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As we presented before (See R. Miyadera, General theory of Russian roulette), the triangle of the list of probabilities has the Pascal's triangle like property. If we make a triangle using the least nonnegative residues of the numerators of the fractions in the triangle, then we get very interesting figures. When the number of the player is 2, then it is very similar to the Sierpinski Gasket. When the number of players is 3, it is slightly similar to the Sierpinski Gasket.
This fact has been already published as Miyadera R. et all.: Pascal like triangles and Sierpinski like gaskets, Visual Mathematics , Vol 9, No.1, 2007, Mathematical Institute of the Serbian Academy of Sciences and Arts.
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