  We introduce and analyze a quantum analogue of the Law of Excluded Gambling
Strategies of Classical Decision Theory by the definition of different kind of
quantum casinos. The necessity of keeping into account entaglement (by the way
we give a staightforward generalization of Schmidt's entanglement measure)
forces us to adopt the general algebraic language of Quantum Probability Theory
whose essential points are reviewed. The Mathematica code of two packages
simulating, respectively, classical and quantum gambling is included. The deep
link existing between the censorship of winning quantum gambling strategies and
the central notion of Quantum Algorithmic Information Theory, namely quantum
algorithmic randomness (by the way we introduce and discard the naive
noncommutative generalization of the original Kolmogorov definition), is
analyzed
