PRACTICE GUIDE HRT
HRT Probability & Estimation Practice Test
Hudson River Trading does not publish the shape of its probability & estimation screen, and candidates describe it as 10 to 20 questions in 15 to 45 minutes, roughly one to three minutes per question, answered by picking one of the options.
Those are ranges across firms running this format rather than Hudson River Trading's own figures, so treat them as the shape to train against and check the instruction screen on the day for the marking rule.
Outcry is not affiliated with Hudson River Trading and has no access to their assessment content. This guide describes an assessment format that candidates report publicly; the questions here are generated by Outcry and are not Hudson River Trading’s own.
What it screens
An automated trading firm known for research-driven strategies and a heavy C++ and algorithms bar.
- ✓Expected value computed fast and used to make a decision
- ✓Conditional probability and Bayes updates without formal notation
- ✓Ranking likelihoods rather than computing them exactly
- ✓Fermi estimation: decomposing an impossible question into three easy ones
Where it sits at Hudson River Trading
An automated trading firm known for research-driven strategies and a heavy C++ and algorithms bar. What that means for the screen is that the questions tend to be drawn from the work rather than from a textbook, so the format below is the shape to train against rather than a syllabus.
Candidates also report 2 other screens at Hudson River Trading, covered separately on this site. Where a firm runs several, they usually sit in one round rather than spread across the process, so the pacing of the whole set matters more than any single section.
The format
Hudson River Trading does not publish this screen's shape, and it varies between firms, so these are the ranges candidates report rather than exact figures.
| Questions | 10 to 20 |
|---|---|
| Time | 15 to 45 minutes |
| Per question | one to three minutes |
| Negative marking | Varies by firm and year |
| Answer style | Multiple choice or a typed number |
| Where it sits | First round, or a second technical screen |
What it tests, with a worked example
Every example below is generated by Outcry, drawn from the same question generators the timed drills run. None of them is Hudson River Trading’s.
Conditional probability
Bayes' rule in disguise: a test result, a signal, a drawn card, and what it implies.
Example
Roll a fair die until every face has appeared at least once. What is the expected number of rolls?
Answer 14.7
Coupon collector: 6·(1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6) = 14.7.
Estimation under uncertainty
A number nobody knows exactly, reasoned to the right order of magnitude out loud.
Example
A balance reports which of two groups is heavier, or that they match. Exactly one bar in a batch is heavier than the rest. With 4 weighings and worst-case luck, what is the largest batch you can guarantee to pin down?
Answer 81
Counting outcomes: 4 weighings produce 3^4 = 81 distinguishable results, and each result can name at most one bar. The bound is met by thirds - weigh 27 against 27 and whichever way it falls you are left with 27 candidates and 3 weighings.
Ranking outcomes
Ordering several events by likelihood, where only the exact order scores.
Example
A non-dividend-paying share trades at $43.73 and the 9-month funding rate is 2.76% continuously compounded. The 9-month forward on 250 shares is quoted at $44.25. What is the trade?
- Buy the forward, short the shares and lend the proceeds: $98.66 at delivery
- Nothing, the difference between $44.25 and $43.73 is just the cost of carry
- Buy the forward, short the shares and lend the proceeds: $130.00 at delivery
- Buy the forward, short the shares and lend the proceeds: $96.64 at delivery
- Sell the forward, buy the shares with borrowed cash: $98.66 at delivery
Answer Buy the forward, short the shares and lend the proceeds: $98.66 at delivery
The fair forward is the spot carried to delivery: F = $43.73 x e^(0.0276 x 0.7500) = $43.73 x 1.020916 = $44.6446. The quote is $44.25, so the forward is cheap by $0.3946 a share. Buy the forward, short the stock at $43.73 and lend the proceeds: the deposit grows to $44.6446, the forward takes $44.25 of it, and the difference is kept. On 250 shares that is $98.66 at delivery. The gap between the forward and the SPOT, $0.52, is mostly carry and is not the edge. $96.64 is that edge discounted back to today, which is what it is worth now rather than at delivery.
Waiting times and repeated trials
How long until the first success, and why the answer is rarely the average you expected.
Example
An index rises 2.3% on 5 days and falls 2.3% on 5 other days. What is the net change over the 10 days, as a percentage?
Answer -0.26
Each up-down pair multiplies to 1 − 2.3%² = 1 − 0.05%. With 5 pairs the drag is about −5 × 0.05% = -0.26%.
Symmetry arguments
Questions that collapse to one line once you notice the two cases are mirror images.
Example
A fair coin is flipped 4 times. What is the chance every flip is heads, as a percentage?
Answer 6.25
(1/2)^4 = 1/16 = 0.063, or 6.25%.
Reading the question exactly
At least, exactly, and given that - the three phrases that change the answer entirely.
Example
A puts in 3,000 for 4 months and B puts in 13,000 for 9 months. They clear 33,000 of profit. What is A's share?
- 16,500
- 10,153.85
- 6,187.5
- 3,069.77
Answer 3,069.77
Profit follows capital multiplied by time. A contributes 3,000 x 4 = 12,000 and B contributes 13,000 x 9 = 117,000, so A takes 12,000 / 129,000 of 33,000 = 3,069.77.
What a good score looks like
Probability rounds are usually marked as part of a wider battery, so a standalone threshold is rarely reported. Where candidates do describe one it clusters around getting two thirds of the items right, with the caveat that these sections are short enough that two mistakes move you a long way.
How to train for it
- 01Work the standard results until they are recall, not derivation: complement, conditional, binomial mean and variance, geometric expectation.
- 02Do them timed. A probability question you can solve in four minutes and the paper gives you ninety seconds for is a question you cannot solve.
- 03Sanity-check the magnitude before committing. A probability above one or an expectation outside the range of outcomes is a caught error, and these papers plant both as options.
TRAIN IT HERE
The drills that match each section
Likelihood Ranking
Order events from most to least likely - the exact screen-question format.
Fermi Estimation
Piano tuners in Chicago, atoms in a body - scored on order of magnitude.
Quitters Never Lose
A casino stopping-strategy game that is secretly a martingale lesson.
Tail Risk
Rare events and fat tails, and what they do to a plain expected-value estimate.
SIT THE FULL BATTERY
All the sections back to back on one clock, marked the way the real screen marks them, with a by-skill breakdown at the end. Included with any pass.
Also reported at Hudson River Trading
Common questions
- Is the HRT probability & estimation test multiple choice?
- Reported as multiple choice or a typed number. Formats move, so treat this as the shape rather than a guarantee.
- How long is the HRT probability & estimation test?
- Candidates report 10 to 20 questions in 15 to 45 minutes, roughly one to three minutes per question.
- Is there negative marking on the HRT probability & estimation test?
- It varies by firm and by year. Where a paper does mark negatively, skipping beats guessing; where it does not, answer everything. Check the instruction screen before you start - it is always stated there.
- How do I practise for it free?
- Every drill linked on this page is free to play, with no account, inside a daily run cap. Questions are generated fresh each run, so there is nothing to memorise between attempts.