Besides the colored pixels, you can also see numbers for the Pascal-like triangles reduced modulo
. Please see the third snapshot.
be fixed natural numbers such that
. There are
players seated in a circle. The game begins with the first player. Proceeding in order around the circle, a box of cards is passed from hand to hand. The box contains
red cards and
white cards. A player draws a card when the box is received. Once a card is drawn, it will not be returned to the box. If a red card is drawn, the player loses and the game ends. Let
be the probability of the
player losing the game. Then for fixed numbers
, the list
forms a Pascal-like triangle.
The denominators of the list form Pascal-like triangles, and these triangles, reduced modulo
, are displayed. These triangles depend on the number
of players. To make the situation simple,
If you want to know the mathematical background of the game, see R. Miyadera, T. Hashiba, Y. Nakagawa, T. Yamauchi, H. Matsui, S. Hashiba, D. Minematsu, and M. Sakaguchi, "Pascal-like Triangles and Sierpinski-like Gaskets," Visual Mathematics: Art and Science Electric Journal of ISIS-Symmetry
Because of the Pascal-like property, the triangles can be made by a kind of cellular automaton that has a kind of boundary condition.