# The "truel"

**Discrete Mathematics**Level 3

Smith, Jones & Brown are fighting a three-person duel. Smith is a sure shot, killing 100% of the time. Jones kills with an 80% accuracy rate, and Brown a mere 50%. Each of them in turn gets one shot at a time, and they roll a 6-sided die to see who goes first, with each of them having a 1/3 chance of winning (and then roll again to see who goes second, with the two remaining contestants each having half a chance.)

Assuming they all use the best strategy, who has the best chance of winning the truel?

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