2 ms·
> 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 h
by tomp 9y ago
> 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.
- OscarCunningham 9y agoGood point. So our methods are similar, but yours puts the randomness in the choice of hand rather than the choice of integer. But in the (10,20) case your method gets exactly 50% and not more than 50%.
- deleted 9y ago[deleted]
- sirclueless 9y agoThis is why your choice of threshold matters. Your strategy should be to choose a threshold randomly from any distribution that is non-zero everywhere (such as a normal distribution), then choose a hand uniformly at random. 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.