Where the Banker Edge Comes From: The Math of Baccarat in Plain Numbers

Baccarat is the simplest card game on the casino floor. You pick a side, Player or Banker, and the dealer does everything else. There are no decisions after the bet, so the whole game is arithmetic, and the arithmetic is worth knowing.

This article walks through it with figures computed by enumerating every possible hand from an eight-deck shoe under the standard drawing rules, which is how the probability calculator at Baccarat.gg produces its numbers.

Three bets, Three Very Different Prices

Out of every 10,000 hands dealt from an eight-deck shoe, Banker wins 4,586, Player wins 4,462 and 952 are ties. Set the ties aside, since they push the two main bets, and Banker wins 50.68 percent of decided hands to Player's 49.32 percent.

That is the whole story of the game, and the pay table is built around it.

Player pays even money. Because Player wins slightly less often than it loses, the house edge on a Player bet is 1.24 percent. Over a long run, a player betting 100 units a hand on Player gives up about 1.24 units a hand.

Banker also pays even money, less a 5 percent commission on winning bets. The commission exists because Banker wins more often than it loses; without it a Banker bettor would have the edge over the house. With the commission, Banker's house edge is 1.06 percent, the lowest of the three.

Tie pays 8 to 1 at most tables. A tie comes up 9.52 percent of the time, so a fair payout would be about 9.5 to 1. At 8 to 1 the house edge is 14.36 percent, more than thirteen times the Banker figure. Some tables pay 9 to 1, which brings the edge down to 4.84 percent. Still the worst bet on the layout, but no longer the worst by a mile.

Why Banker Wins More Often

The two sides are dealt the same way, two cards each, with tens and face cards counting zero and totals above nine losing their first digit. The difference comes entirely from the third-card rules.

Player goes first and follows one rule: draw on a total of 0 to 5, stand on 6 or 7. Banker goes second, and when Player has drawn, Banker's decision depends on what Player's third card was. Banker with a 3 draws against anything but an 8. Banker with a 4 draws against a 2 through 7. Banker with a 5 draws against a 4 through 7. Banker with a 6 draws only against a 6 or 7. Banker with 7 always stands.

Take a hand where Player holds a 5 and Banker holds a 4. Player must draw. Suppose the third card is an 8, which drops Player to a total of 3. Banker's rule says a 4 stands against an 8, so Banker keeps its 4 and wins the hand without taking a card. Reverse the situation and Player, who had to act first without seeing anything, would have had no such option.

This is the entire source of the Banker advantage. The rules were set so that the side acting last acts on more information, and the 5 percent commission was the casino's way of charging for it.

What the Commission Really Does

A 5 percent commission on winning bets is not the same as a 5 percent house edge. Banker only wins about 45.86 percent of hands, so the commission costs the bettor 5 percent of that, about 2.29 percent of all money wagered. Banker's natural advantage over Player, 1.24 percent before commission, cancels part of that, leaving the 1.06 percent edge.

Run the figures the other way and you find the break-even point. A commission of about 2.7 percent would leave Banker exactly even with the house. Nobody charges that, but some tables charge 4.9 percent instead of 5, and the Banker edge there is 1.01 percent, which is worth a few hundredths of a percent to a high roller and nothing at all to anyone else.

The more common variation is no commission at all, with one catch: a Banker win on a total of 6 pays half. That total comes up on 5.39 percent of all hands, roughly one Banker win in eight, and losing half the payout on those hands raises the Banker edge to 1.46 percent, worse than Player. The version in which a Banker three-card 7 pushes instead of paying, sold under names like EZ Baccarat, lands at 1.02 percent, almost exactly the commission game. The payouts page at Baccarat.gg lists these side by side with the common side bets.

What a Session Looks Like

An edge of 1.06 percent is small enough that no single evening will show it to you. To see what the figures do over time we dealt 100,000 hands from a reshuffled eight-deck shoe with the baccarat simulator at Baccarat.gg, betting one unit on Banker every hand and, separately, one unit on Player.

Banker won 45,563 hands, Player 44,781, and 9,656 were ties, each within a few tenths of a percent of the exact figures. The Banker bettor finished 1,496 units down, 1.50 percent of money wagered; the Player bettor finished 782 units down, 0.78 percent. Neither result matches the long-run edge, and that is the point: after 100,000 hands the expected spread is still plus or minus about 0.6 percentage points, so the better bet can trail the worse one for a very long time. The edge is a statement about the price, not a forecast of any run.

Over a shorter horizon the picture is more familiar. In 100,000 simulated sessions of 100 hands each at flat Banker bets, the bettor finished ahead 44.6 percent of the time. Nearly half of all sessions are winners. All of them are played at a loss of about one unit per hundred wagered.

Why Systems and Patterns Change Nothing

Every bet on the layout carries its own price, and the price is set by the drawing rules and the pay table, not by what happened on the previous hand. Raising the stake after a loss, or after a win, changes how the losses are distributed between sessions; it cannot change the average. The scoreboard patterns casinos display are a record, not a signal. If you want to test that for yourself, the predictor tool at Baccarat.gg lets you pit the common pattern methods against random deals over as many hands as you like, and scores them against the range a fair coin would produce.

The practical conclusion is short. Bet Banker if you want the lowest price, bet Player if the commission bothers you and you accept paying 0.18 percent more for the privilege, and treat the Tie as the long shot it is. Everything else at the table is presentation.