Information theory and player deck choice in online Collectable Card Games.

Using three years of player data of the online Collectible Card Game Hearthstone, we perform an in-depth analysis of the evolution of the game's online landscape over the period 2016--2019. Specifically, by considering the frequencies that deck archetypes are played, and their corresponding win-rates, we are able to provide narratives of the system-wide changes that were made over time, and how players reacted to those changes via their choices regarding deck construction and tactics. Applying the deck frequencies to analyse the system's Shannon entropy, we characterise the salient features of player deck choice over time. Paying particular attention to how system entropy is affected during periods of both small and large-scale change, we are able to demonstrate the effects of increased player experimentation before clear viable decks and tactics emerge. Furthermore, guided by the concept of local active information storage, we construct conditional probabilities that particular decks are chosen, given previous deck frequencies and win-rates. Importantly, these conditional probabilities can be interpreted to simulate understandable player behaviour. Then comparing the Shannon entropy with the expectation value of the local active information storage over all past and current deck choices and win-rates, we are able to test the explain-ability of current player choice based on previous player decision-making.