The first serious study of card counting in baccarat came from Edward Thorp, the mathematician behind blackjack card counting, and William Walden. Their 1966 paper in the Journal of the American Statistical Association, "A Favorable Side Bet in Nevada Baccarat," found that side bets on a natural 8 or 9 could be beaten by counting cards. For Banker and Player they reached the opposite conclusion: in their words, there were theoretical favorable strategies, but none that was practical.
Sixty years later, the same split still holds. Here is what they did and how it compares with today's numbers.
What Thorp and Walden studied in baccarat
In the 1960s some Nevada baccarat tables offered a side bet paying 9 to 1 if a hand made a natural 9, and similar bets on natural 8s. Thorp and Walden worked out how the chance of a natural changes as cards leave the shoe. The main input was simple: how many cards are left, and how many of them are 9s.
When enough 9s remained late in a shoe, the chance of a Banker natural 9 rose above one in ten. At 9 to 1, that made the bet positive. They used the Kelly criterion to decide how much to bet in those spots.
| Chance per hand | House edge | |
|---|---|---|
| Banker natural 9, 8 decks | 9.49% | 5.10% |
| Banker natural 8, 8 decks | 9.45% | 5.47% |
| Banker natural 9, 1 deck | 9.65% | 3.47% |
Those are today's fresh-shoe numbers for the same kind of bet. At the start of a shoe, a 9 to 1 natural bet loses about 5% of what you wager. It only turns positive after the right cards have left, which is exactly what the counting tracked.
A natural bet starts about 5% behind and only turns positive after the right cards leave.
Thorp and Walden found that a side bet could swing positive. Banker and Player could not, in any practical way.
Why the main bets were not worth counting
Banker and Player react weakly to removed cards. Their paper put it as theoretical favorable strategies but none currently practical. Our own calculation agrees. Even if all 32 fours were gone from an 8-deck shoe, Banker would still carry a 0.74% house edge. The full numbers are in baccarat card removal effects.
Removing an entire deck's worth of one card barely moves Banker or Player.
Thorp's name also appeared in a 1964 Sports Illustrated article on his gambling work, which reported a baccarat team that was ahead and had been barred from two casinos. That article is about blackjack mostly. The baccarat research is the 1966 paper.
The same idea in today's side bets
Whether or not a table offers a natural bet today, the same pattern repeats with modern side bets. Dragon 7 and Panda 8 depend on very specific cards, so they react to the shoe much more than Banker and Player. That is why they can turn positive late in a shoe, briefly. See Panda 8 vs Dragon 7 for their odds and the Kelly criterion in baccarat for how sizing works.
The bets that react most to the cards are the narrow ones, not Banker and Player.
At the start of a fresh shoe every bet has a negative expected value. Only the cards left in the shoe can change that, and only briefly. Betting systems can't. Counting doesn't make any single hand safe either. A positive bet still loses most of the time when it pays 9 to 1 or more.
Do the counting without pen and paper
Thorp and Walden had to count by hand. Today the math can run after every hand.
After each hand you enter the cards and tap Calculate, and Baccarator recalculates the odds and expected value for Banker, Player, Tie, pairs and side bets from the cards still in the shoe. If a bet briefly turns positive, it shows a Kelly sizing suggestion. That only appears when expected value is positive, it is a long-run average, and the next hand can still lose. Positive moments are rare and short. You can choose 6 or 8 decks and practice with virtual chips, with no real money involved.
Baccarat card counting history FAQ
Who first studied card counting in baccarat?
Edward Thorp and William Walden, in "A Favorable Side Bet in Nevada Baccarat," Journal of the American Statistical Association, 1966.
Did Thorp beat baccarat?
His work with Walden showed that natural 8 and 9 side bets could be beaten by counting. They concluded that counting the main Banker and Player bets was not practical.
Does card counting work in baccarat today?
Not for Banker and Player. Some side bets can briefly turn positive late in a shoe, and any single hand can still lose.
Baccarator is a math tool for education. No real-money gambling. 18+ only.
