Starcraft Map Imbalance Prediction Based on Chosen Build Order

We utilize the distribution of early building decisions on Starcraft maps to predict the winning percentages in each racial matchup. Tournament replays from 5661 games on 7 maps were parsed. The win rate on a given map was predicted from a regression on the remaining maps’ build order distributions and logistic-space win rates. The method is only highly effective at predicting the outcomes for Zerg vs Protoss games. Our data set was found to be less biased than anticipated, showing that Starcraft is a balanced game despite a great diversity of strategy profiles. 1 Problem Definition The computer game Starcraft has enjoyed such widespread commercial success that South Korea employs 12 professional Starcraft teams whose matches are broadcast on Korean television. In the game of Starcraft players choose to command the armies of one of three races: Terran, Zerg, or Protoss. Unlike chess pieces, which are the same for both sides, the army compositions of each Starcraft race are entirely unique. A game between two players of different races contains many asymmetries. Despite the many asymmetric factors influencing the game, Starcraft is considered to be a balanced game in that all three races have successful professional players. Starcraft games are played on many different “maps” which change the fundamental board layout. Maps differ from each other in attributes such as the ease of acquiring resources, distance between bases, and the openness of the terrain. Figure 1 gives an example of the characteristics of two commonly played Starcraft maps. In professional televised games, most maps favor one race’s chances of winning over another by a 60% − 40% split [1]. The most common bias is a cyclical Terran > Zerg > Protoss > Terran relationship that prevents one race from dominating the others. We wish to investigate whether the overall winning percentage in a match between two given races on a given map can be predicted from the early game decisions made by the players. One of the most important decisions in Starcraft consists of choosing which buildings a player constructs. Buildings either allow the player to collect more income, to produce more units for the player’s army, or to allow high tech units into the player’s army. We consider only the construction of buildings and not individual troops, since the number of possible build orders quickly becomes combinatorially intractable otherwise. The important information we can learn from buildings lies in the order they are built. Attempting to define a game state based on the mere presence of buildings would not be valid (given that troops and money reserves are not accounted for in the state). The time at which a building is built matters greatly because this information conveys intention to either invest in long term resource gathering or raise an army quickly for a decisive all-in push. For example, a Terran player’s first two buildings usually will be either a Supply Depot then a Barracks or a Barracks then a Supply Depot. The order matters greatly. Building the Supply Depot before the Barracks is more common and allows the main base to produce resource gathering units without ceasing. Building a Barracks before a Supply Depot gives faster access to military units but requires a pause in the production of resource gathering units and thus implies unusually early aggression. Most buildings have prerequisites, so the early build decisions are combinatorially limited and can be represented cleanly as a tree. We only need to concern ourselves with analyzing the earliest few buildings, since after the opening minutes of the game the player will have scouted the opponent and further decisions will be reactionary. We hypothesize that a mixed strategy Nash equilibrium exists between the many possible opening build orders and that experienced players choose their opening builds accordingly as a function of the map characteristics. We expect this condition to hold at high levels of play because if it were not true then there should exist a strategy profile that beats the current top players, and any player using this strategy profile would then become a top player. Initially, the player does not have any information on the opponent’s actions, so in the field of game theory one could compare Starcraft’s early building decisions to