G(r,s,p) Reward Game: A Two-opponent Stochastic Online Game from Hearthstone

Abstract

In this paper, we propose a probabilistic combinatorial game, the G(r,s,p) reward game, in the two-opponent stochastic online game setting. The proposed game rewards players on consecutive wins, whose inspiration is from the winning streak feature in Hearthstone, a free-to-play online digital collectible card game with 100 million players worldwide. Three natural questions to any game player are rigorously answered by a simplified-and-complicated methodology: how likely does a specific player lose the game; How long the game is expected to take till that player loses the game; Whether there exist specific amounts of stars that player starts the game but his or her fortune will be (resp. never be) that amount again.