Blackjack is actually one of the most popular games in the casino and also has some of the lowest ...
Blackjack: What are the Odds? 1) Ten-value cards / Cards Remaining x Aces / Cards Remaining (16 x 6) / (52 x 6) x 24 / (52 x 6) – 1 96 / 312 x 24/311... 2) Aces / Cards Remaining x Ten-value cards / Cards Remaining
The probability of a blackjack in a single deck game is 4*16/combin (52,2) = 64/1326. So the ...
Your probability of getting an ace and then a 10 is 1/7 X 16/27, or 16/189. Again, you could get a blackjack by getting an ace and a ten or by getting a ten and then an ace, so you add the two probabilities together. 16/189 + 16/189 = 32/189. Your chance of getting a blackjack is now 16.9%.
The odds of being dealt a natural blackjack are merely 4.8%. Following this chart you will see that the most common two card hand, at 38.7%, is a hand totaling 1-16, which is considered a decision hand.
However, we can see that the odds change because the denominator change is smaller when one card is removed from a larger stack. Here's the tree diagram for two decks: The probability of being dealt a Blackjack has fallen to 64/1339, which is approximately 4.780%
The odds to get a blackjack (natural) as arrangement: 128 / 2652 = .0483 = 4.83%. 4.83% is equivalent to about 1 in 21 blackjack hands . (No wonder the game is called Twenty-one !)
What are the odds of getting a 10 in blackjack? Your probability of getting a ten on your second card is 16/51. There are 16 cards in the deck with a value of ten; four each of a jack, queen, king, and ten. So your probability of being dealt an ace and then a 10 is 1/13 X 16/51, or 16/663. What are the odds of losing 5 hands in a row at blackjack?
Espresso Games software offers a Lucky 7 side bet in one of their blackjack games, which follows this format. They use eight decks and I presume no three-card guarantee. The following table shows their pay table and all the odds. The lower right cell shows a house edge of 7.83%.