rock useage will fall as Paper rises, and Scissors will then rise to beat Paper. However, there will always be a little bit of Rock, because as soon as Paper is used that first time, Scissors will start to rise, meaning Rock people will use Rock attempting to out-predict the Scissors users. Etc. etc. etc. So by the time the cycle goes in a full loop, when Rock becomes popular again... there will be some Paper and Scissors in the metagame.
Quite simply put: the Metagame it would spiral inwards towards this (or some other) Nash equalibrium. I would assume the same applies to Pokemon, but due to the complex nature of Pokemon, we can't predict the spiral nearly as easily. But I feel an expert Pokemon player will be able to always stay ahead of the curve in this regard.
EDIT: one more thing. There is a Nash Equalibrium in every game, they just might be very very difficult to find >_> But when looking at the game from this perspective, it becomes obvious that two expert-level players are going to be playing close to the Nash Equalibrium (to minimize the damage the opponent can do). That is why I feel "prediction" will eventually simply boil down to luck. What makes the Nash Equalibrium so great is that it has been mathematically proven to exist in every game. RPS is the simplest of cases, but yes, one exists for Pokemon.
I can say what it is for any given situation? No, I'm not that good yet. But as players get better and better, prediction becomes more and more like Luck as both players approach that strategy.
Rock: 1/14 times (~7%)
Scissors: 3/14 times (~21%)
Paper: 10/14 times. (~71%)
Scissors @ 100% == Opponent wins 10 points, Scissors wins 10 points.
Paper @ 100% == Opponent wins 3 points, Paper wins 3 point
Rock @ 100% == Paper wins 10 points, Rock wins 10 points.
Clearly, no matter what ratio the opponent sets his weights to be, he'll never break even.
That said, what becomes interesting with the Metagame is when people for some reason start at 100% Rock. However, I can simply predict that very quickly, Rock useage will fall as Paper rises, and Scissors will then rise to beat Paper. However, there will always be a little bit of Rock, because as soon as Paper is used that first time, Scissors will start to rise, meaning Rock people will use Rock attempting to out-predict the Scissors users. Etc. etc. etc. So by the time the cycle goes in a full loop, when Rock becomes popular again... there will be some Paper and Scissors in the metagame.
Quite simply put: the Metagame it would spiral inwards towards this (or some other) Nash equalibrium. I would assume the same applies to Pokemon, but due to the complex nature of Pokemon, we can't predict the spiral nearly as easily. But I feel an expert Pokemon player will be able to always stay ahead of the curve in this regard.
EDIT: one more thing. There is a Nash Equalibrium in every game, they just might be very very difficult to find >_> But when looking at the game from this perspective, it becomes obvious that two expert-level players are going to be playing close to the Nash Equalibrium (to minimize the damage the opponent can do). That is why I feel "prediction" will eventually simply boil down to luck. What makes the Nash Equalibrium so great is that it has been mathematically proven to exist in every game. RPS is the simplest of cases, but yes, one exists for Pokemon.
I can say what it is for any given situation? No, I'm not that good yet. But as players get better and better, prediction becomes more and more like Luck as both players approach that strategy.
Somewhere along the thread this turned from a discussion of skill into highly advanced maths. And I'm not sure where or when that happened O.O