> if Alice picks 10 and 20 and opens 10 first then you have a 0% chance of winning.
No because you pick the hand (i.e. it’s essentually random), so you still have 50% chance of first revealing 20 and gettingit right.
No because you pick the hand (i.e. it’s essentually random), so you still have 50% chance of first revealing 20 and gettingit right.
Choosing zero as a threshold deterministically does not work for all choices that Alice can make because, as you say, for some choices such as (10,20) it gives you exactly 50% chance to win. But as long as there is always a non-zero chance that you chose a threshold between Alice's numbers, then there is a > 50% chance that you win the game.