The rules, as written in the engine
Baccarat is a game with no choices after the chips go down. Two hands, Player and Banker, get two cards each. Cards count at face value, aces as one, tens and faces as zero, and only the last digit of the total matters. Whichever hand is closer to nine wins. A fixed table decides whether either hand takes a third card. Because nobody decides anything, the probability of every outcome is a finite sum — which makes baccarat one of the few casino games that can be priced exactly rather than estimated.
That last line matters. The demo deal draws every card with replacement, as if from an infinite deck: each rank is one in thirteen on every card, ten-valued cards four in thirteen. That is the deal priced below. The real-money deal is produced by the house service and verified from its ticket; the payouts are the same, and the last section shows how much the figures would move on a finite shoe.
Who wins, and how often
| OUTCOME | EXACT FRACTION | PROBABILITY | ABOUT |
|---|---|---|---|
| Banker wins | 2,212,744 / 4,826,809 | 45.8428% | 1 in 2.18 |
| Player wins | 2,153,464 / 4,826,809 | 44.6147% | 1 in 2.24 |
| Tie | 460,601 / 4,826,809 | 9.5426% | 1 in 10.48 |
Exact enumeration over up to six cards with the engine’s drawing rules, cross-checked against three million deals run through the demoDeal function itself. Excluding ties, Banker takes 50.68% of decided hands.
| EVENT | PROBABILITY |
|---|---|
| A natural (either hand 8 or 9 on two cards) | 34.28% |
| Player draws a third card | 50.37% |
| Banker draws a third card | 43.58% |
| Deal ends with 4 cards | 37.87% |
| Deal ends with 5 cards | 30.32% |
| Deal ends with 6 cards | 31.81% |
Banker wins more than Player for one reason: it acts second. Player’s rule looks only at Player’s own total. Banker’s rule looks at its own total and at the card Player just drew, and the table is built so Banker draws when that card makes drawing favourable and stands when it does not. The advantage is about 1.23 points of win probability, and it is all information.
Five spots, priced
| SPOT | PAYS | WINS | HOUSE EDGE | EDGE PER DECIDED HAND | COST PER 100 BETS OF 10 |
|---|---|---|---|---|---|
| Banker | 0.95 : 1 | 45.84% | 1.0640% | 1.1762% | 10.64 |
| Player | 1 : 1 | 44.61% | 1.2281% | 1.3577% | 12.28 |
| Tie | 8 : 1 | 9.54% | 14.1170% | — | 141.17 |
| Player pair | 11 : 1 | 7.69% (1 in 13) | 7.6923% | — | 76.92 |
| Banker pair | 11 : 1 | 7.69% (1 in 13) | 7.6923% | — | 76.92 |
House edge is the expected loss as a share of the amount staked, counting a tie as a returned stake. The per-decided-hand column divides by the 90.46% of deals that are not ties, for readers comparing with tables that quote it that way. Cost is the expected loss in units.
The ordering is the whole strategy the game has. Banker is the cheapest bet on the table, Player close behind, and the gap between them is 0.16 points. Tie costs about thirteen times as much as Banker per unit staked. The pair bets sit in between, and they are the ones whose price depends most on how the cards are dealt.
Backing Player and Banker at the same time, with equal stakes, does not hedge anything. Whichever side wins, the other loses, the commission is taken on Banker’s wins, and a tie returns both. The combined position loses 1.15% of the total staked — the average of the two edges — and the combined position can never finish a hand ahead.
Why Banker pays 0.95
| COMMISSION | BANKER PAYS | PLAYER’S EXPECTED RESULT PER UNIT |
|---|---|---|
| None | 1 : 1 | +1.2281% |
| 2% | 0.98 : 1 | +0.3113% |
| 2.5% | 0.975 : 1 | +0.0821% |
| 3% | 0.97 : 1 | −0.1471% |
| 4% | 0.96 : 1 | −0.6056% |
| 5% (this engine) | 0.95 : 1 | −1.0640% |
Break-even commission: 1 − P(Player) ÷ P(Banker) = 2.68%. Below it the Banker bet would favour the player.
Paid at even money, Banker would be a bet the player wins over time — the reverse of Player, and by exactly the same margin, because Banker’s win is Player’s loss. The commission exists to take that back and a little more. Anything above 2.68% makes Banker a house bet; the traditional 5% leaves it at 1.06%, still below Player’s 1.23%. The commission is not a tax on winning. It is the price of the information Banker’s drawing rule has and Player’s does not.
The Tie bet shows the same arithmetic from the other side. A tie comes up once in 10.48 deals, so a fair Tie bet would pay about 9.48 to 1. At 8 to 1 the edge is 14.12%. For comparison only, a table paying 9 to 1 on the same deal would charge 4.57%; this engine pays 8 to 1.
What a finite shoe would change
| SPOT | INFINITE DECK (DEMO DEAL) | EIGHT-DECK SHOE | SIX-DECK SHOE |
|---|---|---|---|
| Banker | 1.0640% | 1.0579% | 1.0558% |
| Player | 1.2281% | 1.2351% | 1.2374% |
| Tie | 14.1170% | 14.3596% | 14.4382% |
| Either pair | 7.6923% | 10.3614% | 11.2540% |
Shoe figures are exact enumerations of a freshly shuffled shoe with cards drawn without replacement, for comparison. They are not a statement about how the real-money deal is dealt.
For the three main spots, the number of decks barely matters: Banker and Player move by less than a hundredth of a point between an infinite deck and eight decks. The pair bets are different. A pair needs the second card to match the first card’s rank, and in a finite shoe the first card has already used up one of that rank. On an infinite deck the chance is exactly 1 in 13; in an eight-deck shoe it is 31 in 415, and at the same 11 to 1 payout the edge rises from 7.69% to 10.36%.
Player 1:1, Banker 0.95:1, Tie 8:1, pairs 11:1 — Banker is the narrowest edge on the tableBaccarat →
What is the house edge on Banker in baccarat?
On this engine’s deal, with Banker paying 0.95 to 1, the house edge is 1.06% of the amount staked (1.18% if ties are excluded). On a standard eight-deck shoe the same rules give 1.058%.
Is it better to bet Banker or Player?
Banker costs less: 1.06% against 1.23% on Player, even after the 5% commission. Banker wins 45.84% of deals and Player 44.61%, because Banker’s drawing rule can react to Player’s third card.
Why does the Banker bet charge a commission?
Without it Banker would favour the player by 1.23%. Any commission above 2.68% turns it back into a house bet; the 5% commission leaves a 1.06% edge.
What are the odds of a tie in baccarat?
A tie comes up in 9.54% of deals, about once in 10.48. The Tie bet pays 8 to 1 here, which gives it a 14.12% house edge — the most expensive main bet on the table.
Are the pair side bets worth it?
They cost more than Banker or Player. A pair comes up 1 time in 13 on the engine’s demo deal and pays 11 to 1, an edge of 7.69%. On an eight-deck shoe the chance drops to 31 in 415 and the edge rises to 10.36%.
- Betkyo engine source: SPOT_PAYOUT, demoDeal() and the demo settlement in baccarat/baccaratApi.ts (payouts, third-card rules, ties returning Player and Banker stakes, pairs by matching rank, independent card draws)
- Exact calculations written for this article: full enumeration of the drawing rules on an infinite deck and on six- and eight-deck shoes without replacement, commission and tie-payout sweeps, and a three-million-deal run of demoDeal as a cross-check
