What got me thinking about this is I remember reading somewhere that there was a high-school (I think) football coach in the US that always went for it on 4th down, every game, all season, they had a fantastic record.
I think there are some statistical anomalies in sports/games that are being underutilized. For instance, the guy who won so much money on Je0pordy obviously had a really good grasp of his likelihood of getting a question right, and so optimized/maximized his return by betting aggressively.
Also, statistically I believe the best aiming point in a shootout in soccer is to aim straight at the goalie. It probably plays to the risk of a goalie looking silly if they just stand there in the middle and don't even try to dive/guess one side or the other, so they do that, leaving the center shot as the most likely to score.
Interesting stuff for me.