Compute asymptotic of optimal strategy as tends to infinity


The convict has 2 possible escape routes - main highway and forest - and pursuing sherif F can cover only one of them. If sherif F and convict take different routes, escape is sure; if both take highway route, convict will certainly be caught. If both go through forest, probability of escape is 1 - 1/n where n is integer. Determine optimal mixed strategy for sherif F and  convict. Determine asymptotic of optimal strategy as n tends to infinity. Prove that if either party follows optimal strategy convict will escape with probability n/(n+ 1) independent of strategy of other party.

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Mathematics: Compute asymptotic of optimal strategy as tends to infinity
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