The law of large numbers: one session against the average of 320 players
Predict where the average player's balance goes, then watch one session and the average of 320 players on the same chart. You will see variance dominate a single session while the average tracks the house edge more closely the longer play runs.
How it works
Each simulated bet is an even-money wager that wins with probability (1 − edge) ÷ 2, so every $1 bet loses the edge on average and expected end = $200 − bets × $1 × edge. On European roulette, where one green zero among 37 pockets gives an edge of 1 ÷ 37, about 2.7%, that means $194.60 after 200 bets, $173 after 1,000 and $65 after 5,000. The typical spread of a single session grows only with the square root of the number of bets, about $14 after 200 and $71 after 5,000, while the expected loss grows in step with the bets.
Once you have predicted the average player's direction, 320 players start at $200. The chart draws in two stages: one bright session traces first, then a faint fan of the other sessions and a red line for the average of all 320 fade in, with a dashed line at the start. Choose the game, from blackjack at 0.5% to American roulette at 5.26%, and a horizon of 200, 1,000 or 5,000 bets; 'Replay' draws new random numbers. The readouts show the average end, the share of players who finished above $200, and the best and worst finishes.
Because some sessions end ahead, the edge can look like something that only happens to unlucky players. The average line shows it applies to everyone at once, and the share still ahead shrinks as play lengthens: on European roulette the tool's first run has about a third of players ahead after 200 bets, about a fifth after 1,000 and very few after 5,000. The UK Gambling Commission's guidance describes the same narrowing for real games: for a game with a standard deviation of 5.6, the 95% range around the designed RTP is about ±4.9 points after 50,000 games and ±1.1 points after 1,000,000.
What it leaves out: All four games are modelled as one even-money bet at their edge, which leaves out blackjack decisions and slot prize tiers, and balances can drop below zero because no player is stopped when the $200 runs out. Built for adults (18+) as a teaching simulation, it cannot move the edge of any game it names.
Sources
Checked on 2026-11-05. Independent, not affiliated. 18+.
- UK Gambling Commission: How to calculate return to player (RTP), live RTP performance monitoring guide (last updated 25 January 2021)gamblingcommission.gov.uk
- Pennsylvania Code: 58 Pa. Code § 617a.1, Roulette ball; Roulette wheel and table; physical characteristics (current through 56 Pa.B. 6006, 5 September 2026)pacodeandbulletin.gov
- Pennsylvania Code: 58 Pa. Code § 617a.4, Payout odds (Roulette) (current through 56 Pa.B. 6006, 5 September 2026)pacodeandbulletin.gov
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