Calculator
Example Data Table
| Bankroll | Win Probability | Odds | Full Kelly | Half Kelly Stake |
|---|---|---|---|---|
| 1000 | 55% | 1.00 | 10% | 50 |
| 2500 | 53% | 1.00 | 6% | 75 |
| 5000 | 60% | 0.90 | 15.56% | 388.89 |
Formula Used
Kelly fraction: f = (b × p - q) / b
Loss probability: q = 1 - p
Fractional Kelly: adjusted stake fraction = f × fractional Kelly percent
Stake amount: stake = current bankroll × adjusted stake fraction
Expected value per dollar: EV = (p × b) - q
Expected log growth: G = p × ln(1 + f × b) + q × ln(1 - f)
How To Use This Calculator
Enter your starting bankroll first. Add your estimated coin flip win probability. Use 1 for even money net odds. Set fractional Kelly to reduce risk. Add simulation count and flip count. Set stop loss and take profit limits if needed. Press calculate to view results above the form. Use CSV or PDF buttons to export the same model.
Understanding Kelly Coin Flip Betting
A coin flip can look simple. Yet bankroll choices change everything. The Kelly Criterion helps estimate an ideal stake when a bettor has a measured edge. This simulator turns that idea into a practical bankroll model. It compares expected value, optimal fraction, drawdown, ruin risk, and long run growth.
Why Kelly Size Matters
Flat betting ignores changing bankroll size. Full Kelly adapts each stake to current capital. It can grow fast when the edge is real. It can also swing sharply. Fractional Kelly reduces that volatility. Many users test half Kelly or quarter Kelly before using larger exposure.
The calculator accepts win probability, payout odds, bankroll, flip count, and simulation count. It also includes maximum stake limits, minimum stake rules, stop loss levels, and take profit targets. These controls make the model closer to real betting plans. They also show when a mathematical edge still feels too risky.
Reading The Results
A positive Kelly fraction means the stated edge supports a bet. A zero result means the game is not favorable. The recommended stake shows the first wager after fractional and cap rules are applied. Average final bankroll shows typical growth across runs. Median final bankroll helps when extreme wins pull the average upward. Worst run and max drawdown reveal downside pressure.
Risk Of Ruin And Drawdown
Risk of ruin is not only bankruptcy. In this tool, it can reflect hitting a severe bankroll threshold or stop loss. Drawdown measures the drop from a previous peak. A strategy can be profitable and still produce painful drawdowns. That is why bankroll protection inputs matter.
Practical Use
Start with conservative values. Test several probabilities near your estimate. Small changes in edge can greatly change stake size. Compare full Kelly with fractional Kelly. Then review CSV or PDF exports. Use the results as planning support, not as a promise of profit.
Good simulation work checks many paths. One lucky run proves little. Thousands of runs show the spread of possible outcomes. The best plan is often the one you can follow calmly during losses. Kelly math can guide that plan, but discipline controls execution.
Repeat testing often, because new assumptions can change every staking decision quickly before play.
FAQs
What is the Kelly Criterion?
It is a staking formula. It estimates the bankroll percentage to bet when probability and payout odds are known.
Can this calculator handle biased coin flips?
Yes. Enter any win probability between 0.01% and 99.99%. A biased coin can be modeled with a probability above or below 50%.
What does payout odds mean?
Net payout odds show profit per unit staked. Use 1 for even money. Use 0.90 when a winning 1 stake earns 0.90 profit.
Why use fractional Kelly?
Fractional Kelly lowers stake size. It reduces volatility and drawdown, while still following the Kelly direction.
What happens when Kelly is negative?
A negative Kelly result means the bet has no mathematical edge. The calculator then recommends no Kelly stake.
What is risk of ruin here?
It is the share of simulations ending at or below your chosen ruin threshold. It also reflects severe bankroll damage.
Why use many simulations?
More simulations show more possible bankroll paths. This helps reveal average outcomes, bad runs, and upside spread.
Are results guaranteed?
No. The simulator models probability, not certainty. Real results can differ because coin outcomes are random.