A Game That Produce Pascal-like Triangle

The members of our club have been studying a game that produces Pascal-like triangle for more than 20 years. When we published our research in a English math magazine, an English mathematician called it "Pascal-like triangle". We use this name in this web site. __We present our research so that many people know that ordinarly high school students can discover new formulas in mathematics.__

What kind of game？

On the table there is a pile of cards, and players are around it.

The cards on the table consists of red cards and white cards.

Players take out cards from the pile according to an arranged order, and by an arranged rule

a player became a loser. Then the game ends.

For a certain type of rules of making a loser, the probability of a certain player's losing in the game

constitute a Pascal-like triangle. If the rules are appropriate for the Pascal-like triangle,

any order of player's taking out cards is OK.