Model Assumptions — Simplified Simulator
A transparency report for our simulator and bankroll tools.
This page explains the basic math and assumptions that power our calculators. It is meant to help you understand what the results show and what they do not model.
How to use this page
- Read the assumptions before you use the calculator.
- Use the formulas below to see how hand outcomes and their probabilities are set.
- Note the limitations: this is a risk/pressure model, not a full blackjack rule simulator.
Summary
- Blackjack hands draw their result from a table of real blackjack outcomes in base-bet units, including 3:2 blackjacks (+1.5), doubled bets (±2), and split hands. The table comes from a 10-million-round simulation of 6-deck blackjack (dealer stands on soft 17, double after split, split up to four hands) played with basic strategy.
- House edge (user input) sets the average: probability is moved between one-unit wins and one-unit losses so the average result per hand equals the negative house edge. The spread of results (a standard deviation of about 1.15 units per hand) stays the same.
- The Roulette and Baccarat presets model each bet as an even-money win (+1 unit), push (0), or loss (-1 unit). Push rate: 9.5% for baccarat, 0 for roulette.
Formulas
Even-money presets: let p = push rate, e = house edge (decimal). Then:
winProb = ((1 - p) - e) / 2 lossProb = ((1 - p) + e) / 2
Blackjack: let m = the outcome table's built-in average result per hand. The calculator moves (m + e) / 2 of probability from the one-unit win to the one-unit loss, which makes the average exactly -e.
How simulations work
- Run N sessions (user-selected). Each session plays M hands at a fixed unit size.
- For each hand, draw an outcome from the blackjack table (or the even-money probabilities for other presets) and change the bankroll by outcome × unit. The bankroll never goes below $0, and a session busts when it can no longer cover the unit.
- Collect ending bankrolls, bust points, and summary statistics (average ending bankroll, P10/P90, bust rate).
Limitations
- Blackjack: no card counting, deck-composition tracking, insurance, surrender, side bets, or table-specific rules. Enter a higher house edge to approximate rules like 6:5 payouts or a dealer who hits soft 17.
- Slots are not modeled with even-money bets: real slot results swing far more, so the Slots buttons link to the Slot Bankroll Survival Calculator, which models slot volatility with calibrated payout presets.
- Bet sizing is fixed per hand for each simulated session (no progressive systems simulated).
- Intended to measure bankroll pressure and variance, not exact hand-level expectation for advanced strategies.
References
See the site pages for deeper explanations: How We Calculate Odds, Blackjack Bankroll Calculator.