If the pursuer's bridge selection is causally independent of the fugitive's die roll, the mixed strategy provides no consequentialist justification superior to any pure strategy yielding equal expected utility.

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causally independent(describing the relationship between the pursuer's choice and the fugitive's die roll): When two things happen completely separately from each other, so one thing has no effect on whether the other happens.
consequentialism(Applied to terrorism and legal punishment): The view that practices are judged solely by their consequences, such that a practice is wrong only if it has bad consequences on balance.
expected utility(Cited as a domain where aggregated probabilities play a key role): A calculation that aggregates probability-weighted outcomes to determine the overall value of a decision
mixed strategy(The uniform three-way randomization over bridges is the mixed strategy under analysis.): A strategy in which a player assigns probabilities over available actions and randomizes according to that distribution.

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