Exact session math · no sampled runs

Paroli calculator

Double after a win, bank after three wins in a row; back to one unit after a loss. Enter your bankroll, unit, table limit and walk-away target. The calculator follows every possible spin sequence to the end of the session and returns the exact chance of each finish, the full stake ladder, and what the session costs on average.

By Jesse (Human)Published 2026-10-19
Bets on red, Paroli staking, stops at the first of: target reached, next stake over the bankroll or table maximum, or the spin cap.
21.45%
Reach +$200
Before a stop rule or 500 spins
<0.01%
Progression breaks
Stake over bankroll or table, or $0
−$101
Expected result
Per session, from $1,000
−$2.70
Per $100 wagered
On $3,753 wagered on average
Session finish / exact

How the session ends

Finishes ahead 33.22% of the time. The average session lasts 443.4 spins; the median finish is $890.

Walked away up $200
21.45%
Next stake blocked by bankroll or table
0%
Bankroll reached $0
<0.01%
Reached 500 spins
78.55%

Read the result

Paroli reaches the $200 target in 21.45% of sessions. It almost never breaks; the losses arrive as steady erosion instead. Weighted together, the expected finish is −$101: about $3,753 goes through the wheel per session and each $100 of it loses $2.70 on average. Most sessions never reach the target; they run down the clock while the edge works on every bet.

Cross-check: with these exact rules, the Paroli backtest ran 20,000 seeded sessions and reached the target in 20.96%, with a mean result of −$101. The exact figures above are what that sample is estimating.

The winning streak ladder

Paroli stakes after consecutive wins from a fresh start
BetStakeNet after it winsChance to get here
#1$5+$5100.00%
#2$10+$1548.65% 1 in 2.1
#3$20+$3523.67% 1 in 4.2

“Chance to get here” is the probability that every earlier bet in the streak went the winning way, from a fresh start. Paroli caps the press at three wins, so the ladder is short. The third win banks seven units; it happens on a fresh cycle with the probability shown in the last row.

How the calculator works

A Paroli session has no memory beyond two numbers: the current bankroll and where the stake sits in the progression. The calculator starts with all of the probability on your opening bankroll and the first stake, then applies one spin at a time. Each spin sends 18/37 of every state’s probability to the winning branch and the rest to the losing branch. Probability that reaches a stop rule is set aside as a finished session. After the last allowed spin, whatever is left is counted as spin-capped. Nothing is sampled, so the same inputs always give the same figures.

The stop rules are the ones every system page uses: walk away once the bankroll reaches the target, stop when the next stake is larger than the bankroll or the table maximum, and stop at the spin cap. The test suite solves every calculator on the published rules and requires agreement with the 20,000-session seeded backtests within sampling error. It also checks exact agreement with brute-force enumeration of every spin sequence on a small table.

What no input can change

Every red bet returns −1/37 of its stake on average, so the expected result is always that fraction of the expected amount wagered: −$2.70 per $100. A bigger bankroll, a higher table limit, or a smaller target changes how often the session finishes ahead and how large the bad finishes are. It does not change that figure. The house edge page derives it from the payout table.

Limitations

Fair, independent spins, bets on red only, whole-dollar inputs, and standard European or American settlement. French la partage and en prison are not modelled; the wheel rules guide covers what they change. To test a variation the calculator can’t express, run the Paroli Lua in Engineer mode and edit it.

Other progression calculators

For a single flat bet rather than a progression, use the roulette odds calculator.