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Is Minimax really an optimal strategy in games

100%

Kościuk K.

tom Z. 6

63-75

In theory, the optimal strategy for all kinds of games against an intelligent opponent is the Minimax strategy. Minimax assumes a perfectly rational opponent, who also takes optimal actions. However, in practice, most human opponents depart from rationality. In this case, the best move at any given step may not be one that is indicated by Minimax and an algorithm that takes into consideration human imperfections will perform better. In this paper, we show how modeling an opponent and subsequent modification of the Minimax strategy that takes into account that the opponent is not perfect, can improve a variant of the Tic-Tac-Toe game and and the game of Bridge. In Bridge we propose a simple model, in which we divide players into two classes: conservative and risk-seeking. We show that knowing which class the opponent belongs to improves the performance of the algorithm.

Algorytmy grające w gry często używają strategii Minimax. Algorytm Minimax zakłada perfekcyjność przeciwnika, który wybiera zawsze najlepsze ruchy. Gracze jednakże mogą nie działać całkiem racjonalnie. Algorytm, który weźmie to pod uwagę może dawać lepsze wyniki niż Minimax. W pracy przedstawiono jak modelowanie gracza i modyfikacje algorytmu Minimax mogą poprawić wyniki w grze kółko-krzyżyk i w brydżu. W brydżu zaproponowany został prosty model, dzielący graczy na dwie kategorie - konserwatywny i ryzykowny. Eksperymenty pokazały, że wiedza, do której klasy graczy należy przeciwnik, poprawia działanie algorytmu.

Effect of inerter in traditional and variant dynamic vibration absorbers for one degree-of-freedom systems subjected to base excitations

71%

Barathwaaj D. L. , Yegateela S. , Vardhan V. , Suresh V. , Kaliyannan D.

Mechanics and Mechanical Engineering

2019

tom Vol. 23, nr 1

9--16

In this paper, closed-form optimal parameters of inerter-based variant dynamic vibration absorber (variant IDVA) coupled to a primary system subjected to base excitation are derived based on classical fixed-points theory. The proposed variant IDVA is obtained by adding an inerter alone parallel to the absorber damper in the variant dynamic vibration absorber (variant DVA). A new set of optimum frequency and damping ratio of the absorber is derived, thereby resulting in lower maximum amplitudę magnification factor than the inerter-based traditional dynamic vibration absorber (traditional IDVA). Under the optimum tuning condition of the absorbers, it is proved both analytically and numerically that the proposed variant IDVA provides a larger suppression of resonant vibration amplitude of the primary system subjected to base excitation. It is demonstrated that adding an inerter alone to the variant DVA provides 19% improvement in vibration suppression than traditional IDVA when the mass ratio is less than 0.2 and the effective frequency bandwidth of the proposed IDVA is wider than the traditional IDVA. The effect of inertance and mass ratio on the amplitude magnification factor of traditional and variant IDVA is also studied.