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Solving Endgames in Large Imperfect-Information Games such as Poker
Ha, Karel ; Hladík, Milan (advisor) ; Bošanský, Branislav (referee)
Title: Solving Endgames in Large Imperfect-Information Games such as Poker Author: Bc. Karel Ha Department: Department of Applied Mathematics Supervisor: doc. Mgr. Milan Hladík, Ph.D., Department of Applied Mathematics Abstract: Endgames have a distinctive role for players. At the late stage of games, many aspects are finally clearly defined, deeming exhaustive analysis tractable. Specialised endgame handling is rewarding for games with perfect information (e.g., Chess databases pre-computed for entire classes of endings, or dividing Go board into separate independent subgames). An appealing idea would be to extend this approach to imperfect-information games such as the famous Poker: play the early parts of the game, and once the subgame becomes feasible, calculate an ending solution. However, the problem is much more complex for imperfect information. Subgames need to be generalized to account for information sets. Unfortunately, such a generalization cannot be solved straightaway, as it does not generally preserve optimality. As a consequence, we may end up with a far more exploitable strategy. There are currently three techniques to deal with this challenge: (a) disregard the problem entirely; (b) use a decomposition technique, which sadly retains only the same quality; (c) or formalize improvements of...
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Separation axioms
Ha, Karel ; Pultr, Aleš (advisor) ; Loebl, Martin (referee)
The classical (point-set) topology concerns points and relationships between points and subsets. Omitting points and considering only the structure of open sets leads to the notion of frames, that is, a complete lattice satisfying the dis- tributive law b ∧ A = {b ∧ a | a ∈ A}, the crucial concept of point-free topology. This pointless approach-while losing hardly any information-provides us with deeper insights on topology. One such example is the study of separation axioms. This thesis focuses on the Ti-axioms (for i = 0, 1, 2, 3, 31 2 , 4): properties of topological spaces which regard the separation of points, points from closed sets, and closed sets from one another. In this text we discuss their point-free counterparts and how they relate to each other. 1
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