Scoreboards, streaks and the gambler's fallacy
The scoreboards record the past. They can't predict the next hand.
Open this lesson in baccaratton — free, play money
Walk past any baccarat table and you'll see glowing scoreboards full of red and blue circles. Casinos provide them because players love them. Here's how to read them, and what they can and can't tell you.
Bead Plate. One bead per hand, in order: down the column, then on to the next column. Each bead is labelled B (Banker), P (Player) or T (Tie). Red is Banker and blue is Player, but the letter is always there, so you never need the colour.
Big Road. The same results, grouped into streaks. Each column is a run of the same winner: Banker, Banker, Banker goes down one column, and the moment Player wins, a new column starts. Ties don't start a column. They're marked as a slash or a number on the last bead. A long column is a "dragon".
Derived roads (Big Eye Boy, Small Road, Cockroach Pig) are drawn from the Big Road. They compare the length of each column with columns one, two or three to the left, and mark red for "repeating" and blue for "choppy". The app explains them in More → Roads but doesn't draw them. They're patterns of patterns, and they carry no more information than the Big Road.
The gambler's fallacy. After six Bankers in a row, it feels as if Player is due, or that the Banker is "hot". Neither is true. The cards don't remember who won. After a run of Bankers, the next hand is still Banker 45.86%, Player 44.62%, Tie 9.52%, give or take a few hundredths of a percent from the cards already used.
Streaks are just what randomness looks like. In a shoe of about 73 decided hands:
| A run of at least… | happens in about this share of shoes (≈ approx.) |
|---|---|
| 5 | 92% |
| 6 | 69% |
| 7 | 43% |
| 8 | 24% |
| 10 | 6% |
The longest run in a shoe averages about 6.5 hands. Seeing a "dragon" is normal. It doesn't mean the shoe is biased.
Show the math: Is each hand really independent?
Almost. The shoe is dealt without replacement, so each card used changes the odds very slightly. Removing one card from a fresh 8-deck shoe moves the Banker's EV by at most 0.012% (removing a 4 helps the Banker most, removing a 6 hurts it most; lesson 17). The winner of the last hand says almost nothing about which cards were used, so the effect of a streak is smaller still. The table above assumes independent hands with P(Banker | decided) = 279815987114/552096050907 ≈ 50.68%, and is a dynamic-programming result.
Quiz
Banker has won seven in a row. What's the chance the next hand is Banker?
- Much lower: Player is due
- Much higher: Banker is hot
- About 45.9%, the same as always
- 50%
Show the answer
C: About 45.9%, the same as always. The cards have no memory. Past results don't change the next hand's odds in any useful way.
Quiz
On the Big Road, what does a new column mean?
- A tie
- The winner changed
- A new shoe
- A natural
Show the answer
B: The winner changed. Each column is a streak. A new column starts when the other side wins.
Quiz
In a typical shoe, how unusual is a run of 6 or more?
- Very rare, under 5% of shoes
- It happens in most shoes
- It never happens
Show the answer
B: It happens in most shoes. About 69% of shoes have one.