The House Edge in Baccarat in Mines Games
You are perhaps familiar with the drawing rules, card values, and payouts in baccarat if you are interested in how deck number affects your winning odds.
Let’s skip straight to the mathematics of baccarat and look into the probabilities of a standard eight-deck game with a 5% commission on Banker and even-money payouts on winning Player hands. Tie bets pay at standard odds of 8 to 1 when successful.
THE LIKELIHOOD OF OUTCOMES WITH TIES INCLUDED
- Ties between Player and Banker occur approximately 9.51% of the time.
2. The Player hand wins approximately 44.62% of the time and loses the remaining 45.87% of the rounds.
3. The Banker hand is successful approximately 45.87% of the time and loses the remaining 44.62% of the rounds.
THE LIKELIHOOD OF OUTCOMES WITH TIES EXCLUDED
- Ignoring the ties, the Player hand pays out roughly 49.32% of the time and loses the other 50.68% of the rounds.
2. The percentages are reversed for the Banker side as it pays out 50.68% of the rounds on average and loses 49.32% of the rounds.
3. You have surely noticed the winning probability of the Banker side exceeds fifty percent in the second case where we ignored the ties.
Casino operators offset this advantage by imposing a 5% commission on all winning Banker hands. Gamblers receive 95 cents per every dollar wagered on Banker. The bet thus yields a house edge that is nearly identical to that of the Player side.
When we know the probabilities of all three possible outcomes in the game, we can easily calculate their house edges.
All we have to do is multiply the winning probability by the wager and then add the losing probability multiplied by the losses to that result. The losses correspond to a negative expected value (EV), hence the minus sign. In turn, this negative EV reflects the house edge of a bet.
We use decimal numbers rather than percentages in the calculations below since probabilities always range from zero to one on a linear axis, known as a ‘probability line’. The closer an event gets to one, the more likely it is to occur. Zero denotes something is impossible to happen, whereas one indicates an event is certain to happen.
- Expected Value of the Player Bet
(1 x 0.446246) + (-1 x 0.458597) + (0 x 0.095155) = -0.012351
- Expected Value of the Banker Bet
(0.95 x 0.458597) + (-1 x 0.446246) + (0 x 0.095155) = -0.010578
- Expected Value of the Tie Bet
(8 x 0.095155) + (-1 x 0.458597) + (-1 x 0.446246) = -0.143603
When you convert these probabilities into percentages, you get the expected value of all three possible outcomes in baccarat. It is obviously negative and corresponds to the house edges yielded by the Player, Banker, and Tie bets.
- House Edge of the Player Bet = -0.012351 x 100 = 1.24%
- House Edge of the Banker Bet = -0.010578 x 100 = 1.06%
- House Edge of the Tie Bet = -0.143603 x 100 = 14.36%
Note that the percentages above correspond to the long-term advantage the casino holds per hand played since ties are included. The house edges of the Player and Banker bets increase further to 1.36% and 1.17% when we ignore the ties as you can see from the calculations below.
- Expected Value of Player Wagers per Bet Resolved
(1 x 0.4932) + (-1 x 0.5068) = -0.0136
- Expected Value of Banker Wagers per Bet Resolved
(0.95 x 0.5068) + (-1 x 0.4932) = -0.0117
For every $100 wagered on Player, Banker, and Tie, gamblers can anticipate losses of $1.24, $1.06, and $14.36 on average. Another important thing to mention is that the house edges above apply to baccarat games that charge a 5% commission on winning Banker hands.
The mathematical advantage the house holds on Banker jumps to 1.46% in commission-free variations. We know this sounds counterintuitive but it is true. Feel free to read our detailed article on commission versus no commission baccarat for further information on this subject.