[Gator]

The answer I know (and there could be a slightly more optimal strategy) is to let 1/2 the numbers get called and then pick as soon as a higher number is read. This leads to success better then 25% of the time. Second highest number in first half 50% - Highest number in second half 50% -- both events occurring (i.e. guaranteed win) 25%. You can pick up some wins even if it doesn't happen just like that so answer is > 25%.