Which card is bigger?
An adversary writes two different real numbers on two cards, face down, choosing them however she likes. You pick a card at random, turn it over, look at the number, and then must announce whether it is the larger of the two. You win if you are right.
Guessing blindly wins exactly half the time.
Is there a strategy that wins with probability strictly greater than one half, whatever numbers the adversary chose?
Show a hint
Before looking, generate a random number T from a distribution that can take any real value (for example a normal distribution). Compare the number you see with T.
Your answer
Solving needs a free account
Answers, streaks and solutions unlock when you are signed in. Reading the question and the hint stays free.
Discussion
💡 Discussion rules
- No full solutions here. Hints and approaches only.
- Complexity, edge cases and intuition are the point.
- Interview experiences are welcome. Respect your NDAs.
Loading discussion…
Learn the concepts
The theory behind this question.