How long a run of banker really lasts

Baccarat streaks are runs of the same winner: banker five times, player four times, and so on. They feel like information. They are not. Each hand in an 8-deck shoe starts from almost the same odds, and long runs show up in most shoes simply because a shoe has dozens of hands. Below are the numbers: how likely a run is from any given hand, how likely it is somewhere in a whole shoe, and what the scoreboard can and cannot tell you.

The odds behind every hand

Everything on this page starts from three figures. They are the standard 8-deck probabilities published by Wizard of Odds, which counts every possible deal:

The right-hand column matters for runs. On the Big Road, a tie does not end a streak: it is marked as a line on the last circle and the column carries on. So when players talk about "six bankers in a row", they mean six decided hands with no player win between them. Divide banker's 45.86% by the 90.48% of hands that are not ties and you get 50.68%. Wizard of Odds' own runs appendix sets ties aside the same way.

Banker is a slight favourite to win any decided hand. That is also why the house charges a 5% commission on banker wins: after commission, banker still costs you 1.06% of each stake and player 1.24% (see banker or player).

How likely is a run of N from here

The simplest question about baccarat streaks: you are at the table now, ties aside. What is the chance the next N decided hands all go one way? Multiply the single-hand chance by itself N times.

Formula: 0.5068 to the power N for banker, 0.4932 to the power N for player. Our calculation from the figures above.

Seen from one starting point, a ten-run looks rare. One in 894 is the kind of figure that makes a dragon on the board feel remarkable. But a shoe gives a run dozens of places to start, and that changes the picture completely.

Baccarat streaks across a whole shoe

A cut 8-deck shoe gives a few dozen hands. We used 70 as a round figure and asked: what is the chance that a run of length N or more appears at least once anywhere in those 70 hands?

Our calculation. Method: an exact Markov chain over 70 hands, where each hand is banker (45.86%), player (44.62%) or tie (9.52%). Banker or player extends or resets the current run; a tie leaves it as it is. Hands are treated as independent. A run of 200,000 simulated shoes gave the same figures to within a few tenths of a point.

Read the table against the per-hand one. A banker seven-run is a 0.86% event from any single starting point, yet nearly one shoe in four (22.5%) contains one. A run of seven or more on either side, the kind that turns the corner on the Big Road and gets called a dragon, appears in 38.2% of shoes. Over an evening of three or four shoes, seeing one is the normal case.

So baccarat streaks of five or six are not the shoe "running hot". A shoe without one would be the more unusual sight: about one shoe in nine has no five-run on either side.

Dragons, chops and why baccarat patterns don't predict

The names on the board describe shapes in past results. A dragon is a long column. A chop is banker and player alternating. Both are ordinary features of random sequences, and they are about equally common. Using the same 70-hand model:

• a chop of eight or more alternating results appears in 20.6% of shoes;
• a run of eight or more on one side appears in 20.7%.

Neither shape changes the next hand. After five banker wins, the sixth decided hand goes to banker about 50.68% of the time, the same as after five player wins or after a chop. The chance of six bankers in a row was about 1 in 59 before the first one landed. Once five have landed, only the last hand is left to happen, and its odds are the usual ones.

Strictly, baccarat hands are not perfectly independent: cards leave the shoe and are not replaced, so the odds drift slightly as the shoe goes on. That drift depends on which ranks have been dealt, not on who won. A column of red circles says nothing about which ranks are left. How small those shifts are, and why they do not pay at online tables, is covered in baccarat card counting.

The gambler's fallacy, in two forms

Betting on baccarat streaks usually rests on one of two opposite beliefs.

1. "Player is due." After a long banker run, the other side must catch up. It does not need to: the shoe has no memory of the circles, and over 70 hands a small lead for one side is routine.
2. "Banker is hot." A run will keep going because it has started. It will not do so any more often than 50.68% per decided hand.

Both cost money in a quiet way. Betting player to break a dragon swaps a 1.06% edge for a 1.24% edge. Raising the stake because a streak "has to end" increases the total you put through the table, and the expected loss is always total staked times the edge. Betting systems that grow after losses run straight into the run lengths in the table above; baccarat strategy works through Martingale and its relatives with numbers.

Following baccarat patterns is fine as a way to pick a side for fun, as long as the stake stays the same whichever circle you are reading.

The score counts what each casino publishes about its licence, ID checks and withdrawal limits, not how its baccarat lobby looks.

What the scoreboard is good for

A scoreboard is a record, and records are useful for things that are not predictions:

• Counting hands. You can see how far into the shoe the table is and how many rounds you have played.
• Counting ties. In 70 hands you would expect about 6.7 ties. If you are tempted by the tie, the board shows how rare it is in practice, and the tie bet page shows its 14.36% edge.
• Checking pace. Rounds per hour drive your cost per hour more than any side choice.
• Spotting your own tilt. If you notice you are reading the board to justify a bigger bet, that is the signal to stop.

How each board is drawn, from the Bead Plate to the derived roads, is explained on reading the Big Road.

Checklist before you bet on baccarat streaks

1. Is the stake the same as before the run began? If not, why?
2. Are you switching to player only to break a banker run? That costs 0.18% more per bet.
3. Have you set a loss limit and a time limit for this session?
4. Would you make the same bet on a fresh shoe with an empty board? If yes, the streak is irrelevant to it; if no, the streak is driving the decision.
5. Does the table you play at pay out to your own wallet without long holds? That question matters more than any column of circles.

If a session stops being fun, the responsible gambling page lists where to get help.

Questions and answers