The probability that the player has a winning blackjack equals 4.75% x (1 - 4.56%).

The odds are a little bit down due to the effect of removal. It goes down because the player already has an ace and a 10 out of the shoe. After you take out the two player cards, there will be 23 aces left by the time it's the dealer's second card.Īssuming the player has a blackjack, the probability that the dealer gets one as well is 4.56%. There will be 95 10-point cards left in the shoe out of 310 cards. Once the player has a blackjack, what is the probability that dealer will get one? Well, again, the dealer could get the ace and the 10 in either order thus the two. If the dealer gets a blackjack too, then it doesn't make any difference. However, in order for this pay to make any difference, it must be a winning blackjack. The probability the player gets a blackjack is equal to 4.75%. It's just as likely to get the ace first in a blackjack as a blackjack, starting with a 10-point card. There are 24 aces in the shoe, and 311 cards left. Assuming the player's first card is a 10-point card. The probability that the first card the player gets is worth 10 points, is 96 / 312 because there are 96 10-point cards, 16 x 6 is 96, and 312 total cards in the shoe. Let's assume six decks of cards, which is the norm, and that the player has no knowledge of any other cards in the deck. How important is that rule mathematically? The player will get 30% of a bet more with every winning blackjack if he's playing 3 to 2 blackjack as opposed to 6 to 5.

I hate to have to insult your intelligence by even pointing this out, but 3 / 2 = 1.5, 6 / 5 is 1.2. Frankly, I have no idea why other than out of a ignorance of math. You see a lot of players playing 6 to 5 blackjack even at high amounts. The topic of this Wizard of Odds Academy video will be on the importance of a blackjack paying 3 to 2 odds in blackjack as opposed to 6 to 5, which is a very common rule variation right now.

Does blackjack have the best odds