Baccarat Streaks, Stats and Score Boards

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The game of baccarat lends itself well to mathematical analysis. There are only two basic bets, Player or Banker, and a finite number of outcomes that produce wins, losses and ties. Anyone who has played the game has noticed that the number of times the Banker wins tends to be roughly equal to the number of times the Player wins, but often with considerable streakiness. Studying the probability of results can help shed some light on what to expect in the course of play.

Probability of Winning Runs

Because the Banker hand follows the Player hand in order of play, it is slightly more likely to win on any given deal. When six decks of cards are in play, the exact probability of the Banker winning the deal is 45.87% versus 44.63% for the Player. The remaining 9.51% of all deals can be expected to result in a tie. If ties are treated as non-events, the Banker hand can be expected to claim 50.68% of all wins, while the Player hand will win 49.32% of the time.

Since the probable results of a hand of baccarat are skewed slightly toward the Banker, the likelihood of consecutive wins by the Banker hand is similarly tilted in the Banker’s favour. Specifically, there is a 12.67% chance of exactly two Banker wins in a row versus 12.33% for the Player hand. This unbalance becomes even more pronounced as the number of wins in a row becomes greater, namely 6.42% vs. 6.08% for three wins, 3.25% vs. 3.00% for four wins, 1.65% vs. 1.48% for five wins, and so on.

Basic Statistics

Because the Player hand is exposed before the Banker’s cards are revealed, it is possible to predict with some accuracy the likelihood of the Player hand winning for certain totals. For example, when the Player hand totals zero on the first two cards with eight decks in play, the probability of winning is just 27.88%, the probability of losing is 65.46% and the likelihood of a tie is 6.66%. The Player’s odds improve with each additional point held on two cards, from a 28.28% chance of winning on one point to 29.03% on two points, 30.34% on three points, etc. The odds do not tip in the Player’s favour until the total reaches six points, which explains why the Player hand always hits on totals of 0~5.

Those who seek to gain some advantage in playing baccarat by counting cards may wish to know the effect of certain cards removed from the deck. Unlike blackjack, in no case does the removal of any card, 0~9, shift the odds of winning in favour of the Player hand. The Banker always holds the advantage. But removal of 6’s or 7’s tends to reduce the number of Ties, while the absence of small cards, 2~4, aids the Banker.

Keeping Score

Baccarat tables of the past used to provide participants with scoring sheets and two-colour pencils with red and blue tips to help keep track of hands played, Nowadays, of course, most table feature electronic score boards to serve that function. The displays feature the results of each hand played since the start of the shoe. Most serious players ignore these, knowing that the odds do not change much from hand to hand and that past history is no predictor of the future. However, superstitious player rely on the score boards to identify streaks and patterns that are presumed to be auspicious.

On most such score boards, Player hand wins are marked as blue circles, Banker hand wins are in red and Ties may be identified in green or as slash marks. Many have numeric running counts of the number of wins for each hand on display, too. The electronics do not, however, keep track of what cards have been played.

Published on: 25/11/2013

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