We consider a one-dimensional version of the board game RISK and discuss the problem of how a defending player might choose to distribute his armies along a chain of territories in order to maximize the probability of survival. In particular, we analyze a Markov chain model of this situation and run computer simulations in order to make conjectures as to the optimal strategies. The latter sections of the paper analyze this strategy rigorously and use results on recurrence relations and probability theory in order to prove a related result.
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Glass, Darren and Todd Neller. "Optimal Defensive Strategies in One-Dimensional RISK." Mathematics Magazine 88.3 (June 2015), 217-230.
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Original version is available from the publisher at: http://www.maa.org/press/periodicals/mathematics-magazine/mathematics-magazine-june-2015