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$\begingroup$ "If we exclude strategies that involve saying "largest" or "smallest" at random (which cannot exceed 50% win rate)" - why not? A mixed strategy could be better than a pure strategy. $\endgroup$
– Deusovi ♦
Commented Jul 3 at 13:34
$\begingroup$ You're right. I think I took the problem the wrong way by trying to figure out Bndrew's best strategy and not Andrew's best strategy (which I end up doing in the last paragraph). @ralphmerridew just posted an answer that is less confused and way more concise; I encourage upvoting his answer :) $\endgroup$
– Jujustum
Commented Jul 3 at 14:07
1

$\begingroup$ @Deusovi : Sure, a mixed strategy can be better, but is it always implicit that mixed strategies are allowed? Having access to a random coin that is independent of the given numbers seems like a nontrivial advantage. $\endgroup$
– Plop
Commented Jul 4 at 8:02

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