• Communications for Statistical Applications and Methods
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• v.20 no.2
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• pp.157-168
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• 2013

This paper deals with the history of one of the well-known and historically important problems in probability, "Gambler's ruin". This problem was first solved by Pascal and Fermat and published by Huygens in 1657. It was studied and extended by many probabilists in early years and thus, it became an important problem in probability history, introducing many new concepts. We would like to introduce the problem in detail to readers and share the ideas on how new problems are developed, relating to old problems.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.185-193
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• 1996

In this paper we consider the gambler's ruin problem with N players and derive the formula for computing the expected ruin time when the initial fortunes of all N players are the same. And we present an example for the case of N = 5.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.147-151
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• 2001

In discrete red and black, you can stake any amount s in your possession, but the value of s takes positive integer value. Suppose your goal is N and your current fortune is f, with 0$\frac{1}{2}$ where the house has the advantage over the player, and with the value of p greater than $\frac{1}{2}$ where the player has the advantage over the house. The optimum strategy at any f when p<$\frac{1}{2}$ is to play boldly, which is to bet as much as you can. The optimum strategy when p>$\frac{1}{2}$ is to bet 1 all the time.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.475-480
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• 2000

In a game called red and black, you can stake any amount is in your possession. Suppose your goal is 1 and your current fortune is $f$, with 0$p$ and lose your stake with probability, $q$=1-$p$. In this paper, we consider optimum strategies for this game with the value of $p$ less than $^1/_2$ where the house has the advantage over the player, and with the value of $p$ greater than $^1/_2$ where the player has the advantage over the house. The optimum strategy at any $f$ when $p$<$^1/_2$ is to play boldly, which is to bet as much as you can. The optimum strategy when $p$>$^1/_2$ is to bet $f\cdot\alpha$with $\alpha$, a sufficiently small number between 0 and 1.