Many Small Bets
One coin flip is a gamble. A thousand of them, each with a positive edge, is almost a sure thing. Configure your "dice" and watch the law of large numbers take over.
The Bet
Each outcome has a payoff and a chance (weights auto-normalize to probabilities).
How Many Tries
Across 2000 simulated lifetimes, each playing this bet 200 times.
| Metric | Value |
|---|---|
| edge per bet expected value, one try | €0.50 |
| expected after 200 ± €78 typical swing | €100 |
| in profit after 1 bet a single roll is a gamble | 50% |
| in profit after 200 many rolls, near-certain | 91% |
One bet lands in profit only 50% of the time, but repeat it 200 times and you finish ahead 91% of the time. Small positive edges compound into near-certainty.
Where 25 lifetimes end up
Cumulative profit over the course of 200 bets. Each thin line is one lifetime; shaded bands are the ±1σ / ±2σ range.
- Expected: The expected-value line: cumulative profit if every bet landed exactly at its EV.
- Likely range: The ±1σ / ±2σ spread across simulated lifetimes.
- Break-even: Where cumulative profit is exactly zero.
Final outcome distribution
How 2000 lifetimes finish after 200 bets.
91% of lifetimes end in profit.
- Bars: In profit: Runs that finished on this side of break-even.
- Bars: At a loss: Runs that finished on this side of break-even.
- break-even: Where the two choices finish exactly level.
- Bars: straddles break-even: This bucket spans both sides of break-even, so it is neither a clean win nor a clean loss.
- Example: a coin flip paying +€6 / −€5 at 50/50 has an edge of +€0.50.
- Why the bands narrow: total profit grows faster than the spread around it, so a positive edge eventually outruns the noise and almost every path lands above zero.
Probability of each outcome
- p_i: probability of outcome i
- w_i: outcome i's weight
Edge per bet (expected value)
- p_i: see Probability of each outcome above
- payoff_i: outcome i's payoff
Spread per bet (standard deviation)
- EV: see Edge per bet above
Expected total and spread after N bets
Expected(200) = 200 × EV Spread(200) = √200 × SD
- N: number of bets (numBets, floored to an integer, clamped to 1–10,000)
Probability of finishing in profit
- sims: number of simulated lifetimes (2,000)
- balₛ(N): simulated lifetime s's cumulative profit after N bets, the running sum of N draws from the outcome distribution
Assumptions behind every figure: how this site models the market →
Every model leaves things out. Here is what this one does not see:
- Every bet is modelled as a fixed-size, statistically independent draw. Real repeated bets (side projects, trades, career moves) are often correlated with each other or with wider market conditions, so the law-of-large-numbers convergence shown here is more optimistic than a set of genuinely correlated bets would allow.
- There is no ruin constraint: a simulated lifetime can run deep into negative territory mid-sequence and keep betting the same fixed stake next round regardless. A real bettor who can't cover a big loss, or who must shrink their stake after one, faces a worse path to "in profit" than these lines show.
- Probabilities and payoffs are treated as exactly known and fixed for the whole run. Real edges are estimated from imperfect information and can drift, so a bet that looks positive-EV here can quietly be negative-EV in reality if the estimate is wrong.
- No fees, spread, tax on winnings, or time value of the capital staked between bets. The pure edge charted here is a ceiling on the real return, not a floor.