Russian Roulette probability game - Quitters Never Lose

A shrinking elimination wheel where every safe spin compounds a 97%-of-fair multiplier and every wrong answer marks another losing number.

You start with a $100 bankroll, choose a wheel of 5, 6, 8, 10, or 20 numbers, stake $5, $10, $20, or $50, and mark one number as yours. Each spin lands uniformly on one active number. Land on a marked number and you are out - the whole stake is gone. Land on anything else and that number is removed from the wheel for good, your multiplier compounds, and you may spin again or cash out (cashing out is available any time after your first safe spin).

Before every spin you answer a probability question about the current wheel - survival odds over one or several spins, symmetry arguments over your marked numbers, and the like, all computed from the live wheel state. Answer wrong and you must mark an ADDITIONAL number before you are allowed to spin: a wrong answer worsens your odds as well as your score.

The payout mechanism is printed on the wheel: with s safe numbers out of n active, the fair multiplier for a safe spin is n/s (the reciprocal of your survival probability), and the game offers exactly 97% of fair, rounded to 2 decimals. That missing 3% is the house edge, taken on every single spin.

Why quant interviews test this

This is the quant-interview double-or-nothing structure in pure form: a sequence of bets, each individually near-fair but slightly negative, with an option to stop. Interviewers pose it to see whether candidates evaluate the per-step EV (0.97 here) or get drawn along by the running multiplier, and whether they recognize optimal stopping - when every continuation is -EV, the optimal stop is now.

The shrinking wheel is also a clean without-replacement conditional-probability generator, the same math as urn problems and depleting order books: survival probabilities chain as products of changing fractions, and the most common error - frozen denominators - is precisely what phone screens are calibrated to catch.

The Russian Roulette guide covers how scoring works, the strategy that wins, a worked example and the mistakes most players make.

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