Staking Plans Compared

Those are two separate problems, and most bettors only work on the first one. This guide sits between bankroll management — which explains why staking matters at all — and the Kelly criterion, which is the mathematically optimal answer. Here we line up every plan you're likely to meet and ask one question of each: what does it do to your money during a bad run?

What a staking plan can and cannot do#

A staking plan cannot create an edge. This isn't an opinion, it's arithmetic. The expected value of a run of bets is the sum of the expected values of each individual bet, and each of those equals your stake multiplied by the per-unit edge on that bet. Change the stakes however you like: if the per-unit edge is negative, every term in the sum stays negative.

So what does a staking plan control? Three things: how fast a genuine edge compounds, how deep your drawdowns get, and whether the worst plausible losing run leaves you with anything to bet with. That last one is the whole game.

Level stakes, flat stakes, and percentage of bankroll#

The word "flat" gets used for two different plans, so be precise about which one you mean.

• Level stakes — the same cash amount on every bet. Ten units a bet, whether your balance is 500 or 5,000. Simple, easy to audit, and the only plan under which a straight comparison of profit across bets is meaningful. It's what most published track records use.
• Fixed fraction of the starting bankroll — you set the unit once (say 2% of your opening balance) and leave it. Behaves identically to level stakes until you reset the unit.
• Percentage of current bankroll — you recalculate before every bet. 2% of whatever you hold right now. This is what Tofiko's bankroll guide means by flat staking, and it's the one with the useful mathematical property below.

Why percentage-of-current-bankroll cannot bust you#

Stake a constant fraction f of your current balance and every loss multiplies your bankroll by (1 - f). After any number of losses your balance is the starting amount times (1 - f) raised to the number of losses. That expression gets small, but it never reaches zero. A fixed cash stake subtracts; a fractional stake multiplies, and multiplication by a positive number can't land you on zero.

Compare the same 2% stake defined two ways, through losing runs of increasing length:

Both columns hurt. Only one of them ends the story. The trade-off is that a fractional plan also recovers more slowly, because the stakes you bet back with are smaller — protection and growth are the same dial turned in opposite directions.

Kelly and fractional Kelly#

Kelly is the plan that stakes in proportion to your edge. For decimal odds d and your estimated probability p, the fraction of bankroll to stake is (p × d - 1) ÷ (d - 1).

Kelly maximises long-run growth, but only if p is right. It is brutally sensitive to overconfidence: overestimate your probability and Kelly obediently overstakes, and the overstaking compounds. Since nobody's probability estimate is exact, almost everyone who uses Kelly seriously uses a fraction of it — a quarter or a half. Quarter Kelly keeps most of the growth rate with roughly a quarter of the volatility, and it forgives a mis-estimated edge instead of punishing it. Run your own numbers through the Kelly calculator and note how fast the recommended stake moves when you nudge the probability by two points.

Note what Kelly does after a loss: your bankroll is smaller, so the next stake is smaller. Every sane staking plan does this. Every plan in the next section does the opposite.

The progressions: Martingale, Fibonacci, d'Alembert#

These are the plans that raise your stake after a loss. They are marketed as systems. They are ruin wearing a system's clothes.

• Martingale — double after every loss, reset after a win. Each win recovers everything lost in the sequence plus one base unit. The cost of a run of k losses is base × (2^k - 1), which grows exponentially while your bankroll doesn't. With a base stake of 1% of your bankroll, seven straight losses require 127% of it: you're out one bet before you get to place it. The full autopsy is here.
• Fibonacci — step up the sequence 1, 1, 2, 3, 5, 8, 13 after a loss, step back two after a win. A slower ramp than Martingale, which means it survives longer runs and takes correspondingly longer to recover. Same exponential ending, delayed.
• d'Alembert — add one unit after a loss, subtract one after a win, on the theory that wins and losses "even out". They don't. Coins have no memory and neither do football matches; the belief that a loss makes a win more likely is the gambler's fallacy with a French name.

Choosing one#

If you have no reliable probability estimate, you have no business using Kelly — stake a flat 1-2% of your current bankroll and spend your effort on the estimate instead. If you do have calibrated probabilities, quarter or half Kelly is the defensible choice, capped so that no single bet exceeds a few percent of the bankroll regardless of what the formula says.

And whichever you pick, record the stake and the price you took on every bet. Profit is too slow a signal to tell you anything useful; closing line value answers much sooner, but only if the numbers were written down at the time.