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External sampling and outcome sampling are two ways of defining the sets $Q_1, \dots, Q_n$. I think your mistake is that you think of the $Q_i$ as fixed and taken as input in these shampling schemes. It is not the case. In external sampling, there is as many sets $Q_{\tau}$ as there are pure strategies for the opponent and the chance player (a pure strategy ...


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I have calculated an upper bound and modified a calculation of a lower bound for a similar game. I assume the real size is closer to the upper bound. $$ 7.36 \cdot 10^{27} \leq |SPADES| \leq 3.09 \cdot 10^{72} $$ Upper bound The State-space complexity of Spades can be computed by counting for each possible starting state (deal), all the possible sequences ...


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