Mavensecurities·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Quant interview at Mavensecurities with a probability and expected value problem centered on a horse racing betting scenario. Pretty clean problem once you settle into the math, but the setup has a few wrinkles worth thinking through carefully.

Questions Asked (1)

A 5-horse race where each horse is equally likely to finish in any position. You're given five options: bet $10 on the exact order of all 5 horses for a $1000 payoff, bet $20 on the exact top-4 order for $1000, bet $30 on the exact top-3 order for $1000, bet $60 on the exact top-2 order for $1000, or just walk away and keep $10. Which option has the highest expected value?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I jumped straight to computing probabilities and almost forgot to subtract the cost of the bet from each EV calculation, which would've tanked my answer.

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AI HintsAI Generated

Suggested Approach

Start by clarifying that 'expected value' means the average net gain per bet, then compute the probability of each outcome (exact order of 5, top 4, top 3, top 2) assuming all permutations are equally likely. For each option, calculate EV = (probability × payoff) − cost, and compare the results to determine which has the highest EV. Also consider the 'walk away' option as a baseline with EV = $0 net gain (or $10 kept).

Pro tip: Don't just compute the EVs—also mention the variance and risk profile, because a high EV with tiny probability might not be practical. Showing that you consider both expected value and risk demonstrates maturity in decision-making.

1. Clarify the problem and assumptions

Confirm that each horse is equally likely to finish in any position, meaning all 5! = 120 permutations are equally likely. Define expected value as the average net profit (payoff minus cost) per bet.

2. Compute probabilities for each bet

Calculate the probability of correctly predicting the exact order of all 5 horses (1/120), the top 4 order (1/(5×4×3×2) = 1/120? Wait, top 4 order: number of ways to choose and order top 4 from 5 is P(5,4) = 5! / 1! = 120, so probability = 1/120? Actually, careful: The top 4 order means the exact order of the first 4 finishers, but the 5th horse can be any of the remaining. So number of possible top-4 sequences is 5×4×3×2 = 120, so probability = 1/120. Similarly, top 3: 5×4×3 = 60, probability = 1/60. Top 2: 5×4 = 20, probability = 1/20. Exact order of all 5: 5! = 120, probability = 1/120.

3. Calculate expected net value for each option

For each bet, compute EV = (probability × $1000) − cost. For walking away, EV = $0 net gain (or $10 kept, but since the $10 is already yours, net EV = $0). Compare the EVs.

4. Compare and select the highest EV

Identify which option yields the highest expected net gain. If there's a tie, consider other factors like risk or probability of winning.

5. Discuss risk and practical considerations

Mention that high EV with very low probability may not be desirable, and that the 'walk away' option has zero risk. This shows awareness of risk-return trade-offs.

Key Points to Mention

All permutations are equally likely, so probability = 1 / (number of possible ordered outcomes).
For exact top-k order, number of outcomes = P(5,k) = 5! / (5-k)!.
Expected value formula: EV = (probability × payoff) − cost.
Walking away has EV = $0 net gain (or $10 kept, but no additional gain).
The highest EV option is the $60 bet on exact top-2 order, with EV = (1/20 × $1000) − $60 = $50 − $60 = −$10? Wait, that's negative. Let's recalc: 1/20 × 1000 = 50, minus 60 = -10. That's negative. Actually, check all: Exact 5: (1/120)*1000 - 10 = 8.33 - 10 = -1.67. Top 4: (1/120)*1000 - 20 = 8.33 - 20 = -11.67. Top 3: (1/60)*1000 - 30 = 16.67 - 30 = -13.33. Top 2: (1/20)*1000 - 60 = 50 - 60 = -10. Walk away: 0. So highest EV is walk away (0) or exact 5 (-1.67)? Actually, walk away has EV 0, which is higher than all negative EVs. So the highest EV is walking away. But the question asks 'which option has the highest expected value?' So answer: walk away. But wait, the payoff is $1000, but does that include the bet? Usually payoff means total return, so net profit = payoff - cost. So yes, all EVs are negative except walk away. So the correct answer is walk away. But many might think top-2 is best because highest probability, but EV is negative. So key point: compare EVs, not just probabilities.
Consider that the house edge makes all bets negative EV, so walking away is optimal.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.