Practice · Quant prep · Five Rings
Five Rings interview
Five Rings publishes almost nothing about its interviews, but candidate accounts agree closely. The first conversation is a rapid screen, and most people are cut there.
The process, from Five Rings's own pages
- Offices. New York, Boca Raton, London and Amsterdam, trading in a wide range of markets. Source
- What the role involves. Traders run strategies in live markets, tune model parameters to conditions, and feed what the market does back into their models, working with senior traders from the start. Source
- Who they want. Quantitatively focused, quick to learn, intellectually curious, detail-oriented and self-starting. Source
What candidates report
Candidate accounts describe the same sequence. A recruiter call opens with a few minutes on why trading and why the firm, then about ten to twenty rapid questions with 15 to 30 seconds each: mental arithmetic and estimates. Next come two or three video interviews with traders on probability, expected value and game theory, where a question is usually followed by a twist and then a generalisation. Some candidates describe a dice or betting game played live, then a final round. Several say accuracy counted for more than speed on the first call.
What Five Rings is testing
The screen tests estimation as much as arithmetic: roots, powers and quantities you can reason your way to. The useful habit is anchoring on something you know, such as 2¹⁰ ≈ 10³ or the population of a city, and adjusting from there, out loud.
The trader rounds test whether you account for future decisions, not only the next step. Candidates mention games where you choose when to stop, and the right answer depends on the value of the options you keep by continuing. The problems below include two of that kind.
Six practice problems
Written by us to match the types Five Rings is publicly reported to ask. None is a copy of a Five Rings question.
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Estimate 10^0.3 to two decimal places.
Show the answer
About 2.00 (exactly 1.995…)
2¹⁰ = 1024 ≈ 10³, so 2 ≈ 10^0.3 almost exactly. log₁₀ 2 = 0.301, which puts 10^0.3 at 1.995. Knowing log₁₀ 2 and log₁₀ 3 ≈ 0.477 turns a whole class of root and power questions into mental arithmetic.
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Roughly how many litres of water does an Olympic swimming pool hold?
Show the answer
About 2.5 million
An Olympic pool is 50 m by 25 m, and at least 2 m deep: 2,500 m³. A cubic metre is 1,000 litres, so about 2.5 million litres. State each assumption as you make it; the interviewer cares about the chain as much as the number.
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A deck holds 2 red and 2 black cards, shuffled. You turn cards over one at a time; each red pays you £1 and each black costs you £1. You may stop whenever you like. What is the game worth with the best strategy?
Show the answer
£2/3
Work backwards, valuing each position by the better of stopping (0) and drawing. One red, one black left: drawing gives ½(1) + ½(−1 + 1) = ½, because after a black the last red pays you back. One red, two black: ⅓(1) + ⅔(−1 + ½) = 0, so stop. Two red, one black: ⅔(1 + ½) + ⅓(−1 + 2) = 4/3. Full deck: ½(1 + 0) + ½(−1 + 4/3) = ⅔. The deck is fair on average, and the option to stop is what makes it worth ⅔.
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You roll one die and I roll two dice and keep the higher. The higher number wins, and ties are rolled again. What is my probability of winning?
Show the answer
25/36 ≈ 0.69
Of the 216 equally likely outcomes, my higher die beats your die in 125 and ties it in 36. Ties are replayed, so my chance is 125/(216 − 36) = 125/180 = 25/36.
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A walker starts at 0 and each second steps +1 or −1 with equal probability. What is the expected number of seconds until it first reaches +5 or −5?
Show the answer
25
For a fair walk started at 0, the expected time to leave the interval (−a, b) is a × b, here 5 × 5 = 25. The identity comes from the martingale X² − t: at the exit time, E[X²] = 25 equals the expected time.
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An integer is chosen uniformly from 1 to 1000. What is the probability it is divisible by 2, 3 or 5?
Show the answer
0.734
Inclusion–exclusion: 500 + 333 + 200 − 166 − 100 − 66 + 33 = 734 multiples, so 0.734. Equivalently, 1 minus the chance of avoiding all three, about (1/2)(2/3)(4/5) = 0.267.
Practise under time
How to prepare for Five Rings
Drill the rapid screen until 20 seconds a question feels unhurried, and learn the handful of logarithms and powers that make estimates quick. For the trader rounds, practise stop-or-continue games by working backwards from the end, and say your reasoning as you go: the rounds are built so that the question changes under you.
Have a Five Rings screen booked? The assessment hour runs you through the rapid format and tells you honestly whether you would pass it today. The assessment hour.