Bankroll Management Calculator: Flat, Fraction or Kelly

A bankroll management calculator turns one question into a number: how much of your bankroll goes on the next bet. Most tools run one of three rules (a flat unit, a fixed fraction of the current bankroll, or the Kelly criterion), and none of them changes the house edge. What the rule changes is how hard the bankroll swings and how likely it is to run dry.

The input boxes on most calculator pages hide that choice. This guide sets out what each rule computes, then compares the Kelly fractions using the figures from a published worked example.

What the calculator is computing

Every sizing rule answers the same thing: the stake for the next bet, given the bankroll you hold now. The rules differ in whether that stake moves when the bankroll moves.

What is a betting unit?

A betting unit is the standard stake every bet is measured in. A flat-unit calculator divides your bankroll into a number of units you choose and stakes one unit per bet, so the stake only changes when you decide to recalculate. A fixed-fraction or Kelly calculator recalculates after every result, which is why its stake falls during a losing run and rises during a winning one.

Why no sizing rule beats the house edge

A sizing rule cannot turn a negative bet into a positive one. The Wizard of Odds puts it plainly: whatever betting system is used, the ratio of money lost to money won approaches the house edge in the long run.

His own simulation shows it. Across the betting systems he ran, the loss-to-win ratio came very close to 7/495, the house edge on the craps pass line. So read any calculator's output as a plan for variance and survival, never as a route to profit.

The Kelly criterion, in Kelly's own terms

Kelly's original paper starts from a point most calculator pages skip. He notes that a gambler could bet the entire capital each time and that this would maximize the expected value of the capital, and he still does not adopt it.

His alternative is to stake a fixed fraction of capital on every bet and pick the fraction that maximizes the exponential growth rate G. The reasoning shows up in any sequence of bets: an all-in bettor who loses once has nothing left to grow, however good the average looked on paper.

Full, half and quarter Kelly compared

Scaling Kelly down costs some growth and buys a large cut in ruin. A 2024 paper in the journal Entropy works through a game with win probability 0.5, where a loss costs the whole stake and a win pays 1.5 times the stake, and reports the trade-off for each fraction.

The paper calls fractional Kelly a common heuristic for reducing risk while keeping a high return. In this game, quarter Kelly almost never reaches ruin yet keeps almost half the growth rate. Two cautions apply. Ruin in the paper means the bankroll dropping below a set floor, not literally to zero. And the game favours the bettor, which a house-edge casino game does not, so take the table as the shape of the trade-off rather than a casino plan.

What a bankroll management calculator app should show you

A useful calculator app tells you which rule it is running and what that rule does to your risk, not just a stake figure. Before you trust one, check that it shows:

• The rule by name. Flat units, fixed fraction or Kelly, and whether the stake is recalculated after each result.
• Fractional Kelly options. Half and quarter settings, the fractions the worked example compares.
• How it defines ruin. The floor it counts as ruin, and whether that floor is zero or a stop-loss you set.
• That the house edge stays put. Any tool that implies a staking pattern improves the long-run result is misreading the maths.

Guide questions

Does a bankroll calculator change the house edge?

No. It decides how much you stake, not what each bet pays. Over a long run your losses measured against the money you bet drift toward the house edge whichever sizing rule the calculator applies.

Why not bet the whole bankroll if that maximises expected value?

Kelly accepted that all-in betting maximises the expected value of capital and still rejected it. A single loss ends an all-in bettor, so he chose the fraction that maximises the long-run growth rate instead.

Is half Kelly safer than full Kelly?

In the published worked game it is. Smaller Kelly fractions are a standard way to cut the risk of ruin, and half Kelly gave up only a quarter of the median growth rate to get there.

What does risk of ruin mean in a calculator?

It is the chance that the bankroll falls to a floor you set and stays out of play. Check where the tool puts that floor: it is often above zero, the point where you would stop or could no longer place a minimum stake.

Sources and further reading

• Bell System Technical Journal (J. L. Kelly Jr.): A New Interpretation of Information Rate, July 1956
• Entropy (Basel) 2024, 26(7):600: Analyzing Sequential Betting with a Kelly-Inspired Convective-Diffusion Equation, 15 July 2024
• Wizard of Odds: Betting Systems, undated, accessed October 2026