What is Probability

Probability is a concept in mathematics and statistics used to measure the likelihood of a certain event occurring. In the game of baccarat, probability refers to the ratio or chance that a specific betting outcome will occur among all possible outcomes.
Probability is typically expressed in the form of a decimal, percentage, or fraction. For example:

• The probability of the Banker winning is 0.458597 (approximately 45.86%), which means that over the long run, the Banker is expected to win about 45.86% of the time.

Mathematical Definition of Probability:

In mathematics, the formula for probability is:

• P(E) = Number of favorable outcomes for event E / Total number of possible outcomes
• Number of favorable outcomes for event E: Refers to the number of possible cases where event E occurs.
• Total number of possible outcomes: Refers to all possible outcomes in the game.
  
  For example, in baccarat, the probability of "Banker Win" is calculated based on the proportion of outcomes where the banker wins among all possible game results.

Application of Probability in Baccarat:

In the game of Baccarat, all outcomes are based on predefined rules and governed by randomness. Therefore, probability is a core concept when calculating the likelihood of Banker win, Player win, or Tie.

Probability Data in Baccarat:

Assuming a standard 8-deck shoe is used, the following probabilities have been calculated based on statistical data:

1. Banker Win:
   • Probability = 0.458597 (approximately 45.86%)
   • This means that in all games, the Banker wins in about 45.86% of the outcomes.
   
   
2. Player Win:
   • Probability = 0.446247 (approximately 44.62%)
   • This means that in all games, the Player wins in about 44.62% of the outcomes.
   
   
3. Tie:
   • Probability = 0.095156 (approximately 9.52%)
   • This means that in all games, a Tie occurs in only about 9.52% of the outcomes.

Characteristics of Probability:

1. Range of Values:
   The value of probability lies between 0 and 1:
   • P(E) = 0: Indicates the event is impossible.
   • P(E) = 1: Indicates the event is certain to happen.
   • For example, the total probability of all possible outcomes in Baccarat must equal 1: P(Banker Win) + P(Player Win) + P(Tie) = 1
   
   
2. Certainty and Randomness:
   Probability describes the likelihood of a random event occurring. It cannot predict the outcome of a single game but reflects long-term trends. For example:
   • Although the probability of Banker winning is 45.86%, the Banker may not win in a single round.
   • If 1,000 rounds are played, the Banker is expected to win approximately 458 rounds (according to probability theory).
   
   
3. Mutual Exclusivity of Events:
   In Baccarat, Banker win, Player win, and Tie are mutually exclusive events, meaning only one of these outcomes can occur in a single round. The total probability of all outcomes is 1.

How to Use Probability to Support Betting Decisions?:

Probability helps players understand the likelihood of different betting options, allowing for more rational strategy development:

1. High-probability options are more stable:
   The Banker has the highest probability (45.86%) and the lowest house edge (1.06%), making it the most stable choice.
   
   
2. Low-probability options carry higher risks:
   The Tie has the lowest probability (9.52%) but offers a high payout (1:8). This type of bet attracts risk-seeking players, but long-term betting tends to result in losses due to its high house edge (14.36%).
   

How to Use Probability to Support Betting Decisions?:

1. Probability and Odds:
   Odds are designed based on probability. For example:
   The Banker bet has a higher probability, so the casino offers odds of 1:0.95 and charges a 5% commission.
   The Tie bet has the lowest probability, so the casino offers higher odds of 1:8 to attract players.
   Probability and Expected Value:
   By combining probability with odds, players can calculate the Expected Value (EV). For example:
   
   
2. Banker Expected Value:
   P(Banker wins) × Odds − P(Banker loses) × Payout
   = 0.458597 × 0.95 − 0.541403 × 1 ≈ -0.010579
   (This means that over the long run, betting on Banker results in an average loss of about 0.01 units per unit wagered).

Further Reading:

Expected Value (EV)