Weighted House Edge in Baccarat: A Mixed-Wager Cost Worksheet

A table's advertised “house edge” is usually quoted per type of bet, not for an entire mixture of Banker, Player and Tie wagers. When several bet types are combined, the expected cost of the total money wagered depends on how much is assigned to each. This article demonstrates the arithmetic with a fictional £100 total—without suggesting that mixing bets improves the chance of winning.

Start with a clearly defined reference game

For standard eight-deck punto banco with a 5% Banker commission and a Tie wager paying 8-to-1, the Wizard of Odds reference tables give approximate house edges of 1.0579% on Banker, 1.2351% on Player and 14.3596% on Tie. These are long-run expected losses relative to amounts staked, not promises about individual results. Different rules and payouts change the figures.

A fictional £100 split across three wager types

Imagine a theoretical allocation of £50 to Banker, £30 to Player and £20 to Tie. We are analysing the financial exposure, not recommending those bets. Apply each edge to that wager's stake: Banker expected loss is £50 × 0.010579 ≈ £0.529; Player is £30 × 0.012351 ≈ £0.371; Tie is £20 × 0.143596 ≈ £2.872. Add them: £0.529 + £0.371 + £2.872 ≈ £3.771 expected loss on £100 total staked.

Thus the stake-weighted house edge is approximately 3.77%, even though two of the three individual bets have much lower quoted edges. The reason is that the £20 Tie allocation contributes over £2.87 of the expected cost.

What the formula means

If stakes are S₁, S₂ ... and edges are h₁, h₂ ..., then total expected loss = Σ(S × h). Divide by total amount staked for the weighted edge. Because expected values are additive, the formula still works if the bets occur in the same round, even though their outcomes are related. Correlation affects the range of actual results, not this sum of expectations.

Do not confuse turnover with the initial budget

A person can stake more than their starting balance over a session by repeatedly staking amounts. If £100 is staked in total, the worksheet uses £100 as the denominator; it does not infer a £100 deposit, bankroll or guaranteed loss. See our RTP, turnover and expected-loss guide for those accounting distinctions.

What if the paytable is different?

A Tie paying 9-to-1 instead of 8-to-1 has a different expected value; a non-commission Banker rule may replace the standard 5% charge with a conditional payout restriction. Recompute every component using the actual table rules. Our Tie payout comparison shows why the quoted price matters.

What the calculation is good for

The worksheet is a way to assess theoretical cost and avoid treating an average house edge as a universal property of “baccarat.” It cannot forecast the result of the next hand. A mixed collection of negative-expectation wagers remains negative in expectation; diversification across them does not create a winning system. For adults choosing to engage, spending limits and a willingness to stop are more useful than attempts to optimise a progression.