Radio Astronomy Systems Research Group

Here is a strategy that guarantees a 50/50 chance of winning:

Flip over any card, and note the number. Reject that card.

Flip over another card. If this second number is smaller than the first, it cannot be the largest so you declare the third to be the largest. If this second number is larger than the first, you declare it (the second number) to be the largest.

Here is the Win/Loss breakdown using this method: (assume the numbers are simply 1, 2, and 3)