Baccarat Probability Calculator

Open the Baccarat Probability Calculator and leave Bet Type on the default, Banker. That is the only input: Banker, Player, or Tie. Press calculate. With Banker selected the tool returns Win Probability 45.86% and House Edge 1.06%. Those two figures are the standard eight-deck punto banco results after the 5% commission on winning banker bets is taken into account. They are not estimates from a short shoe; they are the published composition-dependent probabilities used by card-counting literature since Edward Thorp and Peter Griffin tabulated the game.

Switch Bet Type to Player. Win Probability drops to 44.62% and House Edge rises to 1.24%. Player pays even money with no commission, yet it still loses more often than Banker because the drawing rules are asymmetric: Banker acts last and stands or draws according to a tableau that slightly favours the banker's two-card total. The 1.18 percentage-point gap between the two win rates is exactly why casinos can offer Banker at 19-to-20 (a 5% tax) and still keep a thinner edge than Player.

Switch to Tie. Win Probability is 9.52% and House Edge is 14.36%. A typical tie pays 8-to-1. Fair odds on a 9.52% event would be about 9.50-to-1, so the posted 8-to-1 price is a 14-plus-percent tax. Do not treat a streak of player or banker decisions as evidence that a tie is "due." The calculator does not simulate a depleting shoe or a side bet; it reports the long-run frequency of each main-bet outcome under an eight-deck wash.

Use the three-way comparison as a table-selection filter. If a live table offers Banker at no commission, the edge on that bet collapses toward zero and can even flip slightly positive depending on the remaining cards; this tool will still show 1.06% because it assumes the standard 5% commission. If a table pays 9-to-1 on Tie instead of 8-to-1, the 14.36% figure is too pessimistic. Read the felt, then interpret the output. The calculator is a lookup of canonical math, not a shoe tracker.

After you have the three rows in your head — Banker 45.86% / 1.06%, Player 44.62% / 1.24%, Tie 9.52% / 14.36% — you can price any proposition that is a linear combination of those events. A banker-or-tie "either" wager, an insurance-style player pair, or a dragon bonus all inherit these base frequencies. Start here, then layer the side-bet paytable on top rather than treating a colourful felt as a new game.

Baccarat is a comparison of two two-to-three-card totals, each taken modulo ten, with no player decisions after the bet is placed. The modern casino product is punto banco: the house banks every hand, a shoe of six or eight decks is used, and a printed tableau dictates third-card draws. Chemin de fer, the European ancestor still dealt in a few French and Italian rooms, rotates the bank among players and lets the banker choose whether to draw on five. The probabilities in this calculator are for punto banco with an eight-deck shoe and a 5% commission on winning banker bets, which is the default in Macau, Las Vegas, and most online studios.

The game's reputation as a "rich person's coin flip" is mathematically fair. Banker wins about 45.86% of settled hands, Player 44.62%, and the rest tie. After commission, the house keeps just over one percent of banker action and about 1.24% of player action. That is thinner than American roulette, most craps proposition bets, and every keno ticket, which is why baccarat became the volume engine of high-limit rooms. It is not a skill game in the blackjack sense. The tableau is mandatory. Card counting can theoretically flag a rare positive-count banker or player bet, but the bet-spread required is so large, and the edge so small, that Thorp, Griffin, and later Stanford Wong all described it as a curiosity rather than a profession.

Side bets are a different species. Player pair, banker pair, either pair, lucky six, dragon seven, and the countless "super six" variants carry house edges from the high single digits into the twenties. This calculator ignores them on purpose. If you need pair frequencies you must count the combinatorial ways two hole cards match by rank in an eight-deck shoe, which is a different generating function. Mixing a 1.06% main bet with a 10% pair bet in the same session does not "average" to 5.5%; the pair bet dominates the expected loss because it is a larger edge applied to the same chip.

History matters for interpreting the numbers. French baccarat and chemin de fer used a different drawing culture and often a single-deck or three-deck source. Macau's squeeze ritual and the English "banco" shout do not change the combinatorics of an eight-deck shoe. Online RNG baccarat that shuffles every hand is even closer to the infinite-deck limit, which moves the three probabilities by a few hundredths of a percent. The 45.86 / 44.62 / 9.52 split quoted here is the eight-deck, no-cut-card, full-composition figure that professional literature treats as the reference.

Limits of the tool: it does not adjust for a cut card that burns fifteen or twenty cards, for a continuous shuffler, for no-commission banker that pushes on a six, or for a 50% commission on banker six (the "super six" main-bet variant). Those rule forks each move the banker edge by a few tenths of a percent. Treat 1.06% as the headline number for standard punto banco, then read the table's posted exceptions before you scale a session's expected loss.

Punto banco probabilities on an eight-deck shoe are the output of a full enumeration of the drawing tableau, not of a night's bead plate. Banker wins 45.86 percent of hands, with a 1.06 percent house edge after the 5 percent commission on winning banker bets. Player wins 44.62 percent, with a 1.24 percent edge. Tie occurs 9.52 percent of the time and, paid at eight to one, carries a 14.36 percent edge. Edward Thorp's early computer counts and Peter Griffin's combinatorial enumerations agree to two decimals on those eight-deck frequencies. The tableau is what breaks the symmetry between Banker and Player.

Derivation of the edges from the frequencies. Let p_B, p_P, and p_T be the probabilities of banker win, player win, and tie, summing to one. On a commission table a winning banker unit returns 0.95 of net profit, a winning player unit returns 1, and a tie typically pushes Banker and Player while paying eight to one on the tie wager. House edge on Banker is one minus (p_B times 1.95 plus p_T times 1), because a tie returns the banker stake. With p_B equal to 0.4586 and p_T equal to 0.0952 that expression is about 0.0106, the 1.06 percent on the page. Player edge is one minus (p_P times 2 plus p_T times 1), about 0.0124. Tie at eight to one is one minus (p_T times 9), about 0.1436, because a winning tie ticket is worth nine units including stake.

Tableau rules that generate the 1.24-point frequency gap. Player draws a third card on totals 0 through 5 and stands on 6 and 7. Banker then draws or stands as a function of its two-card total and, when that total is 3, 4, 5, or 6, as a function of Player's third card. That extra information is worth roughly 1.24 percentage points of win frequency, which the 5 percent commission almost exactly harvests, leaving a residual 1.06 percent tax. Natural eight-deck multisets, not Monte Carlo noise, are what pin the two-decimal display. Six-deck and infinite-deck figures move in the fourth decimal for most purposes.

Worked default. Select Banker: 45.86 percent and 1.06 percent. On a 100-unit banker bet the expected leak is 1.06 per coup. One hundred coups expected-lose 106, independent of any pattern believed to live in the bead plate. Switch to Tie: expected leak 14.36 per 100, more than thirteen times the banker tax. Player sits between them at 1.24. The bead plate is a scoreboard. Independent coups with a tiny serial correlation from a finite shoe do not create a detectable edge without a true-count apparatus and a gigantic spread.

Assumptions. Eight decks. Standard drawing tableau. Five percent commission on banker wins. Tie paid eight to one, not nine to one; a nine-to-one tie would shrink that edge and is not the figure printed here. No pair side bets, no dragon bonuses, no eza. Wong's later tournament notes reuse the same two-decimal frequencies. The enumeration is the lecture. Superstition about Banker after a Player run is not.