Pick lottery game - play Pick 3, 4 or 5

A real Pick 3 lottery ticket where every play type - Straight, Box, Pair - carries the identical 50% house edge.

You fill in a 3-digit ticket, one digit (0-9) per column, on a $1 wager - the same mechanics as a real state Pick 3, and the payout table is modeled on a real state prize table. Before the draw you answer a short question set generated from your own ticket: how many orderings your digits have, what the Box payout should be, the Straight and Box probabilities, and the house-edge punchline.

Three digits are then drawn uniformly at random (each 0-9, independent). Your ticket is checked against every play type at once: Straight (exact order), Box (same digits, any order - only counted when it is not already a Straight), and Pair (your first two digits match the first two drawn, in order). A single draw can hit multiple play types.

The 'way' count is the number of distinct orderings of your digits: 3 distinct digits are a 6-way, a pair like 1-1-2 is a 3-way, and triples are 1-way. It determines the Box payout and probability. As the game's final question forces you to prove, it does not change the value of the bet.

Why quant interviews test this

Lottery pricing is a standard interview warm-up because it packs three testable skills into one prompt: counting permutations with repeated elements, converting counts to probabilities, and comparing an offered payout to the fair payout implied by those odds. The 'every play type has the same edge' punchline is exactly the kind of invariant interviewers love - candidates who compute one EV and assert the pattern show structural thinking; candidates who grind all four show reliability; the best do both.

It is also the cleanest possible example of why EV is the right lens on any priced bet: a 50% house edge is invisible in any single draw and completely decisive over volume.

The Pick 3 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.
• Scratch-Off (Timed, 7 Questions) - Scratch tickets with the odds printed face-up: 7 probability questions per ticket on a 5:15 clock, then a buy-or-walk decision.
• All Probability practice
• Every game guide