For some reason, you must enter an even wager for $1 — win or lose — on one of two outcomes, but there’s a twist: Instead of a fifty-fifty choice like a coin toss, or picking 1-3 or 4-6, this one is pretty easy. Using a fair die (not crooked or “funny” in any way), you can bet that it will show 1,2,3, or 4 on the one hand, or you can bet that it will show 5 or 6 on the other. Those are your choices — 1-4, or 5-6. You know that if you had to do this a hundred times, you would come out money ahead by standing on 1-4, as this will win two times of three.
However, you only have one swing at this. Probably you will still choose 1-4. If you disagree, please let me know why. Assuming that you choose 1-4, there are only two outcomes. Obviously if you win with 1-4, you have chosen correctly. However, if you lose, because in your only throw, the die came up 5-6 — were you wrong?