Educational worksheet. How to calculate theoretical standard punto banco Banker expected return when hypothetical commission rates change from 4% to 5% or 6%.
Commission changes the payment, not the winning hand
A standard Banker wager in eight-deck punto banco often pays one unit of net profit less a 5% commission when Banker wins, loses one unit when Player wins and pushes on a tie. Commission does not change the cards, the automatic drawing tableau or the probability of Banker winning. To compare alternative commission rates correctly, hold the game format constant and change only the deduction on a winning Banker bet. This lesson uses hypothetical 4% and 6% examples for mathematics; it does not claim such rates are offered by a particular venue.
Start with three mutually exclusive outcomes
Michael Shackleford’s standard eight-deck baccarat analysis gives approximately Banker wins 0.458597, Player wins 0.446247 and Ties 0.095156. The entries sum to one. If a Banker win pays a net profit of 1 − c for commission fraction c, the expected net change per unit risked is E(c) = 0.458597 × (1 − c) − 0.446247. Ties contribute zero because the Banker stake pushes. The formula is for the normal Banker main wager; a Banker-six rule or an EZ Baccarat three-card-seven push requires a different calculation.
Worked comparison: 4%, 5% and 6%
At 4%, E = 0.458597 × 0.96 − 0.446247 = −0.005994, roughly a 0.60% house edge. At 5%, E = 0.458597 × 0.95 − 0.446247 = −0.010580, about a 1.06% house edge. At 6%, E = 0.458597 × 0.94 − 0.446247 = −0.015166, roughly 1.52%. These are expected values per unit wagered across a hypothetical large number of standard deals, not expected losses for any individual visit. The tiny differences from more precise published estimates arise from rounding the starting probabilities.
The algebraic break-even commission is not a game recommendation
Setting E(c) equal to zero gives c = 1 − 0.446247 / 0.458597, approximately 2.69%. That number is a mathematical threshold under the exact model stated, not a claim that a venue offers that rate or that a visitor can exploit it. An advertisement using the words “commission free” might instead contain another rule that reduces payouts. In Super 6, a Banker six may be paid differently; in EZ Baccarat a winning three-card Banker seven may push. Reading the actual table rules matters more than a headline rate.
A cash-ledger example
Consider a $100 hypothetical Banker stake under a standard 5% commission game. A winning outcome yields $95 net profit and returns the $100 principal; a losing outcome costs $100; a tie returns the $100 stake with zero net change. At 4% commission, the same winning Banker outcome yields $96 profit; at 6% it yields $94. The extra $1 per winning $100 stake is not one percentage point of house edge per hand, because Banker wins only about 45.86% of all standard deals. That is why the change in house edge for each commission percentage point is about 0.459 percentage points.
How to compare a real rule sheet
Record the number of decks, Banker payout rule, any special Banker total exceptions, whether tie pushes the main wagers and how fractional commission is settled. If any of these differ, do not use the three-row table above as if the games were identical. Also distinguish theoretical expected return from actual session results; short sequences have considerable variation.
Related lessons
5% Banker settlement ledger · Compare no-commission variants
Sources and methodology
Wizard of Odds — Baccarat Basics and game odds; Wizard of Odds — commission-free exceptions. Worked examples are hypothetical, not recorded casino results or predictive systems. Figures are educational estimates for stated rules, not live odds.
For adults in jurisdictions where gambling is legal. Learning the rules does not reduce the financial risks of gambling; stop if it causes harm.