Recently experienced a Jane Street I have to say that this company really lives up to its name. The interviews are not traditional coding interviews, but a collection of probability, expectation, game theory, and auction modeling. The whole process is like doing a high-intensity intellectual game. I'd like to share my questions and thoughts for those who are preparing for quant/trading firms.
Jane Street Interview Process
| Rounds | Field of investigation | Examples of questions | Focus |
|---|---|---|---|
| Round 1 Probability + Basic questions | Probability theory, expectations, combinatorial counting | – 刷墙效率计算 – 硬币投掷期望 – 骰子和 payoff – 熊抓鱼概率 | Basic Math Intuition + Rapid Reasoning |
| Round 2 Game Theory & Strategy Questions | Nash Equilibrium, rational man game, information asymmetry | – 100 元盒子游戏 – 多轮对手固定策略 – 信息价值计算 – 硬币序列博弈 | Strategic Analysis + Modeling Capabilities |
| Round 3 Auction / Market Simulation | Bidding mechanisms, market equilibrium, first/last hand analysis | – 双骰子 auction – EV(先手) vs EV(后手) | Market Intuition + Gaming Strategy |
Jane Street Interview Questions
1 wheel
- A takes 1 hour to paint the wall, B takes 2 hours to paint the wall, how long does it take A and B to paint the wall together?
- Toss 4 coins and the probability of at least two heads.
- Toss 4 coins, one heads is worth $1. After observing the first result, you can either accept the result or toss all the coins a second time. After observing the first result, you can either accept the result or toss all the coins a second time, after the second time you must accept your payoff. ask what your strategy was and how much the expected payoff was.
- 一个骰子 1 – 6，一个骰子 1 – 10，猜两个骰子之和，如果猜中了就可以得到这个和所对应的 payoff，猜多少可以获得最大 expected payoff。
4.1. Follow – up：如果说一个骰子 1 – 20，一个骰子 1 – 30 呢？ - 4 coins flipped two at a time, final expectation (3.5)
- A bear is satiated by eating 3 fish and the probability of catching each fish is 1/2, ask the probability that the fifth fish survives (11/32)
2 rounds
- A box has $100 in it, and your opponent is the rational man. You and your opponent both write numbers on a piece of paper, and if the sum of the numbers 100, you get nothing. Ask what your optimal strategy is.
- Now don't assume your opponent is a rational person. Play the same game 1000 times. The first time, your opponent says he's going to play 80. What do you do?
2.1. Follow – up：（因为我当时问是不是该出 20 所以才有这个 follow – up）如果游戏进行了十次，他每次都出 80，你又会如何权衡？ - Assume again that your opponent is the rational man and will play the game only once, but now there are 10 boxes. 5 boxes contain $40 and 5 boxes contain $50, and then you both have to write 10 numbers for each of the 10 boxes, with the payoff for each box determined in the same way as in the first question. What is your optimal strategy?
3 – 1 假设你购买了一些信息，知道了所有盒子分别装了多少钱。你的对手不知道这些信息，并且不知道你知道这些信息，这时候你的最优策略是什么？你最多愿意出价多少购买这些信息？（50）
3 – 2 每个盒子 20 或 100 呢？（0） - 一直扔硬币（正面概率 2/3，背面 1/3），你先说一个二元序列（HH，HT 等），对手在你之后说。序列先被投出者谁赢，胜 10 元负 – 10 元，你会参加游戏吗？（不会，最大胜率 4/9）
3 rounds
有一个拍卖，有两枚均匀 1 – 6 骰子，抛完后两枚骰子朝上数字之和为 contract 的价值。你和另一个人轮流 bid，先手顺序随机。只能 bid 整数。你可以看到第一个骰子的数字，你对手可以看到第二个骰子的数字。
Optimal strategy: the first person bids 2, then everyone takes turns bidding up + 1. The upper limit on everyone's bids is that if you see a number X, then you can only bid up to 2X, otherwise you will lose money.
EV of going first than second = 5/12, the key to the calculation is to understand that according to the strategy above you can only win if your number is bigger than your opponent.
VO hard? There are people who can help you steady the pace
Jane Street's VO interviews are really testing! The pace was fast and furious, and it was easy to get sidetracked by the follow-up questions if you weren't careful. Good thing I have Programhelp The assistance of the seniors, the whole process to help me run through the logic, simulation of high-pressure scenarios, but also in the key points to remind me, really is a lifesaver ~ If you are also going to face the VO, highly recommended to find them to practice!
