Bankroll Calculator: Sizing Stakes to Survive Variance

A bankroll calculator answers a boring question with arithmetic: given this roll and this stake, what session are you buying?

It is not a tip sheet. It will not tell you which colour is “due.” It will tell you that a $100 roll at $10 a spin is ten first-pass bets, and that recycling wins into more spins stretches turnover and therefore expected leak. That is the same identity used on an RTP calculator mindset: mean cost follows handle, not deposit.

What it is for

• Sizing a flat stake so a planned number of bets fits the roll.
• Checking whether a stop-loss is reachable before the roll is gone.
• Comparing two stakes at the same edge (for example $2 vs $5 on a 6.67% colour).

What it is not for

• Beating house edge.
• Turning a progression into a growth engine.
• Replacing a written gambling budget.

More odds and sizing pieces live in the Games and odds topic. Adults only.

You need four numbers before any formula is useful.

1. Bankroll ($) — cash set aside for play. Not next month’s rent.
2. Stake ($) — one bet. On Roulette that is one colour stake; on Coinflip it is your side of the pot; on Jackpot it is your buy-in.
3. Win probability p — the true chance the bet pays. Purple or Silver on a 15-slot wheel is 7/15 ≈ 46.67%. A fair coin is 50%. A posted crash target uses RTP ÷ multiplier (see the crash cashout page in this cluster).
4. House edge e (or RTP) — keep-rate of the bet. Colour on this site is 6.67% (93.33% RTP). A 0% fee PvP duel is 0% edge between players before anyone talks about skill or match quality.

Derived quantities

If you cannot name p and e, you are guessing. Read the game rules or how it works before you size a stake.

Deposit is not bankroll

Transferring $200 to a wallet and then deciding the stake at the table is how rolls become rent money. The bankroll input is the subset you already labelled entertainment. If that subset is $40, type $40 — not $200. The calculator cannot invent discipline you refused to write down.

Session bankroll vs lifetime bankroll

Some players keep a monthly gambling budget of $200 and a per-session slice of $40. Type the session slice when you size tonight’s stake. Type the monthly figure only when you are checking whether four $40 nights still fit the month. Mixing the two inflates U and quietly authorises a stake you cannot repeat.

Risk of ruin is the chance your bankroll hits zero (or your stop) before you finish the plan — or, in the infinite-horizon version, the chance you eventually go broke if you keep playing the same stake forever.

Flat-bet intuition

On a fair even-money game (p = 0.5, e = 0), ruin is driven only by finite bankroll and stubborn play. On a minus-EV even-money-style bet, the drift is against you, so ruin probability climbs.

A useful teaching approximation for repeated independent bets with win +stake and loss −stake is sensitive to p and to units U. Exact closed forms exist in gambling theory texts; for session planning you usually want a simpler check:

• If U is small (under ~20), one cold streak ends the night.
• If U is large (50–100+) at a modest edge, you can finish a planned n without touching zero more often — you still expect to lose EL dollars.

Worked streak lengths

P(k losses in a row) = (1 − p)^k.

Stop-loss as a softer ruin line

If your stop is −20 units rather than zero, replace “ruin” with “stop hit.” For a $2 stake and a $40 stop, k = 20 losses empties the stop even if cash remains elsewhere. P(20 losses) at p = 0.4667 is (0.5333)^20 ≈ 0.00034 — tiny for a pure streak, but you do not need a pure streak to lose 20 units. A mix of wins and losses with negative drift gets there often enough that the stop exists for a reason.

A bankroll calculator that only prints “units” without showing streak risk is half a tool. Pair units with (1 − p)^k for the k that empties your stop-loss. Variance in gambling explains why short samples look nothing like the mean.

Infinite-horizon warning

If you top up forever at a minus-EV game, eventual loss of any finite fortune is the usual story in the classic ruin models. The entertainment framing rejects that horizon: you play a planned n, then stop. The calculator is for the planned n, not for “until I win it back.”

Volatility is how wide the outcomes swing around the mean. Same edge, different feel.

Low relative swing (frequent small results)

Even-money style bets (colours, coinflips) hit often and miss often. Stake can be a smaller slice of bankroll if your goal is a long session, because single-bet swings are ±1 unit.

High relative swing (rare large pays)

A 14x green-style payout, a high crash cashout, or a long-shot multi-leg ticket can go many bets without a hit. You need more units in the roll for the same planned n, or a smaller stake — not a “system.”

Same edge, two stake maps

Hold e = 6.67% and bankroll = $300.

Expected loss still tracks turnover. If both plans wager $180, EL ≈ $12 either way. The green plan needs the extra units because droughts are longer, not because the edge changed.

Kelly is the wrong growth tool on house games

The Kelly criterion fraction for a binary bet that pays b-to-1 net is f* = (bp − q) / b with q = 1 − p. For a 1-to-1 colour with p = 0.4667:

f* = 2p − 1 = −0.0666 → bet nothing to grow the roll.

That is the calculator’s honest output when someone pastes casino odds into a Kelly sheet. Entertainment staking is a budget fraction, not f*.

Practical entertainment fractions

Many players cap a single stake at 1–2% of the session bankroll on high-swing bets and 2–5% on even-money style bets. Those are discipline rules, not edges. A $200 roll → $4–$10 colours, or $2–$4 on a long shot. If 5% already feels like rent money, the roll is too small for that game.

Progressive stake sizes

Raising the stake after losses shrinks U exactly when variance just hurt you. A bankroll calculator that re-runs after each loss with a doubled stake will show rising ruin risk — that is the tool working, not a bug. Do not “fix” it by ignoring the new U.

A bankroll without a session plan is a leak with a longer fuse.

Write three stops before the first click

1. Loss stop — for example 40% of the session roll. At $150, stop at −$60.
2. Time stop — for example 45 minutes. Clock beats “one more.”
3. Win park — optional: bank a slice of profit and leave. Not required; ego often ignores it.

How the calculator talks to the stops

• Stake such that expected loss over planned n is ≤ loss stop (ideally well under it).
• Example: e = 6.67%, stake $3, n = 40 → W = $120 → EL ≈ $8.00. A $60 stop is loose relative to the mean; the stop exists for variance, not for the mean.
• If EL already exceeds the stop, you planned too much handle. Cut stake or n.

Recycle warning

Deposit $50, stake $2, plan “until it’s gone.” First-pass n ≈ 25. If you rebet wins, n and W grow. Expected loss grows with W. A session budget calculator that ignores recycle understates cost. Count the bets you will actually click.

Link the money rules to poker bankroll management for unit thinking, and to responsible gambling if stops are already broken.

Same 6.67% colour edge. Same goal: about forty bets of entertainment. Scale stake with the roll.

Reading the table

• Units stay near 50 so streak risk stays in the same ballpark.
• EL scales with handle. A bigger roll does not buy a better edge; it buys a larger entertainment budget.
• If $26.68 expected for forty $10 colours feels wrong, the stake is wrong — not the wheel.

Coinflip contrast

$50 into a 0% fee head-to-head pot: edge between players is 0% before matchup quality. Expected fee leak is $0. Ruin is still real: you can lose the $50 in one pot. Units = 1. That is a different calculator row — one bet, binary outcome — not forty colours.

Jackpot contrast

Buy-in $20 into a multi-player pot. Your ticket share is your fraction of the pot; variance is high; “units” is not forty flat spins. Size the buy-in as a small percent of the weekly gambling budget, not as a colour stake.

Aggressive contrast (same $150 roll)

Weekly roll example

Monthly entertainment budget $200 → four weekly slices of $50. Each slice uses the $50 row above. If week one burns the $50, week two does not borrow from week three. The bankroll calculator is per slice; the budget is the parent.

Home page live pots: PVPspinArena.

Work the page as a worksheet, not as permission.

1. Fix the bankroll and the loss stop in writing.
2. Pick the game and write p and e from the real rules.
3. Choose n (how many bets you will sit for).
4. Solve stake ≈ bankroll / target units, then check EL = stake × n × e against the stop.
5. If EL or streak risk fails the stop, lower stake or shorten n. Do not raise edge in your head.

Sanity checks

• Stake > 10% of bankroll on a minus-EV colour is a short night by design.
• “I need this stake to hit a profit target” is not an input. Targets do not change e.
• Topping up the roll mid-session resets the calculator and usually violates the budget.
• If you change p because you “feel hot,” you left the tool. Re-enter the published chance.

After the session

Compare actual net to EL. A $8 expected night that finished −$2 or −$30 is normal variance, not proof the edge moved. A night that finished +$40 does not raise next session’s stake. Log the stake, n, and result; do not log a narrative about being due.

Two clocks, one roll

A loss stop without a time stop invites “I still have cash, so one more.” A time stop without a loss stop invites speeding up stakes to “make the hour worth it.” Run both. If either trips, the session is over — recalculating a higher stake is a new session with a new written roll, not a continuation.

Foundations first

If edge, EV and probability still blur together, start in the Foundations topic and expected value gambling, then return here to size the stake.

A bankroll calculator is a fence. Climbing it after a loss is how rolls disappear. 18+ only.