Using basic strategy should be a must for anyone playing blackjack. This gives you the best chance for a small house edge and it’s fairly easy to learn and remember. However, the numbers and correct gameplay just don’t click with everyone. Not everyone puts learning perfect blackjack strategy first.
Believe it or not, the are people who visit casinos for a fun time that may not always involve walking away as a winner. That’s okay, we’re here to help. There are useful blackjack games online and blackjack apps for mobile devices that can help improve your game. Additionally, we offer useful tips on different ways to play the best blackjack you can.
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. Blackjack Math – Understanding the Math behind Advantage Play This article will explain four of the most common blackjack math terms used by card counters and advantage players, as well as how they affect advantage play and card counting. The program of this blackjack’s brain depends on this so-called “algorithm”; a mathematical formula utilized to produce unequivocally random numbers. It automatically makes long runs of numbers that show random properties one after the other. When you play blackjack for money, each result is completely independent of the precedent. Interested in the mathematical foundations of casino games and the use of mathematics in gaming management practice. T The desire to risk is an essential part of human nature. David Johnston Temples of Chance (1992).
Another way to help you understand how basic strategy works is to look at some of the underlying probability. For example, the odds of a player receiving blackjack are 4.8%. That’s almost five natural blackjacks for every 100 hands played. Meanwhile, a player will be dealt cards totaling between 1 and 16 38.7% of the time. This means that you’ll have to make a decision on whether to stay or hit on approximately 39 of 100 hands dealt.
Likewise, 30% of the hands dealt to a player will be a stay hand of 17-20. That’s right, on 30% of the total hands dealt, you won’t have to make a decision if you’re playing correct basic strategy. Think about this if blackjack seems intimidating. You won’t have to make a move on approximately three of every 10 hands you see.
One of the easier ways to understand why you should hit or stay on certain hands is to learn the dealer and player bust rates. Here is a look at how often the dealer will bust based on their up card:
2 – 35.3%
3 – 37.4%
4 – 39.6%
5 – 41.9%
6 – 42.3%
7 – 26.2%
8 – 24.3%
9 – 23%
10 – 21.3%
Ace – 11.6%
You may hear players say that the dealer has a “bust card” when playing blackjack in a casino. Those are the cards that you can see where the dealer has the greatest chance of busting. According to the probability above, the dealer will bust more than 42% of the time they have a 6 showing. This means that the dealer will bust 42 out of every 100 times they have a 6 showing. That’s just little more than 4 out of every 10 times it’s showing. A dealer will bust when they have a 6 showing than any other card.
If you’ve played blackjack often then you know that the higher the total of the first two cards you receive the more likely you are to bust. Here is the probability of busting on if you hit on hands that you’re dealt with the totals below:
20 – 92%
19 – 85%
18 – 77%
17 – 69%
16 – 62%
15 – 58%
14 – 56%
13 – 39%
12 – 31%
Mathematical Formula For Blackjack Card Game
It’s impossible to bust on the next card if you’re dealt 11 or lower. The next highest card you receive would be a 10 so you can reach 21 but not higher on that individual play. The probability of busting when dealt a 20 if you hit it 92%. You’ll rarely see anyone hit when they receive a 20.
There’s a reason that basic strategy exists for blackjack and the math supports it. Understanding the probable outcome before even playing certain hands will go a long way in making you a better blackjack player. Even if you’re just playing blackjack to hang out with friends, knowing basic strategy will allow your bankroll to last longer. In turn, your good times in the casino will last longer.
Blackjack (also known as twenty-one or sometimes pontoon) is one of the most popular casino card games in the world. The name blackjack comes from the fact that when blackjack was first introduced in the U.S. it wasn't very popular, so casinos and gambling houses tried offering different bonus payoffs. One of those was a 10-to-1 payoff for a hand consisting of the ace of spades and a black jack (that is, the jack of spades or the jack of clubs). With the current rules, a blackjack hand doesn't even need to contain a jack.
Rules
A blackjack game has a dealer and one or more players. Each player plays against the dealer. All players are initially dealt two cards and the dealer is dealt one card face down and one face up (these are called the hole card and up card respectively). Each player can then hit (ask for an additional card) until her total exceeds 21 (this is called busting) or she decides to stand (stop taking cards for the rest of the hand). Face cards count as 10 and an ace may be counted as 1 or 11. After all of the players have finished, the dealer reveals the hole card and plays the hand with a fixed strategy: hit on 16 or less and stand on 17 or more.
The player loses if she busts and wins if she does not bust and the dealer does (observe that if both the player and the dealer bust, the player loses). Otherwise, the player wins if her total is closer to 21 than the dealer's. If the player wins, she gets twice her bet; if she loses, she loses her money. If the dealer and player tie it is called a 'push;' the player keeps her bet but does not earn any additional money. If the player's first two cards total 21, this is a blackjack and she wins 1.5 times her bet (unless the dealer also has a blackjack, in which case a tie results), so she gets back 2.5 times her bet.
Soft Hand. A hand that contains an ace that can be counted as 11 is called a soft hand, since one cannotbust by taking a card. With soft hands, the basic strategy is to always hit 17 or less and even hit 18 if the dealer's up card is 9 or 10 (where the 10 refers to a 10, J, Q, or K).
Doubling down. After the player is dealt her initial two cards she has the option of doubling her bet and asking for one additional card (which is dealt face down). The player may not hit beyond this single required card. With the basic strategy, you should always double with a total of 11, double with 10 unless the dealer's up card is 10 or A, and double with 9 only against a dealer's 2 to 6. (Some casinos only allow doubling down on 11).
Splitting pairs. At the beginning of a hand, if the player has two cards with the same number (that is, a pair) she has the option of splitting the pair and playing two hands. In principle, a pair of aces should of course be split, but in this case blackjack rules allow you to get only one card on each hand, and getting a 10 does not make a blackjack. With the basic strategy, you should never split 10's, 5's or 4's, always split 8's, and, in the other cases, split against an up card of 2 to 7, but not otherwise.
Strategies for the Player
Blackjack is almost always disadvantageous for the player, meaning that no strategy yields a positive expected payoff for the player. In the long run, whatever you do, you will on average lose money. Exceptions exist: some casinos offer special rules that allow a player using the right strategy to have a positive expected payoff; such casinos are counting on the players making mistakes.
The so called basic strategy is based on the player's point total and the dealer's visible card. It consists of a table that describes what you should do in any situation in the game (you can find an example of this table at Wikipedia). Under the most favorable set of rules, the house advantage against a player using the basic strategy can be as low as 0.16%.
Many people assume that the best strategy for the player is to mimic the dealer. A second conservative strategy is called never bust: hit 11 or less, stand on 12 or more. Each of these strategies leads to a player disadvantage of about 6%.
Edward Thorp, in his 1962 book Beat the Dealer
Mathematical Formula For Blackjack Rules
, describes a simple strategy that makes blackjack an almost even game: if the dealer's up card is 2 to 6, play never bust; if it is 7 to ace, mimic the dealer. The exception to this simple rule is that one should hit a 12 if the dealer's up card is 2 or 3. More advanced strategies include features such as taking into account the player's hand composition (as opposed to just considering the point total) and the other players' hands, specially card counting (that consists of keeping track of the cards that have been dealt so as to know the composition of the remaining cards in the deck), and shuffle tracking (which is far more complicated than card counting, and consists in roughly following groups of cards as they are shuffled). These two last strategies are usually forbidden in casinos.
What does it mean to have a 0.16% disadvantage?
When discussing casino games, one usually finds statements such as the ones above saying something like: 'the house advantage in this game is about 0.16%'. A first explanation is the following: betting ten dollars each hand, you will in the long run lose an average of 1.6 cents per hand. It would be nice to have an idea of the probability of winning any particular bet when playing some specific strategy. Indeed, we can infer this from the player's disadvantage. Let's take, as an example, the potential 0.16% disadvantage when playing the basic strategy.
Suppose you bet $1 at each of 10,000 bets playing the basic strategy. Let's call p the total probability of winning a pass line bet (so p is the number we are trying to calculate). If p was, for example, 0.5, it would mean that, on average, half the times you should win the bet, so you would win 0.5 · 10,0000 = 5,000 times. Since each time you win a bet you get twice what you bet and each time you lose the bet you lose all the money, you would end up with 5,000 · $2 = $10,000, that is, the same total amountyou bet (10,000 times $1). In this case, the house advantage is 0%, as is the player advantage.
The same idea applies for any p: if you bet 10,000, you should, on average, win the bet 10,000p times, so your average payoff is $20,000p. In our case, the house advantage is 0.16%, so if you play $10,000, on average you end up with $10,000 - $10,000 · 0.0016 = $10,000 - $16 = $9,984. So we only have to solve the equation $20,000p = $9,984 to get p = 0.4992.
Links
You can find more information on blackjack's rules, strategies, and history on the Internet. For instance, you can try Wikipedia.
A very interesting free on-line blackjack trainer can be found here.
Problems
If you are dealt a point total of 16, what is the probability of busting if you hit, assuming that a whole deck will be used to choose among when you are dealt your next card?
If you are dealt a 3 and an ace, what is the probability of not busting if you hit, assuming that a whole deck will be used to choose among when you are dealt your next card?
Suppose you are the only player against the dealer, and you are in the first hand of a game played with one deck. You are dealt an 8 and a 6, while the dealer is showing a queen. What is the probability that you bust if you decide to hit?