Scratch-off lottery game - play a ticket

Scratch tickets with the odds printed face-up: 7 probability questions per ticket on a 5:15 clock, then a buy-or-walk decision.

You start with a $100 bankroll and pick a ticket priced at $1, $5, $10, $20, $50, or $100. The ticket flips over to reveal its true prize table before you commit to anything - three outcomes (a $0 tier, a mid tier, and a jackpot tier) with exact fractional odds out of 8 or 16. Real lotteries hide this table; the game shows it to you because reading it is the whole skill.

Before you can scratch, you answer a set of probability questions about the ticket you are holding: expected value, Bayes / conditional probability, no-replacement batch odds, combinatorics, the geometric distribution (expected tickets to first win), and an occasional classic puzzle (Monty Hall, a birthday-problem variant, coupon collector). Then comes the decision stage: buy anywhere from 0 to 10 tickets of this design at this price. Choosing 0 walks away and refunds the ticket price in full - the game still shows what the ticket would have paid, for the record.

This variant gives each ticket 7 questions on its own countdown of 45 seconds per question - 5:15 per ticket, shown as a per-round clock that resets with every new ticket. If it hits zero, all unanswered questions are marked incorrect and you are moved straight to the buy decision; the timer never costs you money directly and never ends the session. The session ends only when you cash out or your bankroll hits $0.

Why quant interviews test this

Expected value over an explicit discrete distribution is the single most common opener in quant interviews - it tests whether you instinctively price a bet instead of reacting to its best case. The follow-ups here mirror real follow-ups: conditional probability without replacement (does the candidate update on removed outcomes?), the geometric distribution (time to first success), and Bayes on nested events.

The deeper lesson interviewers probe is bet selection and sizing: a trader who can compute EV but still takes -EV bets, or who sizes the same regardless of edge, fails the job even if the arithmetic is right. Declining the bet - quantity 0 - is frequently the correct answer, and saying so out loud is a strong interview signal.

The Scratch-Off (Timed, 7 Questions) guide covers how scoring works, the strategy that wins, a worked example and the mistakes most players make.

More Probability games

• Blackjack - Real 4-deck blackjack with live exact bust probabilities and a Hi-Lo counting check under a pit-boss timer.
• Russian Roulette - A shrinking elimination wheel where every safe spin compounds a 97%-of-fair multiplier and every wrong answer marks another losing number.
• Pick 3 - A real Pick 3 lottery ticket where every play type - Straight, Box, Pair - carries the identical 50% house edge.
• All Probability practice
• Every game guide