How Five Rings's process runs, as candidates and the firm describe it, and the questions candidates report, each with a worked solution. Free, no sign-up.
Reported online assessment of about 19 maths questions where close approximations are accepted.
Technical interviews are described as very probability-heavy, with an expectation that you explain exactly how you reached each answer. Game theory comes up.
Try each one before opening the solution. Interviewers change the numbers, so learn the method.
Quantitative Trader · Technical · Game theory · reported by a candidate
A two-card poker game: you're dealt an ace or a queen at random, and only you see it. Each player has put $1 in the pot. You may raise $1 or check (checking goes straight to showdown, where the ace wins). If you raise, your opponent can call $1 or fold. Your opponent knows your strategy.
The reported wording is ambiguous about the deal. This is the standard version of the game it describes, the classic bluffing model.
(a) With an ace you always raise. With a queen, what bluffing frequency q makes your opponent indifferent between calling and folding?
Answer and worked solution
Answer: 1/3 ≈ 0.33333
Key idea. At equilibrium your bluffing frequency makes the opponent indifferent between calling and folding.
You raise every ace and a fraction q of queens. A raise is a bluff with probability q/(1 + q).
Calling wins $2 against a bluff and loses $2 against an ace; folding loses the $1 ante.
Indifference: 2·q/(1 + q) − 2·1/(1 + q) = −1.
Multiply by (1 + q): 2q − 2 = −1 − q, so 3q = 1, q = 1/3.
Check. Bluffs are 1/4 of your raises. Relative to folding, calling gains $3 against a bluff and loses $1 against an ace, so it breaks even exactly when a quarter of raises are bluffs.
(b) How often should your opponent call to make your bluff break even?
Answer and worked solution
Answer: 2/3 ≈ 0.66667
Key idea. Now make yourself indifferent, with a queen, between bluffing and checking.
Checking a queen goes to showdown and loses $1.
Bluffing: +$1 if they fold (prob 1 − c), −$2 if they call (prob c): (1 − c) − 2c.
Set 1 − 3c = −1: c = 2/3.
Check. If they called less, bluffing would be profitable; more, and you'd stop bluffing.
(c) What is the game worth to you per hand?
Answer and worked solution
Answer: 1/3 ≈ 0.33333
Key idea. Average over the card you're dealt, using the equilibrium strategies.
Ace: you raise; they call 2/3 (+$2) or fold 1/3 (+$1): (2/3)·2 + (1/3)·1 = 5/3.
Queen: you're indifferent, so value it as checking: −$1.
Game value = ½(5/3) + ½(−1) = ½ × 2/3 = $1/3 per hand.
Check. Positive, because you have information they don't, and you use it with correctly mixed bluffs.
Interviewers may push further: What changes if the raise size is $2?
Trader · Interview · Behavioural · reported by a candidate
Behavioural questions candidates report:
Why Five Rings, and why quantitative trading?
Answer one out loud, as you would in the interview.
Model answer
Three parts, about a minute each. Why trading: a specific moment you got hooked (a game, a market you followed, a decision under uncertainty), not "I like maths". Why this firm: something concrete about how it trades or trains people, ideally from talking to someone there or from its own material. Why you: evidence you already think in probabilities and react well to being wrong. Avoid anything about money or prestige.