Each round is modeled as an even-money wager: win pays +1× the bet, lose costs −1× the bet, with win probability p = (1 − house edge) / 2 so the long-run expectation matches the stated edge exactly. The chart plots your real bankroll path (solid) against the theoretical expectation line (dashed) and a ±2 standard-deviation band computed from the binomial variance of n rounds — this is why "the house always wins" is a statement about the mean, while any single session can land anywhere inside that band.