You play a 100-round game: each round you can either roll a fair 20-sided die (uniform 1 to 20) or “lock in” the current face and collect that same reward for all remaining rounds. You must roll in the first round. What is your optimal stopping / locking strategy and expected value?
Calculate the optimal strategy for heads and tails game
You are playing a game where you flip a coin 5 times. You win if three heads come up in the 5 coin tosses. You lose if three tails come up in the 5 coin tosses. If you win you get £1. If you lose you lose £1. Before each flip you can choose to either double the stakes from their previous value (if you win you get £2n and if you lose you lose £2n where n is the amount you get if you win beforehand) or keep them the same. Are you willing to pay £0.50 to play this game?
Technical Coding Interview: "A trader asks you for the three largest trades made today. How would you find this information? What about the k-largest trades? How can you make this process more efficient?"
Expected value of a game
Give the top 3 numbers from a list without using any helper functions and algorithm. Preferably in one iteration.
Probability sort of type questions
Questions about probability and games, often involving betting
Expected number of throws until you get 2 consecutive heads. Expected number of throws until you get "n" consecutive heads.
Some basic probability questions and brain teasers.
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