Pokémon Battling Explained: Featuring Game Theory
Despite being marketed towards kids, the Pokémon video game series has a surprising amount of depth. The core gameplay of the Pokémon franchise is the turn-based RPG (Role Playing Game) combat system, where two players square off in a battle, each with six of their own Pokémon. Depending on the competitive format, each player may have either one or two Pokémon out at a time. For the sake of simplicity, let’s say each player can only have one out at a time. Each Pokémon has a certain amount of HP (Hit Points), and HP can be lost by getting hit by your opponent’s attacks, which leads us to the goal of the game: to deplete the HP of all of your opponent’s Pokémon.
On a given turn, players select their move simultaneously. When selecting their move, each player has a variety of actions to choose from, but for the sake of simplicity let’s just keep it to two: attacking the opposing Pokémon or switching their current Pokémon for another on their team. There are benefits and detriments to each option, but to better understand those, it is worthwhile to understand two concepts: Pokémon Typing and Option Priority.
Every Pokémon has an elemental type; some even have two! Every attack also has an elemental type. The key idea here is that some types will be more or less effective on a given type. For example, let’s take the Fire and Water types. Like you would expect, a Water type attack will be especially effective on a Fire type Pokémon, while a Fire type attack will be less effective on a Water type Pokémon. So to apply this to a Pokémon battle, let’s say Player 1 has a Fire type Pokémon with a Fire type attack and Player 2 has a Water type Pokémon with a Water type attack. What should Player 1 do? To attack is to do damage to your opponent (obviously), but to switch? How does that even work? That’s where the second principle, Option Priority, comes in. In short, when you choose to switch Pokémon, you automatically go first (Typically, turn order is determined by each Pokémon’s “speed” stat). So if, say, Player 1 has a Grass type Pokémon on their team, it may be wise to switch their Fire type out for the Grass one, assuming Player 2 will attack given their type advantage. Here is the scenario in a gains table:
| Player 2 Attacks | Player 2 Switches | |
| Player 1 Attacks | (1, 4) | (4,0) |
| Player 1 Switches | (2,1) | (0,2) |
While the actual values are somewhat arbitrary, this effectively demonstrates the payoffs of each option. If Player 1 (P1) and Player 2 (P2) both attack, they’ll both do damage to each other’s Pokémon, but Player 1’s attack will be “not very effective” (half damage) while Player 2’s attack will be “super-effective” (double damage). If P2 switches and P1 attacks, P1 will do double damage while P2 switches into a Grass type Pokémon, which is weak to Fire type attacks. If P1 switches to their Grass type and P2 attacks, P2’s attack will not be very effective (hence the 1 point) while P1 has put themselves in an optimal position for a counterattack on the next turn, gaining them points. If both players switch, we’re still in the same situation: P2 has the type advantage, so they get 2 points. Given this layout, there is no pure strategy Nash Equilibrium or Dominant Strategy, but what about a mixed strategy Nash Equilibrium? It turns out we can calculate the mixed strategy Nash Equilibrium. If p is the chance that P1 attacks and q is the chance P2 attacks, p = 1/5 and q = 4/5.
While it may seem like a Pokémon battle is a game of chance (given there is a mixed but not pure strategy Nash Equilibrium), there is actually a lot more nuance in a Pokémon battle that we haven’t touched upon. Remember how I said earlier that players have access to a variety of move options on their turn and there are Pokémon with more than one type? It turns out that by including additional elements, such as the things listed previously, status moves, stat-changing moves and held items, Pokémon battle outcomes are not randomly generated. There is a lot of strategy involved; trust me, its really fun! Try it out for yourself! https://pokemonshowdown.com/
Sources:
Type Effectiveness: https://pokemondb.net/type
Essentially the play-style used in the example (Hyper Offensive): https://www.reddit.com/r/stunfisk/comments/684yv7/an_overly_offensive_title_an_introduction_to/