Pick the highest card, the secretary problem
Asked at Jane Street
A shuffled deck of distinct-valued cards is revealed one at a time. After seeing each card you must immediately either take it (ending the game) or reject it forever and move on. If you reach the last card you must take it. You win only if the card you take is the single highest in the deck.
What is your strategy, and what is your probability of winning?
Show a hint
You can only judge a card by whether it beats everything seen so far. A good policy first samples to learn the scale, then pounces. Where's the cutoff?
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.