Bankroll Simulator
See the luck in your betting plan before you bet it
At -110 with a 54% true win chance, each bet has an expected value of 3.1% of the stake. Over 1,000 bets the middle result is $1,618 from a $1,000 start, but 1 season in 20 ends below $587 and 1 in 20 ends above $2,611. 14% of the simulated seasons finish down.
Edge Per Bet
3.1%
Break-even win chance 52.4%
Middle Result
$1,618
Average $1,629
Bad Luck (5th %ile)
$587
Good luck (95th) $2,611
Seasons That Finish Down
14%
Chance To Lose Half
12.6%
Bankroll touches 50% of start
Chance To Go Bust
1.6%
Bankroll below one bet
Typical Worst Drawdown
33%
Median peak to low point
Bets To Prove This Edge
3,791
Profit 2 standard deviations above zero
The dark band holds half of the 2,000 simulated seasons. The light band holds 90% of them. The dashed line is your starting bankroll.
Square root of n. At $20 per bet, the expected profit after 1,000 bets is +$618. The luck band (1 standard deviation) is $602. The profit grows with the number of bets, but the luck band only grows with its square root.
Kelly size. Full Kelly at this edge is 3.4% of the bankroll per bet. A quarter Kelly is 0.9%.
Test the edge sooner. Results need 3,791 bets to prove this edge. Closing line value can show it in a few hundred. See how BankrollSZN grades its own picks on the Model Track Record, and log your own bets in the Bet Tracker.
For entertainment and education only. Not financial advice. If you or someone you know has a gambling problem, call 1-800-GAMBLER.
What this bankroll simulator does
The simulator plays out your betting plan thousands of times. You enter a bankroll, a price, your true win chance, a bet size and a number of bets. It runs 2,000 seasons of those bets and shows the range of results, from the bad luck case to the good luck case.
A single season is one draw from that range. A bettor with a real edge can finish down, and a bettor with no edge can finish up. The chart shows how wide that range is, so you can size bets for the losing runs you will face.
Why variance grows with the square root of the number of bets
Your expected profit grows in a straight line with the number of bets. The spread of results around that profit grows with the square root of the number of bets. Four times the bets gives four times the expected profit, but only two times the spread.
That is why a small sample proves nothing and a large sample proves a lot. After 100 bets at -110, the luck band is about plus or minus 19 units. A 3 percent edge expects 3 units in that time, so the result is mostly luck. After 10,000 bets the band is about plus or minus 190 units and the edge expects 300 units, so the edge shows through.
How many bets it takes to prove an edge
The simulator shows the number of bets you need before your expected profit is two standard deviations above zero. At that point a profit is hard to explain with luck alone. For a 2 percent edge at -110 it is about 9,000 bets. Most bettors never place that many bets at one edge, which is why closing line value is a better test of skill than win rate.
Closing line value asks a different question: did the market move toward your side after you bet? Each bet gives one small, low noise reading, so a few hundred bets can show an edge that results alone need thousands of bets to show. See the Model Track Record page for how BankrollSZN grades its own picks this way.
Flat stakes, percent stakes and the Kelly criterion
Flat stakes bet the same amount every time. Percent stakes bet a fixed share of the current bankroll, so bets shrink after losses and grow after wins. Percent stakes cannot go to zero, but a long losing run still cuts the bankroll hard.
The Kelly criterion gives the bet size that grows a bankroll fastest for a known edge: (b x p - q) / b, where b is the decimal odds minus 1, p is your win chance and q is 1 minus p. Full Kelly has very large drawdowns, and your true win chance is an estimate, not a fact. Most professional bettors use a quarter to a half of the Kelly size.
Frequently asked questions
How much should I bet per play?
Most bettors with an edge keep each bet between 1 and 3 percent of the bankroll. Use the simulator to see the chance to lose half the bankroll at the size you want to bet. If that chance is more than you can accept, bet smaller.
What is a normal losing streak for a winning bettor?
Longer than most people expect. Take a bettor who wins 54 percent at -110 and bets a flat 3 percent of a $1,000 bankroll. That is a real edge, but over 1,000 bets the median worst drawdown is about 45 percent, and about 1 season in 4 drops to half the bankroll at some point. The median longest losing streak in those seasons is 8 bets in a row, and 1 season in 10 has a streak of 11 or more.
What is risk of ruin?
The chance that a run of losses takes the bankroll below the size of the next bet, so you cannot keep betting. With flat stakes the simulator reports it as the chance to go bust. With percent stakes the bankroll never reaches zero, so the simulator reports the chance to lose half of it.
Why does the simulator need my true win chance?
The price tells you the break-even win chance. Your edge is the gap between your true win chance and that break-even point. If you do not know your true win chance, use the break-even point plus a small edge, such as 1 to 3 percent, and see how wide the results are.
Is this bankroll simulator free?
Yes. No account is needed and all of the math runs in your browser.