# Blackjack combinations

We first present the probabilities attached to card dealing and initial predictions. In making this calculus, circumstantial information such as fraudulent dealing is not taken into account (as in all situations corresponding to card games). All probabilities are calculated for cases using one or two decks of cards. Let us look at the probabilities for a favorable initial hand (the first two cards dealt) to be achieved. The total number of possible combinations for each of the two cards is C(52, 2) = 1326, for the 1-deck game and C(104, 2)=5356 for the 2-deck game.

Probability of obtaining a natural blackjack is P = 8/663 = 1.20663% in the case of a 1-deck game and P = 16/1339 = 1.19492% in the case of a 2-deck game.

Probability of obtaining a blackjack from the first two cards is P = 32/663 = 4.82654% in the case of a 1-deck game and P = 64/1339= 4.77968% in the case of a 2-deck game.

Similarly, we can calculate the following probabilities:

Probability of obtaining 20 points from the first two cards is P = 68/663 = 10.25641% in the case of a 1-deck game and P = 140/1339 = 10.45556% in the case of a 2-deck game.

Probability of obtaining 19 points from the first two cards is P = 40/663 = 6.03318% in the case of a 1-deck game and P = 80/1339 = 5.97460% in the case of a 2-deck game.

**Probability of obtaining 18 points from the first two cards is** P = 43/663 = 6.48567% in the case of a 1-deck game and P = 87/1339 = 6.4973% in the case of a 2-deck game.

Probability of getting 17 points from the first two cards is P = 16/221 = 7.23981% in the case of a 1-deck game and P = 96/1339 = 7.16952% in the case of a 2-deck game.

A *good* initial hand (which you can stay with) could be a blackjack or a hand of 20, 19 or 18 points. The probability of obtaining such a hand is calculated by totaling the corresponding probabilities calculated above: P = 32/663 + 68/663 + 40/663 + 43/663 = 183/663, in the case of a 1-deck game and P = 64/1339 + 140/1339 + 80/1339 + 87/1339 = 371/1339, in the case of a...

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