臺灣博碩士論文加值系統

甲、乙兩人進行一場賽局，每局輸的人要給贏的人一塊錢，賽局持續進行到某人輸光所有的錢為止。本文設定甲每局的勝率函數是隨著甲當時的賭金遞增且對稱於兩人總賭金的一半，我們先求出甲贏得總賭金的機率，接著研究不同的勝率函數如何影響甲贏得總賭金的機率以及賽局結束時所需局數的期望值與變異數。

Abstract
Two people A and B play a game. In each play, the loser must pay a dollar to the winner. The game goes on until one of the players is ruined. In this study, we set the win probability function of each play to be increasing with A’s present amount of money and symmetric about the half of two people’s total amount of money. We first get the
probability of A winning the total amount of money, and then we study the effect of win probability function on the probability of A winning the total amount of money, and
mean and variance of the number of plays required to finish the game.

1. 前言\ 1
2. 贏得總賭金的機率\ 6
2.1 贏得總賭金機率的推導\ 6
2.2 贏得總賭金的機率比較\ 8
3. 局數的期望值比較\ 18
4. 局數的變異數比較\ 22
5. 參考文獻\ 26

Gunnar Blom, Lars Holst and Dennis Sandell (1994).
Problems and Snapshots from the World of Probability.
Springr-Verlag, New York.

Sheldon Ross (1940).
A First Course in Probability. Pearson Education
International.