Read a roulette session: reconcile every row

A roulette ledger should let you reconstruct the wallet without guessing what a number means. Here is a short exact worked trace, using the opening four pockets of our matched-spin example: 7, 20, 0, 32.

Declare the opening state

The wallet starts with 100 practice units. A one-unit Martingale bets red on a European wheel, doubles after a loss and resets after a win. Zero loses in full. A winning even-money bet returns twice its stake, including the original stake.

Each balance equals the previous balance minus stake plus total returned. Net equals total returned minus stake. Applying both returned and net to the balance would count the same winnings twice.

Interpret the zero row

On spin three, 0 is neither red nor black. The two-unit red wager returns nothing under these declared rules. Its net is −2, and the following requested stake becomes four. Calling zero a push would alter both the wallet and every later stake.

The strategy transition happens after settlement. The four-unit wager is placed before spin four’s pocket is known. Using the winning pocket to choose that wager would leak future information into the trace.

Read drawdown independently of final profit

The highest balance before the decline is 101. The low point is 98, a three-unit drawdown from that peak. The final balance 102 is two units above the starting wallet. Ending profit and peak-to-trough decline describe different parts of the same path.

Total wagered is eight units across these four spins. A 102-unit ending wallet does not mean that only two units were exposed. Wagers can recycle the same funds through several rounds.

A trace is not a distribution

This selected four-spin path demonstrates accounting and state. It provides no estimate of a strategy’s long-run success rate. To compare many sessions, retain early stops, state the bankroll and table maximum, and distinguish actual observed sample results from exact theoretical probabilities.

The audited native engine saves trace and path data for simulation interpretation. This article’s table is a manually declared mathematical example, not an exported native app session. Read app simulation outputs for that source-backed distinction, payouts for return conventions and simulation methodology for repeated-trial analysis.