The original thread will be posted here but you can find it here as well (all credit goes to McGrue for the OP!)
Introduction
Game Theory is the study of decision making by individual agents (players) in response to others in any given scenario (game). It is applicable to all walks of life, so why not Pokemon? The aim of this thread is to give you a new perspective on battling, with the long term goal of educating the masses.
Assumptions
1. Players are rational.
This must be true if you expect to predict accurately.
2. Players aim to maximize their chances of winning.
Otherwise, there is nothing to it.
The Importance of Information
As anyone who has scouted a tournament opponent (or been the victim of scouting) will testify, knowing your opponent's team gives you an undeniable edge. However, scouting a battle can tell you so much more; notably how risk loving or risk averse your opponent is (how often does he switch out of a neutral match up? does he use fire blast over flamethrower? etc). All these tidbits cumulate to provide you with a profile to work with later.
Before a battle, you need to know just how good your opponent is, so you can associate him with a profile; for example weaker players will switch out of immediate dangers, stronger players will account for secondary dangers (your likeliest predictions) and the strongest players will be familiar with all sorts of mind games (I know that you know that I know that you know that I know that you know... etc).
During a battle, you need to figure out as soon as possible whether your profiling is accurate. This applies for even familiar opponents, because nobody battles the same on different days, for any number of exogenous reasons. Further, given that players tend to be more cautious early on (perhaps because they are doing the same thing!), this is more difficult than touted.
Catalogue all information that occurs during the battle, and in particular note the turns where you outplay your opponent and vice verse. After a while, the strongest players will develop a sense of what is going on, and press home their advantage. Essentially, a battle amongst the best players is a race to pigeon hole how well their opponent is playing on that particular day (all else held equal), and predict accordingly.
The strongest players are able to adjust their style if they realize that they are being outplayed.
The Choice Band Dilemma
This is a play on The Prisoner's Dilemma, but it is slightly more complicated. Consider the following (not unlikely) scenario:
~Bug catcher Aeolus leads with choice band Heracross with megahorn/close combat/stone edge/pursuit
~Schoolboy Batpig leads with Swampert with earthquake/stone edge/ice beam/stealth rock
~Bug catcher Aeolus is a good battler, schoolboy Batpig is top of his class.
~Neither player knows anything about the other's team.
Clearly the matchup favours Heracross and with a lack of information, we can safely assume Aeolus will not switch. The question is what attack he will use. If Swampert stays, it will certainly use stealth rock. Given this, Aeolus does best with close combat or megahorn. If Swampert switches, neither of these rate to be optimal, as the new pokemon will likely resist one or both. The risk of predicting no switch and Batpig changing to a ghost means megahorn is a better option than close combat.
Given a switch, pursuit will not damage Swampert significantly and more or less forces Aeolus to switch on turn two. Therefore, if Batpig switches, Aeolus does best with stone edge. We have thus concluded that given this scenario, Heracross will only ever use megahorn or stone edge (through similar analysis, you can be reasonably sure that a choice band Tyranitar will use crunch as its first attack etc).
Since Batpig is top of his class, he understands this mechanism and assigns a probability for which attack Aeolus will choose. He knows that if he leaves Swampert in to megahorn, the price could be defeat. On the other hand, if Heracross uses stone edge and Swampert stays in, not only has he laid stealth rock first turn, but Heracross must switch second turn.
Since Aeolus is merely a “good” battler, Batpig decides that Heracross will stone edge 70% of the time (arbitrary example), expecting a switch. If neither player began with a team edge over the other, Batpig needs this play to win 30% more battles than he would otherwise, to break even in the long run and justify staying in.
Decision Tree
In the above scenario, I used words to describe something that is easier to communicate visually. Observe the generalized decision tree of one turn in Pokemon battling (N is a third agent “nature” also known as “luck” i.e. hit/miss, CH? and RNG):
It is important to note that A and B act simultaneously with the same information set (the tree suggests B acts after A). The payoffs are expectations based upon the probability of that outcome. More precisely, there should be 4 options rather than “attack” and 5 options over “switch”, but that would over complicate things.
Independence
Subsequent decisions are more interesting. The outcome of a repeated matchup will not only depend on the situation of the battle, but some causation can be attributed to what has happened before. The good battler tries to be unpredictable by not adhering to patterns, but the best battlers always consider each situation on its merits.
Undoubtedly, you will have gathered more information about your opponent's team, thus changing the probabilities and expected payoffs of every possibility. Mind games really kick in now, and your profiling better be accurate.
Commitment
If you want someone to do something, commit to an action that obliges them to do just that. For example in real life, if you want your girlfriend to go to a football match with you when she would rather watch a teen flick, book the tickets in advance. This incurs an additional cost to not going to the football, so she is more likely to err in your favour.
Similarly, commitment occurs in pokemon with choice items. Once you lock yourself into an attack, you can only continue to use that attack, or switch. Since your attacking option is known, your opponent can only react optimally to that attack. For example, by committing to ice beam for a kill, your opponent is unable to switch to a Salamence who could otherwise dragon dance and sweep.
Comment
These methods may seem mechanical and even long winded, but after accumulating experience, you will find that they become almost second nature. Other battlers may well recognize in themselves everything that I have said, but probably have never thought about battling so explicitly. This is kind of short (honest) because I got fed up with it halfway through. I might add stuff later depending on interest.
---
Often when playing a game we're forced with difficult decisions that will either mean we win a game or lose a game. We might think player A will switch when really he's given up on keeping the pokemon alive, and in return we might lose the advantage which we once had. This is where we come into a player's style. When battling someone it's key to watch when they switch, how they attack, and when they think they're safe to set up. One too many times have I seen a Suicune come in on a Heatran and think it's a solid move to start stat-upping right away when it's still early in the game, only to be met face to face with a Roserade, Celebi, or even Explosion from Heatran. Was player A wrong to Calm Mind early game? Well it depends on what the Heatran was. Did he see LO recoil? Did he see Leftovers? If he saw nothing is it safe to assume it's Choice Scarf or Specs? All these things fuel how we play.
There's some people that don't pay attention to the logs, however. They'll graze over a Heatran with Leftovers and still fear Explosion off of it. I was playing a match today where I switched in a Tyranitar into a Rotom's Thunderbolt, the player didn't see Leftovers and must have thought that I would be some kind of Choice Set (little did he know I was Expert Belt.) He made a good call and switched Rotom out while a Scizor came in to take a Crunch. Now he didn't see LO damage which fits his idea that Tyranitar is some sort of Choice set. The problem is it's still early game, much of our team is yet to be revealed and he's willing to bet a pokemon on whether or not Tyranitar is Choiced. Every call he made was and seemed correct, so why didn't it pan out for him? This point goes back to the beginning of McGrue's post, "is your profiling accurate?" While it's easy to say "I'd like to improve my prediction/profile/whatever you kids call it," a lot of it comes with experience from the game and what you take out of it.
Introduction
Game Theory is the study of decision making by individual agents (players) in response to others in any given scenario (game). It is applicable to all walks of life, so why not Pokemon? The aim of this thread is to give you a new perspective on battling, with the long term goal of educating the masses.
Assumptions
1. Players are rational.
This must be true if you expect to predict accurately.
2. Players aim to maximize their chances of winning.
Otherwise, there is nothing to it.
The Importance of Information
As anyone who has scouted a tournament opponent (or been the victim of scouting) will testify, knowing your opponent's team gives you an undeniable edge. However, scouting a battle can tell you so much more; notably how risk loving or risk averse your opponent is (how often does he switch out of a neutral match up? does he use fire blast over flamethrower? etc). All these tidbits cumulate to provide you with a profile to work with later.
Before a battle, you need to know just how good your opponent is, so you can associate him with a profile; for example weaker players will switch out of immediate dangers, stronger players will account for secondary dangers (your likeliest predictions) and the strongest players will be familiar with all sorts of mind games (I know that you know that I know that you know that I know that you know... etc).
During a battle, you need to figure out as soon as possible whether your profiling is accurate. This applies for even familiar opponents, because nobody battles the same on different days, for any number of exogenous reasons. Further, given that players tend to be more cautious early on (perhaps because they are doing the same thing!), this is more difficult than touted.
Catalogue all information that occurs during the battle, and in particular note the turns where you outplay your opponent and vice verse. After a while, the strongest players will develop a sense of what is going on, and press home their advantage. Essentially, a battle amongst the best players is a race to pigeon hole how well their opponent is playing on that particular day (all else held equal), and predict accordingly.
The strongest players are able to adjust their style if they realize that they are being outplayed.
The Choice Band Dilemma
This is a play on The Prisoner's Dilemma, but it is slightly more complicated. Consider the following (not unlikely) scenario:
~Bug catcher Aeolus leads with choice band Heracross with megahorn/close combat/stone edge/pursuit
~Schoolboy Batpig leads with Swampert with earthquake/stone edge/ice beam/stealth rock
~Bug catcher Aeolus is a good battler, schoolboy Batpig is top of his class.
~Neither player knows anything about the other's team.
Clearly the matchup favours Heracross and with a lack of information, we can safely assume Aeolus will not switch. The question is what attack he will use. If Swampert stays, it will certainly use stealth rock. Given this, Aeolus does best with close combat or megahorn. If Swampert switches, neither of these rate to be optimal, as the new pokemon will likely resist one or both. The risk of predicting no switch and Batpig changing to a ghost means megahorn is a better option than close combat.
Given a switch, pursuit will not damage Swampert significantly and more or less forces Aeolus to switch on turn two. Therefore, if Batpig switches, Aeolus does best with stone edge. We have thus concluded that given this scenario, Heracross will only ever use megahorn or stone edge (through similar analysis, you can be reasonably sure that a choice band Tyranitar will use crunch as its first attack etc).
Since Batpig is top of his class, he understands this mechanism and assigns a probability for which attack Aeolus will choose. He knows that if he leaves Swampert in to megahorn, the price could be defeat. On the other hand, if Heracross uses stone edge and Swampert stays in, not only has he laid stealth rock first turn, but Heracross must switch second turn.
Since Aeolus is merely a “good” battler, Batpig decides that Heracross will stone edge 70% of the time (arbitrary example), expecting a switch. If neither player began with a team edge over the other, Batpig needs this play to win 30% more battles than he would otherwise, to break even in the long run and justify staying in.
Decision Tree
In the above scenario, I used words to describe something that is easier to communicate visually. Observe the generalized decision tree of one turn in Pokemon battling (N is a third agent “nature” also known as “luck” i.e. hit/miss, CH? and RNG):
It is important to note that A and B act simultaneously with the same information set (the tree suggests B acts after A). The payoffs are expectations based upon the probability of that outcome. More precisely, there should be 4 options rather than “attack” and 5 options over “switch”, but that would over complicate things.
Independence
Subsequent decisions are more interesting. The outcome of a repeated matchup will not only depend on the situation of the battle, but some causation can be attributed to what has happened before. The good battler tries to be unpredictable by not adhering to patterns, but the best battlers always consider each situation on its merits.
Undoubtedly, you will have gathered more information about your opponent's team, thus changing the probabilities and expected payoffs of every possibility. Mind games really kick in now, and your profiling better be accurate.
Commitment
If you want someone to do something, commit to an action that obliges them to do just that. For example in real life, if you want your girlfriend to go to a football match with you when she would rather watch a teen flick, book the tickets in advance. This incurs an additional cost to not going to the football, so she is more likely to err in your favour.
Similarly, commitment occurs in pokemon with choice items. Once you lock yourself into an attack, you can only continue to use that attack, or switch. Since your attacking option is known, your opponent can only react optimally to that attack. For example, by committing to ice beam for a kill, your opponent is unable to switch to a Salamence who could otherwise dragon dance and sweep.
Comment
These methods may seem mechanical and even long winded, but after accumulating experience, you will find that they become almost second nature. Other battlers may well recognize in themselves everything that I have said, but probably have never thought about battling so explicitly. This is kind of short (honest) because I got fed up with it halfway through. I might add stuff later depending on interest.
---
Often when playing a game we're forced with difficult decisions that will either mean we win a game or lose a game. We might think player A will switch when really he's given up on keeping the pokemon alive, and in return we might lose the advantage which we once had. This is where we come into a player's style. When battling someone it's key to watch when they switch, how they attack, and when they think they're safe to set up. One too many times have I seen a Suicune come in on a Heatran and think it's a solid move to start stat-upping right away when it's still early in the game, only to be met face to face with a Roserade, Celebi, or even Explosion from Heatran. Was player A wrong to Calm Mind early game? Well it depends on what the Heatran was. Did he see LO recoil? Did he see Leftovers? If he saw nothing is it safe to assume it's Choice Scarf or Specs? All these things fuel how we play.
There's some people that don't pay attention to the logs, however. They'll graze over a Heatran with Leftovers and still fear Explosion off of it. I was playing a match today where I switched in a Tyranitar into a Rotom's Thunderbolt, the player didn't see Leftovers and must have thought that I would be some kind of Choice Set (little did he know I was Expert Belt.) He made a good call and switched Rotom out while a Scizor came in to take a Crunch. Now he didn't see LO damage which fits his idea that Tyranitar is some sort of Choice set. The problem is it's still early game, much of our team is yet to be revealed and he's willing to bet a pokemon on whether or not Tyranitar is Choiced. Every call he made was and seemed correct, so why didn't it pan out for him? This point goes back to the beginning of McGrue's post, "is your profiling accurate?" While it's easy to say "I'd like to improve my prediction/profile/whatever you kids call it," a lot of it comes with experience from the game and what you take out of it.
