Gambler’s Ruin Model and Ga

Gambler’s Ruin with Catastrophes and Windfalls

We compute ruin probabilities, in both infinite-time and finite-time, for a Gambler’s Ruin problem with both catastrophes and windfalls in addition to the customary win/loss probabilities. For constant transition probabilities, the infinite-time ruin probabilities are derived using difference equations. Finite-time ruin probabilities of a system having constant win/loss probabilities and variab...

Optimal Sampling and Speed-Up for Genetic Algorithms on the Sampled OneMax Problem

This paper investigates the optimal sampling and the speed-up obtained through sampling for the sampled OneMax problem. Theoretical and experimental analyses are given for three different population-sizing models: the decision-making model, the gambler’s ruin model, and the fixed population-sizing model. The results suggest that, when the desired solution quality is fixed to a high value, the d...

Change-point detection of two-sided alternatives in the Brownian motion model and its connection to the gambler’s ruin problem with relative wealth perception

Gambler’s Ruin Problem with Relative Wealth Perception

We consider a modified version of Gambler’s Ruin Problem in which the gambler decides to quit based on the relative change of his or her wealth. For this purpose we consider two possible changes of wealth, namely the upward rally and the downward fall. We define upward rally as the difference of the current wealth and its historical minimum, while the downward fall is the difference of the hist...

Re-seeding invalidates tests of random number generators

Kim et al (Appl Math & Comput 199 (2008) 195) recently presented a test of random number generators based on the gambler’s ruin problem and concluded that several generators, including the widely used Mersenne Twister, have hidden defects. We show here that the test by Kim et al suffers from a subtle, but consequential error: Re-seeding the pseudorandom number generator with a fixed seed for ea...