It has notably achieved a playing strength comparable to good human players at playing go, but it has also shown good performance in card games like Klondike solitaire and skat. Since its introduction in 2006, the UCT algorithm has been the dominating approach for solving games in AI research. However, it has a substantially larger state space than skat and a unique key feature which distinguishes it from skat and other card games: players usually do not know with whom they play at the start of a game, figuring out the parties only in the process of playing. While skat has been extensively studied by the AI community in recent years, this is not true for doppelkopf. We propose doppelkopf, a trick-taking card game with similarities to skat, as a benchmark problem for AI research. Experiments emphasize the impact of the refined skat putting algorithm on the playing performance of the bots, especially for AI bidding and AI game selection. Besides predicting the probability of winning and other hand strength functions we propose hard expert-rules and a scoring functions based on refined skat evaluation features. This paper looks into different skat selection strategies. Prior to the trick-taking and as part of the bidding process, one phase in the game is to select two skat cards, whose quality may influence subsequent playing performance drastically. As within the game of Bridge, in Skat we have a bidding and trick-taking stage. Given the larger number of tricks and higher degree of uncertainty, reinforcement learning is less effective compared to classical board games like Chess and Go. Skat is a fascinating combinatorial card game, show-casing many of the intrinsic challenges for modern AI systems such as cooperative and adversarial behaviors (among the players), randomness (in the deal), and partial knowledge (due to hidden cards). Based on a tournament scoring system, we propose a new ELO system for Skat to overcome these weaknesses. Last but not least, there are internationally established scoring systems, in which the players are used to be evaluated, and to which ELO should align. Secondly, they are game of both skill and chance, so that besides the playing strength the outcome of a game also depends on the deal. Firstly, these are incomplete information partially observable games with more than one player, where opponent strength should influence the scoring as it does in existing ELO systems. The evaluation of player strength in trick-taking card games like Skat or Bridge, however, is not obvious. Besides weaknesses, like an observed continuous inflation, through a steadily increasing playing body, the ELO ranking system, named after its creator Arpad Elo, has proven to be a reliable method for calculating the relative skill levels of players in zero-sum games. Assessing the skill level of players to predict the outcome and to rank the players in a longer series of games is of critical importance for tournament play.
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