In this paper, we derive the result of the classical gambler's ruin problem using elementary linear algebra. Moreover, the pedagogical advantage of the derivation is briefly discussed.

The assessment of knowledge and learning progress in the context of game-based learning requires novel, noninvasive, and embedded approaches. In the present paper, we introduce a mathematical framework which relates the (problem solution) behavior of a learner in the game context to the learner's available and lacking competencies. We argue that a…

This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.