A payout and its event probability must be read together. A rare large win can have a less favourable expectation than a more frequent smaller one. The examples use hypothetical units rather than recommending money stakes.
In this guide
Assumptions of the eight-deck model
Michael Shackleford’s eight-deck classic Punto Banco analysis gives approximately 45.8597% Banker wins, 44.6247% Player wins and 9.5156% ties. With five percent Banker commission, Player at 1:1, Tie at 8:1 and main wagers returned on ties, house edges are about 1.06%, 1.24% and 14.36% respectively. These figures do not automatically apply to banker-7.
Further reading: Michael Shackleford: Eight-deck baccarat analysis
Reconstruct the expectation
Original reconstruction from the rounded model probabilities: one unit on Banker wins 0.95 on a Banker win, loses one on a Player win and is unchanged on a tie. Thus 0.458597 × 0.95 − 0.446247 = −0.01057985, about a 1.058% long-run model disadvantage per unit wagered, not a fixed loss each hand.
For Player, the calculation is 0.446247 − 0.458597 = −0.012350. Fees and settlement rules are already part of that definition. House edge is neither the probability of losing a whole session nor the proportion of hands lost.
Eight-to-one and nine-to-one differ
Using the same rounded probabilities, Tie at 8:1 gives 0.095156 × 8 − 0.904844 = −0.143596. At 9:1 it gives 0.095156 × 9 − 0.904844 = −0.048440. The second pay table has a smaller disadvantage in this model, but not a positive expectation.
A staking sequence does not change a fixed payout
Original doubling sequence: 1, 2, 4, 8, 16, 32. Six losses total 63, with 64 required next. A finite balance and wager limits restrict the sequence. Pushes, commission and special Banker outcomes can additionally prevent a later win from recovering all previous losses.
A history of Banker and Player labels does not identify the remaining shoe composition. Cards are dealt without replacement within a shoe, but this does not imply a simple rule that a streak must be followed by its opposite.
Draw the right lesson from practice
Use our free chips to check values and settlements. Do not compare two short sessions and call the luckier setting a better strategy. A mathematical comparison must explicitly identify decks, drawing rules, commission, exceptions and all payouts.