Most bankrolls do not die of a bad edge. They die of a bad match between stake size and variance — a player with enough money for four hundred spins sitting down at a game that needs three thousand to behave. Volatility labels on a game's info screen tell you almost nothing useful. The underlying number does, and you can turn it into a stake size with one formula.
Volatility is a standard deviation, not an adjective
"High volatility" is shorthand for the standard deviation of the return on a single spin, expressed in stakes. A game with σ = 11 has spin outcomes that scatter about eleven stake-widths around the mean. Studios rarely publish it, but the label maps to a usable range:
|
Label |
Typical σ per spin |
What it feels like |
|---|---|---|
|
Low |
3–5 |
Balance drifts down slowly, frequent small wins |
|
Medium |
6–10 |
Noticeable swings, features every few hundred spins |
|
High |
11–17 |
Long dry runs punctuated by real hits |
|
Extreme |
20–30+ |
Nearly all the return sits in rare events |
Two numbers describe any session
Take a 96.5% game, so an edge of 3.5%, played at €0.60 a spin for 1,000 spins.
Expected loss = spins × stake × edge = 1,000 × €0.60 × 0.035 = €21.00
Standard deviation = stake × σ × √spins. At σ = 11: 0.60 × 11 × √1,000 = €208.71
Sit with that pair for a second. The game's price for the session is €21. The noise around that price is ten times larger. A perfectly ordinary result inside one standard deviation runs from about −€230 to +€188. This is why players are convinced a game is "broken" or "hot" — at session length the edge is completely invisible underneath the variance.
Terminal loss is the wrong thing to plan for
You do not go bust at the end of a session. You go bust at the worst moment during it, and the running minimum of a random walk is considerably deeper than its endpoint.
The reflection principle gives a workable approximation: for a walk with negligible drift, the chance of touching a drawdown of x at some point is roughly twice the chance of finishing below it.
-
Chance of a 1σ drawdown (€209) at some point in those 1,000 spins: ≈ 2 × 15.87% = 31.7%
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Chance of a 2σ drawdown (€417): ≈ 2 × 2.28% = 4.6%
So a bankroll equal to one standard deviation busts roughly one session in three. Two standard deviations gets you to about a one-in-twenty failure rate, which is a defensible planning target.
The sizing rule that falls out of it
Bankroll ≈ 2 × σ × stake × √spins
Divide through by stake and you get the bankroll expressed in units, which is the form worth memorising. For a 1,000-spin session:
|
σ |
Bankroll needed (in stakes) |
|---|---|
|
4 |
253 |
|
8 |
506 |
|
13 |
822 |
|
22 |
1,391 |
A high-volatility game asks for something like 800 times your spin stake to give you a reasonable chance of completing a thousand spins. The "100× your bet" advice that circulates on forums is off by nearly an order of magnitude.
Running it backwards from what you have
This is the version you will actually use. You have €150 and you want roughly ninety minutes, which at a deliberate 550 spins an hour is about 825 spins. Rearrange:
stake = bankroll ÷ (2 × σ × √spins)
-
On a high-volatility game, σ = 13: 150 ÷ (2 × 13 × 28.72) = €0.20 a spin
-
On a low-volatility game, σ = 4: 150 ÷ (2 × 4 × 28.72) = €0.65 a spin
Same money, same clock, and the volatility of the game dictates a stake three times apart. Choosing the game and then guessing the stake is backwards.
Where the return is hiding
High variance usually means the return has been concentrated into a feature. Suppose the bonus round triggers once in 300 spins and pays an average of 180× stake. Its contribution to RTP is 180 ÷ 300 = 60 percentage points. On a 96.5% game that leaves the base game returning just 36.5% — you lose roughly 63 cents of every euro staked while waiting.
And the waiting is longer than intuition suggests. The chance of seeing zero features across 200 spins is (299/300)^200 = 51%. Across 600 spins it is still 13%. Half of all short sessions on that game never touch the thing that pays for the game.
Top prizes are worse. If a 10,000× maximum win contributes 5 percentage points of RTP, it must land about once in 200,000 spins — roughly 364 hours at that pace. It is a real outcome and it is not part of any sane plan.
Hit frequency is a different measurement
A 25% hit frequency sounds generous. But "hit" only means the spin returned something above zero, and on most modern games the majority of hits return less than the stake. Seventeen of those twenty-five hits per hundred spins can still be net losses. Low volatility games have high hit frequency; so do plenty of high volatility games with a dense floor of sub-stake payouts. The two numbers answer different questions and neither substitutes for the other.
When the game is the wrong shape for the bankroll
If the formula spits out a stake below the game's minimum, the correct response is not to play anyway at three times the size — it is to change games. Lower σ is a legitimate lever, and so is a lower edge. A table game with a fraction of a percent of house edge lets a given bankroll survive far more decisions than a 3.5% slot does, because both terms in the arithmetic shrink. That is the appeal of something like Duel Blackjack Live, where 60% Instant Rakeback settles with every hand and takes the effective RTP to 99.78% with no wagering requirements attached — although the honest caveat is bracket, not maths: crypto stakes there start at $10 and run to $100,000, so it is a different bankroll tier entirely from a €0.20 spin, and the standard deviation per hand being near 1.15 rather than 13 does not make it a small-bankroll game.
The five-line pre-session check
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Estimate σ from the volatility label.
-
Decide how many spins you want, from minutes × spins per minute.
-
Stake = bankroll ÷ (2 × σ × √spins).
-
Sanity-check expected loss: spins × stake × edge. If that number is more than you want to spend on entertainment, shorten the session rather than raising the stake.
-
Set the loss limit at the bankroll figure and stop there.
Sizing correctly does not make a slot profitable. A 3.5% edge charged 550 times an hour is still a reliable drain, and no amount of stake discipline changes its direction. What it buys is a session that ends when you decided it would, on money you had already written off.
