Blackjack Strategy Probability

Blackjack, unlike other gambling games is not considered a game of chance, it is one that you can win if you start applying some knowledge. Unlike many other games where the result depends on player luck only, this game provides probabilities depending on the player decisions. Therefore, in order to win you have to know what your probabilities are now and how and when to increase them.

1. Blackjack Strategy Chart
2. Blackjack Probability Math
3. Blackjack Probability To Win

Blackjack strategy probability The total number of possible combinations of two cards from the starting hands is to play with one deck of cards and 2 game packages. The probability of getting a natural blackjack is P = 32/663 = 4.82654% for a 1 game pack and P = 64/1339 = 4.77968% for 2-game packages. This is where basic strategy comes in. Basic strategy takes the probability theory associated with different scenarios in blackjack and expresses it in a table which gives you the correct play to make in every situation. If you stick with the basic strategy you will be making the correct play as determined by probability theory.

Before we take a look at player and dealer blackjack odds, we should consider all the parameters that affect the odds in the game.

Blackjack Rules Variations

Blackjack variations were created to entertain players and provide them with a chance to win more money on side bets. Each rule variation affects the house edge, some rules making a big, others making a minor difference. Most common rule variations can be found at our House Edge Calculator in the «Rules» window. Now, let's take a closer look at the rules and see how they affect the odds in the game.

NOTE: The rules chosen in the table below are most favorable for the player.

Number of decks

The first thing a player should consider when choosing a table is the number of decks used in the game. The more decks there are - the less odds the player has. (See the table - Probabilities – Number of decks)

Dealer hits or stands on soft 17

The main rules of the game are usually written on the table felt and it may say either dealer hits or stands on soft 17. If according to the rules dealer hits soft 17, the game gives the house a 0.2% extra edge.

Rules for doubling

This rule is sometimes called the 'Reno' rule, which restricts doubling only to certain hand totals. Double 9 - 11 affects the house edge increasing it by 0.09% (8 decks game) and 0.15% (1 deck game). Double 10-11 increases the house edge by 0.17% (8 decks game) and 0.26% (1 deck game).

Doubling after Split

If the casino allows a player to double after he splits a pair, the player will get a further edge of around 0.12%.

Resplitting

Most casinos allow players to split again after he/she splits a pair and is dealt another card of the same rank. However, if the casino does not, this means the odds favor the house. As the best hands for splitting are a pair of Aces and 8s, there may be a special rule for Splitting Aces. If the casino allows the player to re-split Aces, the player gets a 0.03% extra edge. Moreover, in most cases if the player splits Aces, the casino will deal only one card per hand and that's it. Allowing players to hit on a hand of Split Aces gives the player an edge of 0.13%. We do not consider this rule in our calculator due to the fact it is almost never used, especially online.

• 1 deck of cards (house edge 0.17%)
• Doubling allowed on any cards
• Doubling allowed after Split and after Hit (player edge 0.12%)

• Early surrender is preferable
• Dealer stands on soft 17 (player edge 0.2%)
• Resplitting any cards allowed (player edge 0.03%)

Extra Rules Affecting Blackjack Odds

European No-Hole-Card Rule

Some blackjack variations are played with a hole card that is dealt to the dealer only after all the players have played their hands. This rule affects player strategy when playing against dealer up 10 or an Ace. In a typical hole-card game the player would know whether the dealer has a Blackjack or not before he makes any decisions. In this game, however, the player is risking a lot more if he decides to double or split. This rule adds 0.11% to the house advantage. However, there may be some casinos that allow the player to push on all the additional bets (doubling down and splitting pairs) if the dealer happens to have Blackjack.

Another Payouts on Blackjack

The classic payout on player Blackjack is 3 to 2. However, some casinos change the payout to increase the house edge. The payout on blackjack thus may vary from 1:1 to 6:5. As a Blackjack hand frequency is approximately 4.8% (see the table Two Card Hand Frequency), the payout of 1:1 will increase house edge by 2.3% and the payout of 6:5 - by 1.4%. The first rule (1:1) is only rarely found , while the second (6:5) can be found at some tables with a single deck blackjack game. The payout on Blackjack is generally written on a table felt.

Best tip
for odds seekers

The easiest way to choose the game with the highest odds is to play blackjack with no extra special rules. Do not forget where your basic odds are hidden - chance to Split, Double Down and get a 3 to 2 payout on Natural.

Dealer wins Ties

Another disadvantage for the player is when the rules of the game say that dealer wins all ties. This rule is almost never used in the classic games, though it can be found in some blackjack variations.

Insurance

The Insurance bet is a casino trick that gives the house a huge edge. The main factor why many players take this bet lies in the fact it costs only half of the original one. However, when the player takes Insurance every time he plays the game, the house edge may raise up to 7%. Added to all the other rules the casino sets on the game and you will see why probabilities are worth learning if you want to quit winners.

Side Bets

All blackjack games that offer side bets seem to be the biggest attraction for blackjack lovers. However, if you consider blackjack odds on these bets, you will notice that no matter how big the jackpot is (as in progressive blackjack rules) or how great the payout is for the pair (as in perfect pairs rules), the odds still favor the house and you are not likely to win.

Blackjack Probabilities charts

The quantity of decks increases the house advantage with each extra deck added to the game. Look for games with the smallest number of decks. However, some games offering a chance to play with 1 deck may only still provide low player odds due to low payouts on Blackjack and other rules. Be sure to check them before you play.

The table on the left describes how often the following hands can appear. The hands are the first two-cards dealt to the player. The frequency stands for the average number of times dealt per deck of cards. As you can see, the most frequent hands dealt are the 'Decision hands' that demand knowledge of blackjack strategy.

In this table you can see the probability of going bust on any hand if the player decides to Hit. This means that with 0% you can never go bust when hitting a hand of 11 or less. As you can see, the table is for hard hand totals as you will 100% bust if you Hit on a hand of hard 21.

You probably already know that in blackjack small cards in the deck favor the dealer while big ones favor the player. In this table you can see that removing 2s from the deck adds a 0.40% of advantage to the player, while if 10's are taken out - the odds are 0.51% for the house.

Blackjack Strategy Chart

Blackjack probabilities are calculated due to different parameters, including the dealer up card. The table on the left depicts how likely it is that dealer will go bust with certain up cards and what the player odds are in this very situation. For example, the highest player odds are when the dealer shows a 6, as he is most likely to go bust with this hand. The lowest player odds are when the dealer's up card is a 10 or an Ace.

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Each decision you make while playing blackjack has a positive or negative
impact on your potential profit or loss. Every situation you have while playing
has a single best way to play.

If you make the correct play it either makes you the most money in the long
run or loses the least amount of money in the long run. This is called basic
strategy.

Some hands lose money in the long run and some win in the long run, so your
job is to make the best possible play to maximize the wins and minimize the
losses.

When you read about the expected house edge in blackjack games based on the
rules the percentages are based on perfect basic strategy. If you don’t use the
proper strategy you give the house a higher edge against you. This can add an
extra one or two percent to the house edge, depending on how far from the proper
strategy you stray.

You can usually find blackjack games with rules that offer a house edge of
less than 1%, and can often find games with a house edge under a half percent.
If you don’t use basic strategy you can be playing with a house edge of 1.5% to
3% instead of a half percent.

This quickly adds up.

If your average bet is $100 and you play 100 hands per hour and you give the
casino and extra 1% you lose an extra $100 per hour. By giving them an extra 2%
it’s $200 per hour.

If you want to play blackjack the first thing you need to do is decide to
always make the best possible play.

You probably realize that there are hundreds of hands when you combine all of
the possible hands you can have with the different up cards the dealer can have.

The good news is that by using a simple chart you can quickly find the best
play. And you can use a strategy chart or card at the table while playing in a
live casino or when playing online.

If you play in a live casino some of the other players may try to pressure
you if you take too long to make a decision. But it’s none of their business and
you can play any way you want as long as you don’t hold up the game too long.

If you’re worried about holding up the game sit in the middle of the table or
to the dealer’s right hand side so you have longer before you have to act. This
gives you more time to consult your strategy chart before being force to make a
decision.

You don’t even need to memorize the best plays.

But with a little effort and time you can quickly memorize the most common
plays and in time memorize all of the best plays.

The next section has a chart and the following section has the hand by hand
explanations. Then you’ll find a section explaining a few ways to start
memorizing all of the plays.

Basic Strategy Chart

This is the most universal basic strategy chart and can be used in all
blackjack games with any rule combinations. A few small adjustments can be made
against certain rules combinations, but it becomes complicated to memorize
multiple charts. We’ve included a short section later explaining these
adjustments for the dedicated player.

The dealer’s up card is listed across the top. Your cards are listed down the
first column to the left. Simply go down the left column until you find your
cards and then go across to the column with the dealer’s card to find the best
play.

The key for each play is as follows:

• Hit – Hit
• Stand – Stand
• DblH – Double
• DblS – Double if permitted, otherwise stand
• Split – Split
• SplitD – Split if double after split is permitted, otherwise hit
• SUR – Surrender if permitted, otherwise hit

Expand Shrink

Text Version and Vision Impaired

Many players use the chart listed above but a few players prefer to read the
correct plays. Having the correct plays written out also is valuable to people
who have vision problems and use software to hear what’s on the page.

We’ve listed the proper plays for each situation below in four sections.
Simply find the section that describes your hand and follow the instructions.

Hands with an Ace or Soft Hands

Any starting hand you hold with an ace is called a soft hand. A soft hand is
when you have an ace that can be used as a one or 11. In the following
combinations, if you have more than two cards, simply add the cards that aren’t
an ace.

This can happen when you start with an ace and a different side card and hit.
Starting with an ace two and receiving a four after hitting leaves you with ace
two four. Looking at the chart you look at the line for a soft 17. Using the
list below you look at the one for ace six because the two and four add up to
six.

• Ace ace – Always split a pair of aces. Split aces as many times as allowed.
• Ace two or soft 13 – You always hit with a soft 13 and double if allowed
  against a dealer five or six.
• Ace three or soft 14 – Always hit and double against a five or six if
  allowed.
• Ace four or soft 15 – You always hit with a soft 15 and double if allowed
  against a dealer four, five, or six.
• Ace five or soft 16 – Always hit and double against a four, five, and six if
  allowed.
• Ace six or soft 17 – Double against a three, four, five, and six if allowed
  and otherwise hit.
• Ace seven or soft 18 – Stand against a dealer two, seven, and eight, hit
  against a nine, 10, or ace, and double if allowed against three, four, five, or
  six.
• Ace eight or soft 19 – Stand at all times.
• Ace nine or soft 20 – Always stand.
• Ace 10 – Blackjack! Always stand.

Pairs

Whenever you have a pair for your first two cards you need to decide if you
should split.

• Two two – Split against a dealer four, five, six, and seven, hit against a
  dealer eight, nine, 10, and ace, and against a dealer two or three split if you
  can double after split and hit if double after split isn’t allowed.
• Three three – Play your hand exactly the same as two two. If double after
  split is allowed split against a dealer two or three, otherwise hit against
  these two cards. Hit against a dealer eight, nine, 10, and ace, and split
  against a dealer four, five, sis, and seven.
• Four four – When double after split is allowed split against a dealer five
  and six, otherwise hit. Hit against all other dealer cards.
• Five five – Never split fives. Hit against a dealer 10 or ace and double
  against all other dealer cards if allowed.
• Six six – Hit against a dealer seven, eight, nine, 10, and ace. Split against
  a dealer three, four, five, and six. Split against a dealer two if double after
  split is allowed, otherwise hit.
• Seven seven – Split against a dealer two, three, four, five, six, and seven.
  Hit against a dealer eight, nine, 10, and ace.
• Eight eight – Always split eights.
• Nine nine – Split against a dealer two, three, four, five, six, eight, and
  nine. Stand against a dealer seven, 10, and ace.
• Ten ten – Always stand with a total of 20.
• Ace ace – Aces should always be split. If you receive another ace on one of
  your split aces you should split again. Do this as many times as possible.

Hard Totals

A hard total is any hand that doesn’t have an ace where you can use it as a
one or 11. In any two card starting hand you can use an ace as either one or 11,
but after you hit one or more times you can reach a total where the ace can’t be
used as an 11 without busting. When this happens you hold a hard hand.

• Hard four – The only hard four is a pair of twos. This is covered in the two
  two line under pairs. If splitting isn’t allowed then always hit with a hard
  four.
• Hard five – Always hit with hard five.
• Hard six – Hit against all dealer cards with a hard six.
• Hard seven – Always hit with a hard seven.
• Hard eight – Hit against all dealer totals with hard eight.
• Hard nine – If double is allowed, double against a dealer three, four, five,
  or six, otherwise hit. Hit against all other dealer cards.
• Hard 10 – When double is allowed, double against a dealer two, three, four,
  five, six, seven, eight, and nine, otherwise hit. Hit against a dealer 10 and
  ace.
• Hard 11 – Double against any dealer car except an ace if doubling is
  permitted, otherwise hit. Hit against a dealer ace.
• Hard 12 – Stand against a dealer four, five, and six. Hit against all other
  dealer cards.
• Hard 13 – Stand against a dealer two, three, four, five, and six. Hit against
  a dealer seven, eight, nine, 10, and ace.
• Hard 14 – Stand against a dealer two, three, four, five, or six and hit
  against seven or higher.
• Hard 15 – Against a dealer two, three, four, five, and six you should stand.
  Against a dealer seven, eight, nine, 10, and ace you should hit.
• Hard 16 – Stand against a dealer total of two, three, four, five, and six.
  Hit against all other dealer totals.
• Hard 17 – Stand against all dealer hands.
• Hard 18 – Always stand with a hard 18.
• Hard 19 – Stand against all dealer hands.
• Hard 20 – Always stand with a hard 20.
• Hard 21 – Stand against all dealer totals.

Surrender

If surrender is allowed you should surrender with a hard 15 against a dealer
10 and with a hard 16 against a dealer nine, 10, or ace. If surrender isn’t
allowed then hit in these four situations.

Adjustments for Different Rules

The chart and instructions above are designed for a game where the dealer
stands on a soft 17. If you play in a game where the dealer hits on a soft 17
you can make the following adjustments.

As we mentioned above, it can be complicated to keep two different charts
straight in your mind so learning the first chart is best. However, there are
only six hands that change so it’s possible to learn and use the differences.

Split hands

Instead of splitting eight eight against a dealer ace,
surrender if allowed, otherwise split.

Soft hands

With a soft 18 against a dealer two and with a soft 19 against a
dealer six double if allowed, otherwise stand.

Hard hands

With a hard 11 against a dealer ace double if allowed, hit
otherwise. With a hard 15 against a dealer ace surrender if permitted, otherwise
hit. With a hard 17 against a dealer ace, surrender if permitted and otherwise
stand.

Insurance or Even Money

Notice that there’s not a single hand that recommends taking insurance or
even money. This is because taking insurance is always a losing proposition.

When the dealer has an ace showing you have the option of making another bet
equal to the size of your first bet that pays two to one if the dealer has a 10
hole card. If you take insurance and the dealer has a 21 you lose your first bet
but get double on your second so you break even.

But when the dealer doesn’t have 21 you lose the insurance bet and your first
bet plays out as normal.

On the surface this may seem like a good bet, but a simple look at the math
behind the bet shows why you should never take insurance.

Blackjack Probability Math

When the dealer has an ace showing she has a blackjack any time a 10, jack,
queen, or king is her down card. This means four of the 13 possible cards pay
off on the insurance bet.

But this also means that the other nine cards, two through nine and ace, make
you lose the insurance bet. This is a ratio of nine to four, with nine losing
cards and four winning cards. But the bet only pays two to one.

The odds of nine to four is worse than two to one, so it’s a losing bet.

Forget your normal hand because it doesn’t have anything to do with the
insurance offer. Insurance is just a bet on what the dealer has as a down card.
And since it’s offered at bad odds you can now see that it should be avoided.

This is just another way the casinos try to be sneaky and build a bigger long
term edge against you.

How to Memorize Basic Strategy

The easiest way to start memorizing basic strategy is to use the chart
provided above to make every playing decision. As you play you’ll start
recognizing the correct play for most hands before checking your chart.

Sign up for a free account at one of our recommended online casinos and start
playing the free blackjack games. You can play over 100 hands per hour in most
cases so you can get a great deal of practice in a short amount of time.

Blackjack Probability To Win

Eventually you’ll only need to check your chart on the most difficult plays
and if you play long enough all of the plays will come from memory.

The other way is more difficult for most players, but if you have a strong
mind for memory you can simply start memorizing the chart.

A quick tip is to group similar hands together.

All of the hard hands totaling four, five, six, seven, and eight are played
the same way. On all of these hands you always hit. If you’re playing a game
where doubling isn’t allowed, you can add all of the hard totals of nine, 10 and
11 to this. As a side note, you should avoid games where doubling isn’t allowed
as they have a higher house edge.

Other easy to learn hands include:

• Always split aces and eights.
• Soft 13 and 14 are played the same.
• Soft 15 and 16 are played the same.
• Soft 17 only has one dealer card played differently than soft 15 and 16.
• Hard 13, 14, 15, and 16 are played the same unless surrender is allowed.
• Hard 10 and 11 are the same except for one dealer card.
• Two two and three three are played the same.
• All of the hard totals 17 and above are played the same.
• All of the soft totals of 19 and above are played the same.

The majority of hands are hard hands and the complete hard hand strategy is
fairly simple. Memorize it first and you’ll find that you won’t need to refer to
the chart often.

The next chart to memorize after you’ve mastered the hard hands is the soft
hands. Most of them are straightforward as well, with the main changes of
knowing when to double down.

Once you have the hard and soft hands memorized the splits will come easy to
finish out your mental chart. You only need to learn the split rules for twos,
threes, fours, sixes, sevens, and nines.

The main thing is to not be afraid that you can’t learn the chart and to get
started right away. Almost anyone can improve their results and reduce the house
edge with a small amount of effort and time.

Card Counting

If you learn how to count cards you can play with a small edge against the
house while playing blackjack. This page is about basic strategy so we aren’t
going to dig into the realm of card counting, but it does have quite a bit to do
with basic strategy.

Card counters learn perfect basic strategy before they start trying to learn
about counting. If you can’t put in the work to learn perfect strategy you have
no hope of being a successful card counter.

Once you master basic blackjack strategy then you should investigate card
counting to see if it’s something you might want to learn. Counting cards online
won’t get you an edge because the software shuffles the cards after each deal,
but if you play live it might be able to help you win or at least play a break
even game.

Conclusion

Learning and using blackjack basic strategy gives you the best chance to win.
It reduces the house edge as much as possible and helps you have more winning
playing sessions.

Most players don’t take the time to learn basic strategy, but if you use the
information above you can quickly start using the best play for every situation.
Use the tips in the how to memorize basic strategy section and you’ll be a
master in no time.

And don’t forget to use the chart provided as you’re learning. Once you get
used to it you can find the proper play in a second or two.