Increasing Odds Of Winning Blackjack Essay

1135 words - 5 pages

Blackjack is a card game in which players will win if they obtained cards that has the value 21 or closest to 21 compared to the dealer without going over it. Cards 2 to 9 have the value according to their numbers; 10, jack, queen, and king are valued 10; and an ace can be valued 1 or 11. A natural blackjack would be an ace with any card valued 10.
The dealer starts the game by giving two cards to all of the players, including the dealer. All of the cards are dealt face up except for 1 of the dealer’s card. After seeing the card, players must decide what they want to do. Common decisions are hitting or standing. Hitting is receiving one more card to the hand while standing is not doing ...view middle of the document...

This probability is calculated considering no other cards have been used, so there are 52 in the beginning.
The probability of getting a blackjack when handed the first two cards is 4.83% or 0.0482654003 to be exact. A blackjack can be obtained by getting a card valued 10 as the first card and an ace as the second card or vice versa. They are mutually exclusive events as an ace cannot be a 10. In 1 deck, there are 4 aces and 16 card valued as 10, which are 4 10s, 4 jacks, 4 queens, and 4 kings. The calculations are shown below:
P (Blackjack) = P ((10 ∩ ace) ∪ (ace ∩ 10))
P (10 ∩ ace) = P (10) x P (ace|10)
P (10 ∩ ace) = 16/52 x 4/51
P (10 ∩ ace) = 16/663
P (ace ∩ 10) = P (ace) x P (10|ace)
P (ace ∩ 10) = 4/52 x 16/51
P (ace ∩10) = 16/663
P (Blackjack) = P (10 ∩ ace) + P (ace ∩ 10)
P (Blackjack) = 16/663 + 16/663
P (Blackjack) = 32/663 = 0.0483 = 4.83%
Using similar method, the probability of getting a good hand, which is a hand-valued at least 18 can be calculated. But before that, the probability of getting a hand valued 20, 19, and 18 must be obtained first. A hand valued 20 can be obtained by (10, 10), (ace, 9), and (9, ace). A hand valued 19 can be obtained by (10, 9), (9, 10), (ace, 8) and (8, ace). A hand valued 18 can be obtained by (ace, 7), (7, ace), (10, 8), (8, 10), and (9,9). There are 16 cards with value 10, and 4 cards each with value 7, 8, 9 and ace.
P (20) = P ((10 ∩ 10) ∪ (ace ∩ 9) ∪ (9 ∩ace))
P (10 ∩ 10) = P (10) x P (10|10)
P (10 ∩ 10) = 16/52 x 15/51
P (10 ∩ 10) = 20/221
P (9 ∩ ace) = P (9) x P (ace|9)
P (9 ∩ ace) = 4/52 x 4/51
P (9 ∩ ace) = 4/663
P (ace ∩ 9) = 4/663
P (20) = P (10 ∩ 10) + P (9 ∩ ace) + P (ace ∩ 9)
P (20) = 20/221+ 4/663+4/663...

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