A fair coin: win $1 on heads, lose $1 on tails. Play once or 100 times — does it matter?

How to answer

On EV, no: EV = 0 per flip, so total EV = 0 either way. Repetition only shrinks the variance of the AVERAGE toward 0 (law of large numbers); the variance of total dollar PnL actually grows with n (std = σ√n). So I'm indifferent on EV — repetition makes the average more predictable, not more profitable. With a true 0-EV bet there's no reason to play.

Key idea: Claiming 100 plays raises EV, or conflating shrinking variance-of-the-mean with shrinking total-PnL variance — the total spread grows with √n.