淡江大學數學系演講公告
主 講 人：陳 文 憲 教授
Department of Mathematics, University of Miami, U.S.A.
講 題： Some Probabilistic Games
日 期：99年6月1日（星期二）
時 間：下午2:30 –3:20
地 點：數學系(科學館S433室)
摘 要：
Two players I and II play the following game: Starting with player I, each player
in turn tosses a coin (with probability p for heads) and obtains 2 points for
heads and 1 point for tails. The game is finished when one of them has n or more
accumulated points, and this player wins the game. It is easy to see that for any p
in the interval [0,1], player I has an advantage because he goes first. Let I(n,p)
be the player I's winning probability and it is a polynomial of degree 2n - 2. For
player II, he wants to find a p*(n) such that I(n,p*(n)) = inf{I(n,p)|0 <= p <= 1}
if n >= 2. What is the limit of p*(n) as n goes to infinity. Now suppose the
players get only 1 point for heads and 0 point for tails. Then what is I(n,p) and
what is the limit of p*(n)?
Another interesting probabilistic game by Professor Wilf, al of U of Penn. will
be mentioned. Extensions of these games will be also proposed.
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