Quant Trading Games: Practice Decisions Under Uncertainty

A useful quant trading practice game gives you a decision, enough information to reason about it and a way to review what you did. Winning one round does not prove the decision was good. A favorable bet can lose; an unfavorable one can win.

The original games below train three different choices: whether to buy information, how to recognize shared risk and when to revise a decision after new evidence. They are written exercises you can run with a notebook, cards or a partner, rather than an interactive trading simulator. All money is imaginary and no real bets are needed.

Games have a documented educational connection to trading. Susquehanna describes using poker to teach traders decision making under uncertainty, expected value and pricing risk. That supports the learning connection; it does not establish that every applicant faces a particular hiring game. For interview context, Jane Street's trading overview emphasizes collaborative reasoning and correcting mistakes. These exercises are our own practice designs, not attributed employer questions.

Keep a decision log before revealing outcomes

Use one row for each round:

Write the first five entries before the result is known. Otherwise it is easy to remember your successful choices as more carefully reasoned than they were.

For these exercises, evaluate choices by expected imaginary profit unless a different objective is stated. That simplifying objective lets us calculate clear answers. Bankroll limits and consequences can change what is sensible; positive expected profit alone does not justify unlimited size.

Game 1: Is the information worth buying?

A contract pays either 10 or zero, each with probability one half. You may buy one contract for 5 or decline. There is no resale, borrowing or transaction cost beyond the stated prices. You are risk-neutral.

Before deciding, you can buy a signal for a fee of 1. The signal is “high” or “low.” It is high with probability 0.8 when the payoff is 10, and low with probability 0.8 when the payoff is zero. The signal mechanism and prior probabilities are known.

Your decisions: would you trade without information? Would you buy the signal? What would you do after each signal?

Show answer and explanation

Without information, the expected payoff is 0.5 × 10 = 5. Buying for 5 has expected profit zero; declining also has profit zero.

The high signal has probability 0.5 × 0.8 + 0.5 × 0.2 = 0.5. After a high signal, the probability of payoff 10 is (0.5 × 0.8) / 0.5 = 0.8. Expected payoff becomes 8, so buying at 5 gives expected trading profit 3.

After a low signal, the probability of payoff 10 is 0.2. Expected payoff is 2, so buying at 5 would lose 3 in expectation. Decline.

Before the fee, the signal-based strategy earns 0.5 × 3 + 0.5 × 0 = 1.5 in expectation. Subtract the fee of 1 to obtain 0.5 net expected profit. Under these rules, buy the signal and buy the contract only when the signal is high.

The signal's maximum worthwhile fee is 1.5 relative to the zero-profit alternative. At that fee you are indifferent by expected profit; above it, skip the signal.

The signal improves decisions because you can act differently after learning it. If you had to buy the contract regardless, the same signal would not improve the expected payoff of that fixed action, and its fee would reduce profit.

A low signal does not mean the contract is certain to pay zero. It means buying is unattractive at this price under the stated probability. Practice saying that distinction aloud.

Run repeated rounds

Make four equally likely hidden state cards: two say “payoff 10” and two say “payoff zero.” Shuffle and draw with replacement each round. To generate the signal, use a fair ten-sided die: on results 1–8 report the state correctly; on 9–10 report the other signal. Record the signal fee even when you decline the contract.

A 10-payoff contract bought for 5 earns 5 before the information fee; a zero-payoff contract loses 5 before that fee. A declined trade after buying information still loses the fee of 1. Sum actual net profit separately from the calculated expected profit.

Ten or twenty rounds can demonstrate variability, but they do not guarantee a positive realized result or establish that the stipulated signal accuracy has been measured reliably.

Game 2: Ten bets, or one risk repeated ten times?

You start with an imaginary bankroll of 20. You may choose one of two packages or decline both. Each winning unit gains 1 and each losing unit loses 1. There are no fees and no leverage.

• Package A: ten independent one-unit bets, each with a 60% chance of winning.
• Package B: ten one-unit bets tied to one common outcome, which has a 60% chance of winning. They all win together or lose together.

Compare expected profit, worst possible loss and probability of losing all ten units. Then decide whether expected profit alone settles which package you prefer.

Show answer and explanation

Each unit's expected profit is 0.6 × 1 + 0.4 × (−1) = 0.2. Both packages have expected profit 2.

Both can lose ten units, leaving bankroll 10. But the probability differs:

• Package A loses all ten with probability 0.4¹⁰ = 0.0001048576, about 0.0105%.
• Package B loses all ten with probability 0.4 = 40%.

Package B's profit is either +10 or −10. Package A's profit can take intermediate values because its outcomes are independent.

A risk-neutral decision maker considering only expected profit is indifferent between the packages. Someone who cares about the distribution of losses may prefer A. Equal expectation does not mean equal risk, and ten labels do not create diversification when all positions depend on the same event.

For a repeatable session, generate each independent outcome with a fair ten-sided die: 1–6 wins, 7–10 loses. For B, roll once and apply the result to all ten units. Compare several packages, recording the dependence assumption before each one.

Now change the bankroll to 6 while keeping a rule that losses must always be payable. Both original packages can lose ten, so neither fits. Reducing exposure or declining is necessary even though both had positive expected profit. For formal growth-based sizing, study the separate Kelly criterion explanation; this game is about recognizing common risk, not deriving a sizing formula.

Game 3: Update before the next decision

A bag is chosen at random, equally likely to be A or B. Bag A contains eight red and two blue tokens. Bag B contains two red and eight blue tokens. Draw a token, observe its color and replace it before the next draw. Conditional on the bag, draws are independent.

After each observed token, you may buy one imaginary contract for 6 that pays 10 if the hidden bag is A and zero if it is B. You may decline, but cannot short or resell. Evaluate each new contract separately by expected profit; assume enough bankroll for the exercise. Do not learn the bag until the round ends.

First you observe red. Then you observe blue. What should you do at each stage?

Show answer and explanation

Initially, P(A) = 0.5 and expected contract payoff is 5, below its price of 6.

After red, P(A | red) = (0.5 × 0.8) / (0.5 × 0.8 + 0.5 × 0.2) = 0.8. Expected payoff is 8, giving expected profit 2 on a new purchase. Buy under the stated objective.

After red followed by blue, the sequence likelihood is 0.8 × 0.2 = 0.16 under A and 0.2 × 0.8 = 0.16 under B. The posterior returns to 0.5. A new contract now has expected profit −1, so decline.

A contract bought after the first red remains an existing exposure; declining the second purchase does not cancel the first. Both contracts would settle on the same hidden bag, so buying again would add common risk.

Try red followed by red. The likelihoods are 0.64 under A and 0.04 under B, so P(A | red, red) = 0.64 / 0.68 = 16/17, approximately 94.1%. The new expected payoff is about 9.41. Explain why observing two tokens is different from observing the same token twice without a new draw.

The assumptions matter: removing tokens instead of replacing them changes the second-draw probabilities. If a partner changes that rule, stop using the original likelihoods and rebuild them.

Review the choices you could justify at the time

After each session, identify one arithmetic error, one assumption you left unstated and one decision that remained reasonable despite losing. If there was no example in a category, leave it blank instead of inventing one.

A simple practice rubric awards one point each for defining the action, using the available information, calculating expected payoff correctly, identifying dependence or constraints, and revising the choice when evidence changes. This is a self-review tool, not an employer scoring system. Keep the score separate from profit.

For quoting, inventory and trade selection, continue with the market-making worked drills. For calculation fluency, use the mental-math exercises. If these games reveal a broader preparation gap, a quant consultation can help you discuss your target role and what to work on next.