Net results use drift × hands/100 and standard deviation × √(hands/100). Enter a steady-play edge after rake and fees. Logged results may already include fatigue and tilt; adding penalties to those figures can double-count their cost. Each career stops when the bankroll is exhausted, with no reloads or stake changes. A Brownian-bridge check estimates crossings between steps; drawdowns are measured at endpoints up to 25 hands apart and may miss intra-step peaks.

Tilt rises after unusually negative blocks, decays over 150 hands, and partially recovers between sessions. Fatigue grows linearly within a session. Learning approaches its limit with a 50,000-hand time constant. An optional normal distribution for true edge is sampled once per career and shared by both scenarios. Recovery represents time away without modeling a calendar; shorter sessions assume more breaks for the same volume.

The two colors share random shocks. Their bands are the 5th–95th percentiles at each time, not a promise that any one career stays inside them. Fixed-stakes Gaussian returns approximate poker variance; this is not a hand-level forecast or a guarantee of future profit. Zero behavior penalties and zero learning reproduce steady play exactly.

Research informs the mechanisms, not these numerical coefficients: Tilt in Online Poker (2020) and Sleep or Play Online Poker? (2021). These studies do not establish the causal benefit of a particular break schedule.