Why Quant & Fit · Interview Question
A coin pays $2 on heads, loses $1 on tails, p=0.5. EV, and what fraction of bankroll per flip?
How to answer
EV = 0.5(2) + 0.5(-1) = +$0.50, strongly positive. Sizing is set by risk of ruin via Kelly: f* = (bp - q)/b with net odds b=2, p=q=0.5, so f* = (2·0.5 - 0.5)/2 = 0.25 — bet 25%. In practice I'd bet a fraction of Kelly (e.g. half) since estimated edge is uncertain and full Kelly punishes drawdowns.
Key idea: Confusing 'positive EV' with 'bet everything' (ignores ruin), or plugging the raw payout (2) into Kelly instead of net odds b.
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