Kelly Criterion Simulator - Calculator & Bankroll Growth Model

KELLY CRITERION SIMULATOR/CALCULATOR

Settings ⚙

Bankroll

Win Probability (%)

Odds

Decimal<br>American

Kelly Fraction<br>1.00

Safe<br>Aggressive

Simulations

10<br>50<br>100

Number of Trades

Run Simulation<br>Reset

Ready

Risk of Ruin<br>0%

Median Result

$0

Risk of Ruin

0%

Median Drawdown

0%

This Kelly Criterion simulator models how a bankroll can evolve across repeated bets when stake size is determined by a Kelly-based capital allocation rule. The model is probabilistic, path-dependent, and designed to show how growth, volatility, and drawdowns interact under fixed assumptions.

Rather than producing a single forecast, the simulator generates many possible bankroll paths under the same input conditions.

The purpose is to show the structural behavior of the Kelly Criterion inside a controlled model, not to provide betting advice, guarantees, or real-world decision support.

What the Kelly Simulator Models

This Kelly Criterion simulator models bankroll evolution as a multiplicative process. Each bet changes total capital by a fraction of the current bankroll, which means growth and loss compound over time rather than accumulating in a flat linear way.

The simulator is built around repeated trials with fixed probability and fixed odds. Because the same capital allocation logic is applied across many simulated paths, the output can show how the Kelly Criterion changes long-run growth behavior, volatility, drawdown depth, and tail outcomes under stable model conditions.

The result is not a single expected bankroll number. It is a distribution of possible outcomes shaped by edge, odds, variance, and path dependency.

How the Kelly Criterion Works

The Kelly Criterion is a capital allocation formula used to determine what fraction of bankroll should be risked when a bettor or investor believes a measurable edge exists. In simple terms, the Kelly fraction increases when the perceived edge is stronger and decreases when the edge is weaker or the payout structure is less favorable.

Inside this simulator, the Kelly Criterion is treated as a formal bankroll sizing rule. The model does not decide whether an edge is real. It only shows what can happen to capital when a fixed edge assumption is translated into repeated Kelly-based exposure.

This matters because bankroll growth is not determined by win rate alone. It depends on the relationship between probability, odds, and stake size. A positive edge can still produce severe volatility if exposure is too aggressive, while a smaller capital fraction may reduce growth but also reduce drawdown pressure.

Kelly Criterion and Growth Optimality

The Kelly Criterion is known for growth optimality in the narrow mathematical sense of maximizing expected logarithmic utility. Within a repeated multiplicative process, that means maximizing long-run geometric growth under the assumptions of the model.

That property is often misunderstood. Growth optimality does not mean smooth growth, safe growth, or low-stress growth. It means the formula targets maximum asymptotic growth, and that objective naturally comes with trade-offs.

Higher expected growth under full Kelly usually means greater volatility, deeper interim drawdowns, and wider outcome dispersion. A bankroll can still experience long and uncomfortable periods of instability even when the model is theoretically growth-optimal over the long run.

Why Bettors Use Kelly-Style Bankroll Models

The Kelly Criterion is commonly discussed in betting environments where capital allocation matters as much as prediction quality. That includes sports betting, model-based betting, some forms of advantage play, and other situations where a participant believes odds and true probability are misaligned.

In those environments, the main question is not only whether a bet has positive expected value. The question is also how much of the bankroll should be exposed when the edge is believed to exist. That is where Kelly-style bankroll models become relevant.

The Kelly Criterion gives a formal answer to the sizing problem. It does not create an edge, and it does not verify whether the underlying probability estimate is correct. It only converts assumed edge and odds into a capital fraction inside a repeated-risk framework.

This is one reason the formula attracts serious attention from disciplined bettors. It sits at the intersection of expected value, bankroll growth, and survival risk rather than focusing on win rate alone.

Full Kelly, Fractional Kelly, and Risk Exposure

Full Kelly is the mathematically complete capital fraction implied by the formula under the model assumptions. Fractional Kelly reduces that fraction, often to half-Kelly or quarter-Kelly, while keeping the same general logic of edge-based sizing.

This matters because full Kelly is often too aggressive for real-world use when the input assumptions are uncertain. Even if the estimated edge is positive, full...