TL;DR
Card Trading Game: Estimation Under Uncertainty: A canonical quantitative trading interview question at intermediate difficulty. Commonly asked at Jane Street, SIG, Optiver, IMC.
By Valenke Exam Prep Team·Last updated 2026-06-01
intermediateGame Theory & Strategy
Card Trading Game: Estimation Under Uncertainty
Asked at: Jane Street, SIG, Optiver, IMC
Problem
You are shown 5 cards from a standard 52-card deck: 3, 7, 10, Jack (11), and King (13). The "value" of the deck is the sum of all 52 card values (Ace = 1, 2-10 face value, J = 11, Q = 12, K = 13).
(a) Estimate the sum of all 52 cards.
(b) Now I offer to trade you the "remaining 47 cards" for . Should you take the deal?
(c) How does your confidence in part (b) change if I'd shown you 20 cards instead of 5?
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