To determine the house edge of the "Super 6" bet in Baccarat, we'll use the formula for calculating the house edge based on the probability and payouts of the bet.
Given:
- The "Super 6" bet pays 12:1 on a banker win with a total hand value of 6.
- Probability of this event occurring is approximately \( p = 0.0539 \) (or 5.39%).
Calculation of House Edge:
1. Expected Value of the Bet:
The expected value (EV) of the "Super 6" bet can be calculated as:
\[ \text{EV} = (P \cdot \text{Payout}) - (1 - P) \]
where \( P \) is the probability of the event happening, and the payout is 12:1.
For a $1 bet (assuming unit stake for simplicity):
\[ \text{EV} = (0.0539 \cdot 12) - (1 - 0.0539) \]
\[ \text{EV} = 0.6468 - 0.9461 \]
\[ \text{EV} = -0.2993 \]
This negative value indicates that on average, the player loses $0.2993 per $1 bet on the "Super 6" bet.
2. House Edge Calculation:
The house edge (HE) is simply the negative of the expected value (since it represents the average profit the house makes per unit bet):
\[ \text{HE} = -\text{EV} \]
\[ \text{HE} = 0.2993 \]
3. Expressing as a Percentage:
To express the house edge as a percentage:
\[ \text{House Edge (\%)} = \text{HE} \times 100 \]
\[ \text{House Edge (\%)} = 0.2993 \times 100 \]
\[ \text{House Edge (\%)} = 29.93\% \]
Therefore, the house edge of the "Super 6" bet in Baccarat, which pays 12:1 on a banker win with a total hand value of 6, and has a probability of approximately 5.39%, is approximately **29.93%**. This indicates that for every $1 bet on average, the casino expects to retain about $0.2993 in profit.
Given:
- The "Super 6" bet pays 12:1 on a banker win with a total hand value of 6.
- Probability of this event occurring is approximately \( p = 0.0539 \) (or 5.39%).
Calculation of House Edge:
1. Expected Value of the Bet:
The expected value (EV) of the "Super 6" bet can be calculated as:
\[ \text{EV} = (P \cdot \text{Payout}) - (1 - P) \]
where \( P \) is the probability of the event happening, and the payout is 12:1.
For a $1 bet (assuming unit stake for simplicity):
\[ \text{EV} = (0.0539 \cdot 12) - (1 - 0.0539) \]
\[ \text{EV} = 0.6468 - 0.9461 \]
\[ \text{EV} = -0.2993 \]
This negative value indicates that on average, the player loses $0.2993 per $1 bet on the "Super 6" bet.
2. House Edge Calculation:
The house edge (HE) is simply the negative of the expected value (since it represents the average profit the house makes per unit bet):
\[ \text{HE} = -\text{EV} \]
\[ \text{HE} = 0.2993 \]
3. Expressing as a Percentage:
To express the house edge as a percentage:
\[ \text{House Edge (\%)} = \text{HE} \times 100 \]
\[ \text{House Edge (\%)} = 0.2993 \times 100 \]
\[ \text{House Edge (\%)} = 29.93\% \]
Therefore, the house edge of the "Super 6" bet in Baccarat, which pays 12:1 on a banker win with a total hand value of 6, and has a probability of approximately 5.39%, is approximately **29.93%**. This indicates that for every $1 bet on average, the casino expects to retain about $0.2993 in profit.
