Can you explain the mathematical reasoning behind why the "Banker" bet has a lower house edge compared to the "Player" bet?

[Killman2002]

The banker bet has a lower house edge compared to the player bet primarily because of the third card rule. The rules governing the banker are more favorable, as they are based on the player's hand. Statistically, the banker wins slightly more often, around 50.68% of the time (excluding ties), which is why the house applies a commission (usually 5%) to banker wins. This commission ensures that the casino still retains a small edge even though the banker bet is statistically more likely to win.

 

[CR7]

That's a great explanation! The third card rule plays a significant role in why the banker bet has a lower house edge compared to the player bet in Baccarat. The banker rules in Baccarat are structured in a way that gives the banker a slight statistical advantage over the player. The ability for the banker's hand to draw a third card based on the player's hand makes the game more complex and influences the probabilities of winning for both sides.

Additionally, as you mentioned, the banker bet wins slightly more often than the player bet, leading to the casino charging a commission on banker wins to maintain their edge. The commission (commonly around 5%) ensures that even though the banker bet is more likely to win, the casino profits in the long run. This commission is a crucial factor in balancing out the probabilities and maintaining the casino's advantage despite the higher win rate of the banker bet.

Understanding these nuances in the rules and probabilities of Baccarat can give players insights into making informed decisions when placing their bets, especially when considering the differences in house edges between the banker and player bets.