To calculate the expected value (EV) of a $10 bet on the "Dragon Bonus" side bet in Baccarat, where the banker wins with a total hand value of 7 and the payout is 30:1, given a probability of 2.32% for this event:
1. Expected Value Calculation:
The formula for EV is:
\[ \text{EV} = (P \cdot \text{Payout}) - (1 - P) \cdot \text{Bet} \]
Where:
- \( P \) is the probability of the event (banker wins with a total hand value of 7),
- Payout is 30:1 (if $10 bet, payout is $10 \times 30 = $300),
- Bet is $10.
Substitute the values:
\[ \text{EV} = (0.0232 \cdot 300) - (1 - 0.0232) \cdot 10 \]
\[ \text{EV} = 6.96 - 0.9768 \cdot 10 \]
\[ \text{EV} = 6.96 - 9.768 \]
\[ \text{EV} = -2.808 \]
2. Interpretation:
The negative expected value (-$2.808) indicates that on average, for every $10 bet on the "Dragon Bonus" side bet in Baccarat under these conditions, the player can expect to lose approximately $2.808.
Therefore, the expected value of a $10 bet on the "Dragon Bonus" side bet in Baccarat, which pays 30:1 if the banker wins with a total hand value of 7, given a probability of 2.32%, is approximately -$2.808.
1. Expected Value Calculation:
The formula for EV is:
\[ \text{EV} = (P \cdot \text{Payout}) - (1 - P) \cdot \text{Bet} \]
Where:
- \( P \) is the probability of the event (banker wins with a total hand value of 7),
- Payout is 30:1 (if $10 bet, payout is $10 \times 30 = $300),
- Bet is $10.
Substitute the values:
\[ \text{EV} = (0.0232 \cdot 300) - (1 - 0.0232) \cdot 10 \]
\[ \text{EV} = 6.96 - 0.9768 \cdot 10 \]
\[ \text{EV} = 6.96 - 9.768 \]
\[ \text{EV} = -2.808 \]
2. Interpretation:
The negative expected value (-$2.808) indicates that on average, for every $10 bet on the "Dragon Bonus" side bet in Baccarat under these conditions, the player can expect to lose approximately $2.808.
Therefore, the expected value of a $10 bet on the "Dragon Bonus" side bet in Baccarat, which pays 30:1 if the banker wins with a total hand value of 7, given a probability of 2.32%, is approximately -$2.808.
