Optiver Interview Questions

Evaluate: (5/16) divided by (12/3).

If a fair coin is flipped until the first heads appears, what is the expected number of flips?

It is 9-9 in a squash match. If I have a 30% chance to win any given point, what is the probability that I win the game?

What is the result of 2/5 + 11/4?

What are the first 5 decimal digits in the decimal expansion of 1/13?

What is the square root of 30,000 (calculated mentally)?

Given $100 to bet and the probabilities of each of 4 teams winning a bracket, how would you allocate your bet to maximize your expected return?

What is the expected value of a card drawn at random from a standard deck of cards, where J=11, Q=12, K=13? Then, what would this expected value become if the value of all hearts cards is doubled?

You start a tennis game at a score of 30-30. You have a probability of 0.6 of winning each point. What is the probability that you win the game?

What is the expected value of a single six-sided dice roll if you are allowed to re-roll once, and keep the higher number from the two rolls?

What is the value of 3/6 + 7/4?

If the probability of a truck arriving in 10 minutes is 0.36, what is the probability that it arrives in 5 minutes?

What is the formula to calculate the angle between the hour and minute hands of a clock at a given time?

There are 25 horses and you want to identify the fastest 3 horses. You can race up to 5 horses at a time, and you do not have a watch to time the races. What is the minimum number of races needed to accomplish this?

You have 3 cards, each labeled with consecutive integers n, n+1, and n+2, where n is unknown. All cards are placed face down. On your turn, you flip one card. After seeing its value, you can either 'stay' and keep that value, or 'flip' another card. If you choose to flip another card, you can again choose to 'stay' and keep that value, or flip the final card and keep its value. Design the optimal strategy for maximizing your expected value.

Calculate the square roots of the following numbers: 600, 6000, 60000, and 24000.

Given $1, $5, $20, and $100 dollar bills, what is the fewest number of bills needed to form amounts ranging from $1 to $100? For example, $4 would require four $1 bills. Bills can be reused, so the number is not cumulative. What is the minimum number of bills you must have to always provide exact change for both a transaction of $x and $(100-x), where x < 100?

What is the smallest multiple of 77 that is greater than 70,000? What about 700,000?

Find the largest 5-digit number such that the pairwise digit sums of its digits are all unique. Find the smallest 5-digit number with the same property. Explain why this property does not work for 7-digit numbers. Does it work for 6-digit numbers?

What happens to the gamma of your position if you are short a straddle?

What is the next number in the sequence: 1/2, 1/3, 1/6, 1/18, 1/108, ...?

Let's play a game where we roll a die, and you receive a dollar amount equal to the number rolled. If you don't like the result, you may re-roll once and receive that result instead. How much would you pay to play this game?

Assign A=1, B=2, ..., Z=26. Find an eight-letter English word such that the sum of the letter values is less than 50.

How many levels can you build with 52 cards (a standard deck of cards)? What is the expected value (EV) of throwing a single die, and the EV of the sum of two dice rolled once and rolled 400 times? How would you create a market based on these expected values?

What is the value of (3/21) divided by (1/7)?

What are the six inputs in an equity option pricing model?

If I roll a die and add each result to a running total, which die face value am I most likely to roll on the final roll that brings the running total to at least 1000?

Suppose you flip 100 fair coins. What is the expected number of heads? What is the probability that exactly this many heads appear? What is the standard deviation of the number of heads?

What is the result of dividing 335 by 7?

Approximate the probability of getting exactly 50 heads in 100 tosses of a fair coin, not as a combinatorial expression, but as a percentage or a simplified fraction.