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Blackjack : The importance of shoes in blackjack

By Daniel Michaels

Level: Apr 13th 2007
These are two common questions many blackjack players have asked:

1. If the number of decks per shoe increases, in what way are the odds of getting a blackjack modified?

2. Do you have an advantage if the probability of making a blackjack is increased, considering the fact that both you and the dealer have the same chance of making a blackjack?

The more the better
Let's start with the second question first. It is better for you if the probability of making blackjack is increased. The reason for this is that when you make blackjack, you win one and a half times your bet, when the dealer makes blackjack, you lose your bet. The tie is not important.

Let’s take this following situation: you bet $20 and both you and the dealer hit 5 blackjacks. Hitting 5 blackjacks will bring you $150 ($30X5), but the dealer's blackjack will cost you $100 ($20X5). You make a $50 profit.

Now the same bet, but both you and the dealer hit 10 blackjacks. You would make $300, but the dealer would cost you $200. Once again you make a profit, but this time it is increased. So you see, the more the better.

The less the more
The answer to the first question: if the number of decks increases, the chances of hitting blackjack reduce. If you would play with a single deck, you will hit blackjack in 4.826% of all hands.

Adding another deck will reduce the number to 4.780%. In a game of four decks, the number will be 4.756%. In a six decks game it will be 4.749%, and in an eight decks game 4.745%.

If you play blackjack using a single deck, you have 52 cards which include four aces and sixteen 10-values. The probability of hitting an Ace as your first card is 4 out of 52, meaning 4/52. The probability of hitting a 10-valued card as your second card is 16 out of 51 (52 cards – the Ace), meaning 16/51.

You can make blackjack by hitting a 10-valued card first, 16/52 and then an Ace, 4/51. Using this formula the overall probability of hitting a blackjack is 0.04826, or 4.826%.
[(4/52)x(16/51)] + [(16/52)x(4/51)]

Let's take the two deck example. There are 104 cards, among them 8 are Aces, and 32 are 10-valued cards. The probability of receiving an Ace as your first card is 8/104, and the probability if hitting a 10 valued card as your second card is 32/103.

Using the same formula, the possibility of hitting blackjack is 0.04780, or 4.780%.
[(8/104)x(32/103)] + [(32/104)x(8/103)]

The difference
So we know that the reduced number of decks increases the chances of blackjack, and that the increased probability of hitting blackjack brings more profit. But how much profit are we talking about?

Let’s say you play 1000 hands using $10 bets. If you use a single deck both you and the dealer expect to make 48.26 blackjacks. You would win $241.30 if you would make that number of blackjacks ($5x48.26).

Using two decks you would make $239.00 ($5x47.8); using four decks: $237.80 ($5x47.56); with six decks: $237.45 ($5x47.49); and using 8 decks: $237.25 ($5x47.45).

The difference is not that much, because changing the game to a single deck, from a six deck one, and placing $10 bets will bring you a $3.85 profit per thousand hands. It's your choice, you decide how you want to play the game.
RELATED GAME STRATEGIES
Lesson 1: Blackjack History
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Speak like a pro. Talk the talk, the walk is up to you!
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