In Ocean’s 13, Livingston Dell says “in blackjack, the best score you can get is 21.” This is such an amazing throwaway line from a movie that was released in 2007. Its brilliance is in the delivery of the obvious statement. The comedy comes from the look on everyone’s face at the table.
Continuing with this line of thinking, the best hand a player can get is a natural blackjack. This is when a player is dealt an Ace with a card that has a value of 10. This card can be a King, Queen, Jack, or the number 10.
Most blackjack games pay 3:2 to a player when he or she is dealt a natural blackjack. On the Vegas Strip, it appears as though the majority of games under $25 only pay 6:5 for a natural blackjack. This is still more than even money but playing at a 6:5 blackjack game instead of a 3:2 game increases the house edge for the casino by 1.39%.
We all love being dealt a blackjack because it pays more and guarantees the hand won’t lose money. However, not everyone who plays blackjack knows how often the prized hand appears. Let’s take a look at the math and see how often, on average, a player will be dealt a natural blackjack.
Blackjack frequency and all gaming math isn’t an exact science. The information isn’t specific to an individual game or session. The math usually shows results over thousands or an infinite number ofgames.
While the “math” says one thing, that doesn’t mean the results will be the same every time a player sits downtown gamble. Over time the results of gaming math should bear out after the ups and downs are averaged out.
With that in mind, let’s take a look at how frequently a player will be dealt a natural blackjack using a formula from Wizard Of Odds:
Let n be the number of decks. The probability of a blackjack is 2*(4/13)*(4n/(52*n-1)). If n=6 the probability is 192/4043 = 4.75%.
In the six-deck example above, a probability a player or dealer will receive a natural blackjack is 4.75%. This doesn’t change much by the number of decks. Between the players and dealer, there should be one blackjack dealt about once every 21 hands on average.
According to a Q & A post at Casino City Times, the odds of a player and dealer having blackjacks at the same time is 0.22%. It seems as though this happens much more often but it only works out to be about one of every 450 hands.
Depending on how many people are playing at a table each player should see the following number of hands per hour:
Full table = 60 hands per hour
3 people = 80 hands per hour
1 person = 120 hands per hour
Last But Not Least
You can read the full script of Ocean’s 13 here. The Ocean’s 11 remake is a great movie but don’t sleep on the better of the two sequels.