League of Legends: the Roles of Junglers in Light of Game Theory
League of Legends (LoL), arguably the most popular video game online, has attracted millions of players worldwide. The goal of each of the two teams in the game is to destroy the “nexus” of the other team. Ranging from pre-game champion selection, mechanical execution, and strategic plays, the decisions each player makes in a game can have different outcomes that ultimately lead to winning or losing the game. The article linked below examined spell casting in LoL in light of game theory and outlined a payoff matrix for the caster and the target. Other than focusing on the micro-play in LoL, I will primarily describe and interpret the roles of “junglers” in the early game, which is also intimately connected to game theory.
Fig 1. A simplification of a typical LoL game
To start off, let’s first have an overview of the game with an illustration. There are four laners (well, a support isn’t actually a laner, but for simplicity we’ll count him/her in) and a jungler in each team. The payoff for each player is gold; a jungler may obtain gold by last-hitting monsters in the jungles or killing players from the other team. Specifically, the act of killing a laner from the opposite site is commonly referred to as “ganking”. Here’s an incomplete list a jungler can do in the early game:
- Farm, i.e. last-hitting monsters and minions to obtain gold;
- Invade, i.e. invading the jungles of the other team to possibly gain more gold by a) killing the jungler of the other team or b) last-hitting monsters in the jungle;
- Gank, i.e. killing laners of the other team.
As such, an example 3×3 payoff matrix for junglers can be written as:
Fig 2. The payoff matrix for junglers
However, there is a major caveat in the game described by the matrix above: we’re treating the probability of successful ganking/invading as 1. But in real games, the probability of successful ganking might be best approximated by a probability distribution that depends on a) champions, b) skill level (i.e. are you a gold or a challenger?), and c) whether the laner plays aggressively or not. In other words, the payoff for each strategy used is more likely to be some P = Const * Pr(Champion, Skill, Laner 1, …, Laner 4) but not a constant. An analogous argument holds for invasion. In fact, the payoff matrix in Figure 2 gives a pure strategy Nash Equilibrium for junglers — to gank — which is hardly ever the case in real games.
Professional LoL teams are paying millions of dollars to hire data scientists who help players make correct decisions based on models heavily influenced by game theory. However, it’s impossibly difficult to come up with a single correct model that accounts for all scenarios, as the metas are constantly changing. And even if we have this perfect model, the best player can still make irrational choices, and the uncertainty and unpredictability in League of Legends is what makes it ever more intriguing.
Source:
https://blogs.cornell.edu/info2040/2018/09/19/game-theorys-relevance-in-league-of-legends/