- Chances Of Winning Blackjack
- Odds Of Winning A Single Blackjack Hand
- Chances Of Winning 5 Blackjack Hands In A Row
- Blackjack Winning Percentage
Blackjack has many wonderful qualities. It’s a game where your decisions matter. It’s also a game where you can get an edge over the casino (if you know how to count cards).
A good example of this practice is roulette, in which a wager on a single number pays 35 to 1 even though the odds of winning are 1 in 37. What are the odds of winning blackjack. Blackjack, however, foils the computation of odds based on random events because there are a number of influences that prevent it from being completely random—most.
Most of all, it’s just plain fun.
But blackjack is more fun when you’re winning more often.
Luckily, it’s a game where the mathematically correct way to play each hand has already been figured out. Computer programmers have run millions of hands of blackjack through simulators to come up with the moves that have the highest expected value.
A word about that:“Expected value” refers to how much a bet is worth. In some situations at the blackjack table, the expected value of a specific decision is positive. It might be more positive than other positive decisions.
In some other situations at the blackjack table, you must choose between the lesser of several evils. If you have a stiff hand, the best you can do is go with the decision that loses you the least amount of money in the long run.
As luck would have it, you only have a handful of totals to make decisions about. The highest possible total you can have without busting is 21. The lowest possible total with 2 cards is 4.
In the post below, I’ll look at each possible total and how it could occur. Then I’ll explain how to play that total based on which cards it’s made of and what the dealer has as her face-up card.
All these explanations are based on basic strategy.
A Total of 21
When you have a total of 21, you should always stand. It doesn’t matter what cards make up that total. It doesn’t matter what the dealer’s up-card is.
You always stand with 21. Any other choice costs money.
A Total of 20
You’ll always stand with a total of 20, too, no matter what the cards are. It also doesn’t matter what the dealer’s face-up card is.
The reasoning behind this is clear. There’s only one possible total the dealer could have which will beat a 20, which means you’ll win with it most of the time.
You might need to decide whether to split a hard total of 20. If you have 2 cards of the same rank, you can put up another bet and start 2 hands using the cards in your hand as the first card of the 2 subsequent hands.
It seems like this might not be a bad idea. After all, any hand with a 10 as its first card is probably going to turn out okay.
It’s a mistake, though. Most of the time, you’ll wind up with 2 hands that aren’t as strong as your total of 20. There are more cards in the deck that aren’t worth 10 or 11 than there are cards which are worth 10 or 11.
A Total of 19
You will ALMOST always stand on a total of 19, regardless of which cards make up the total.
But there’s one exception:
If you have a soft total of 19—an ace and an 8—you’ll double down. But only if the dealer has a 6 showing.
In some casinos, you’re not allowed to double down on a soft total of 19. If that’s the case, you’ll just stand.
On any other total of 19, though, you’ll stand. It’s such a strong hand that it will beat anything except a total of 20 or 21 from the dealer.
But even if you suspect that the dealer has one of those totals, your odds of winding up with a worse hand are too good for it to be a smart move to take another card.
The only reason you double down against a dealer’s face-up 6 is because the dealer is so likely to bust that it’s worth the risk.
A Total of 18
If you have a total of 18 that’s made up of two 9s, you must decide whether to split your hand or not. Most of the time, you will split your hand, but there are exceptions.
You’ll split a pair of 9s if the dealer has a 6 or less showing. You’ll also split 9s if the dealer has an 8 or 9.
If the dealer has a 7, 10, or ace showing, you’ll stand.
If you have a total of 18 that includes an ace that can be counted as 1 or 11, you have a “soft” 18. If the dealer has a 6 or lower showing, and if the casino allows it, you’ll double down on this hand.
If the casino doesn’t allow you to double down on a soft 18, you’ll stand instead.
Chances Of Winning Blackjack
If the dealer has a 7 or 8, you’ll stand on a soft 18.
If the dealer has a 9, 10, or ace showing, you’ll hit a soft 18.
Being able to count the ace as 1 or as 11 gives you some flexibility with how you play this hand. The combination of the possibility to improve your hand and the possibility that the dealer will bust results in the possible doubling down decisions.
Any other total of 18 will be a hard total, and you’ll always stand on a hard total of 18.
A Total of 17
If you have an ace that counts as 1 or 11, you have a soft total of 17. In that case, you should double down if the dealer has a 3, 4, 5, or 6 showing. If the dealer has any other card showing, you should hit this total.
If you don’t have an ace, or if counting the ace as an 11 would bust you, you have a hard total of 17. It’s easy what to decide to do with a hard 17:
Always stand.
A Total of 16
Once you get down to the total of 16 or less, you’re getting into “stiff hand” territory. A stiff hand is one which is likely to bust.
It doesn’t matter, though.
There’s still only one correct way to play each stiff hand, too.
The first kind of total of 16 you should think about is a pair of 8s. You should always split a pair of 8s. The reasoning behind this should make sense. You’re trading a mediocre hand for 2 hands which are likely to improve. More cards in the deck will improve an 8 than will hurt it. Any ace, 10, or 9 will give you a better total than 16. (And there are 16 cards worth 10 in the deck, so that’s almost half the deck in total.)
The second kind of total of 16 to worry about is a soft 16. Again, this is a total where the ace can count as 1 or 11. You will NEVER stand on a soft 16.
You’ll double down on a soft 16 if the dealer has a 4, 5, or 6 showing. If the dealer has any other card showing, you’ll fold.
Finally, you need to know what to do with any other hard total of 16. You’ll stand if the dealer has a 6 or less showing. You’ll hit if the dealer has a 7 or higher showing.
If the dealer has a 6 or less showing, you’re hoping she’ll bust. Otherwise, you’re hoping to improve your hand so that you have a fighting chance.
A Total of 15
A soft total of 15 is easy to play. You’ll play it just like you would a soft total of 16, in fact. You’ll double down if the dealer has a 4, 5, or 6 showing. Otherwise, you’ll hit.
A hard total of 15 isn’t hard to play, either, although it’s a bummer of a hand. Again, you’ll play a hard 15 just like you would a hard 16. Hit if the dealer has a 7 or higher. Otherwise stand.
A Total of 14
If you have a pair of 7s, you need to decide whether to split. You will split if the dealer has a 7 or lower showing. If you don’t split, you’ll treat the hand as any other hard 14.
If you have a soft 14, you will never stand. You’ll double down if the dealer has a 5 or 6 showing. Otherwise, you’ll hit.
If you have a hard 14, you’ll play it just like a hard 15 or 16. Stand if the dealer has a 6 or less showing. Hit if the dealer has a 7 or higher showing.
A Total of 13
A soft total of 13 is played just like a soft 14. You’ll double down if the dealer has a 5 or 6. Otherwise, you’ll hit.
A hard total of 13 is played just like a hard 14, 15, or 16. Stand if the dealer has a 6 or less. Otherwise, hit.
A Total of 12
The first kind of 12 total to worry about is a pair of 6s. (You always consider whether to split first.) You should double down if the dealer has a 6 or lower showing. If not, you’ll treat the hand just like you would any other hard total of 12.
Next, you’ll think about a soft total of 12. This could mean you have a pair of aces. In that case, you always split. (Just remember—always split aces and 8s.)
There’s no other way to get a soft total of 12, so you’re left with the possibility of a hard 12. If that’s what you have, you stand against a dealer 4, 5, or 6. Otherwise, you hit.
A Total of 11
If you have an ace and a 10, you COULD consider that a soft total of 11. But really, you have a blackjack. Just accept your winning with grace.
On any other total of 11, you’ll double down. That’s an easy decision, because you have lots of cards which will increase your total to 21. There’s no real downside to doubling down on an 11, because it’s impossible to bust such a hand.
A Total of 10
You never split 5s. They’re always treated as a hard total of 10.
If you have a soft total of 10, you really have a soft total of 20, and I’ve already covered that. (Think about it.)
With a hard 10, which is really the only way you’ll ever have a total of 10, you’ll almost always double down. The only time you won’t double down is if the dealer has an ace or 10 showing. In that case, you’ll just stand. (You don’t want to put extra money into play because of the increased likelihood that the dealer will have a 21.)
A Total of 9
A hard 9 is played ALMOST exactly like a hard 10. You should double down if the dealer has a 3, 4, 5, or 6. Otherwise, hit.
A Total of 8
You never split a pair of 4s. (In fact, you can remember this rule—never spit 4s, 5s, or 10s.)
In fact, there’s only ONE way to correctly play a hard total of 8. Always hit.
A Total of 7
Always hit a hard total of 7.
A Total of 6
If you have a pair of 3s, split if the dealer has a 7 or lower showing. Otherwise, just hit.
If you have any other hard total of 6, just hit the hand.
A Total of 5
Always hit a hard total of 5.
A Total of 4
If you have a pair of deuces, play it just like a pair of 3s. Split if the dealer has a 7 or lower showing. Otherwise, just hit.
Conclusion
That’s it.
You only have 18 possible starting totals in blackjack. Once you’ve learned how to play each of those totals correctly, you’ve mastered basic strategy.
Why is that a good thing to do?
Odds Of Winning A Single Blackjack Hand
If you’ve mastered basic strategy, the house edge for most blackjack games is between 0.5% and 1%, making it one of the best games in the casino.
If you misplay these hands, the house edge goes up. Most players are bad at basic strategy, by the way. If you look at the casino’s numbers, the average blackjack player is so bad that he’s facing a house edge of between 4% and 5%.
With those kinds of numbers, you might as well play craps or roulette. You don’t have to make any playing decisions with those games.
memorize basic strategy in this way.
One of the most interesting aspects of blackjack is the
probability math involved. It’s more complicated than other
games. In fact, it’s easier for computer programs to calculate
blackjack probability by running billions of simulated hands
than it is to calculate the massive number of possible outcomes.
This page takes a look at how blackjack probability works. It
also includes sections on the odds in various blackjack
situations you might encounter.
An Introduction to Probability
Probability is the branch of mathematics that deals with the
likelihood of events. When a meteorologist estimates a 50%
chance of rain on Tuesday, there’s more than meteorology at
work. There’s also math.
Probability is also the branch of math that governs gambling.
After all, what is gambling besides placing bets on various
events? When you can analyze the payoff of the bet in relation
to the odds of winning, you can determine whether or not a bet
is a long term winner or loser.
The Probability Formula
The basic formula for probability is simple. You divide the
number of ways something can happen by the total possible number
of events.
Here are three examples.
Example 1:You want to determine the probability of getting heads when
you flip a coin. You only have one way of getting heads, but
there are two possible outcomes—heads or tails. So the
probability of getting heads is 1/2.
You want to determine the probability of rolling a 6 on a
standard die. You have one possible way of rolling a six, but
there are six possible results. Your probability of rolling a
six is 1/6.
You want to determine the probability of drawing the ace of
spades out of a deck of cards. There’s only one ace of spades in
a deck of cards, but there are 52 cards total. Your probability
of drawing the ace of spades is 1/52.
A probability is always a number between 0 and 1. An event
with a probability of 0 will never happen. An event with a
probability of 1 will always happen.
Here are three more examples.
Example 4:You want to know the probability of rolling a seven on a
single die. There is no seven, so there are zero ways for this
to happen out of six possible results. 0/6 = 0.
You want to know the probability of drawing a joker out of a
deck of cards with no joker in it. There are zero jokers and 52
possible cards to draw. 0/52 = 0.
You have a two headed coin. Your probability of getting heads
is 100%. You have two possible outcomes, and both of them are
heads, which is 2/2 = 1.
A fraction is just one way of expressing a probability,
though. You can also express fractions as a decimal or a
percentage. So 1/2 is the same as 0.5 and 50%.
You probably remember how to convert a fraction into a
decimal or a percentage from junior high school math, though.
Expressing a Probability in Odds Format
The more interesting and useful way to express probability is
in odds format. When you’re expressing a probability as odds,
you compare the number of ways it can’t happen with the number
of ways it can happen.
Here are a couple of examples of this.
Example 1:You want to express your chances of rolling a six on a six
sided die in odds format. There are five ways to get something
other than a six, and only one way to get a six, so the odds are
5 to 1.
You want to express the odds of drawing an ace of spades out
a deck of cards. 51 of those cards are something else, but one
of those cards is the ace, so the odds are 51 to 1.
Odds become useful when you compare them with payouts on
bets. True odds are when a bet pays off at the same rate as its
probability.
Here’s an example of true odds:
You and your buddy are playing a simple gambling game you
made up. He bets a dollar on every roll of a single die, and he
gets to guess a number. If he’s right, you pay him $5. If he’s
wrong, he pays you $1.
Since the odds of him winning are 5 to 1, and the payoff is
also 5 to 1, you’re playing a game with true odds. In the long
run, you’ll both break even. In the short run, of course,
anything can happen.
Probability and Expected Value
One of the truisms about probability is that the greater the
number of trials, the closer you’ll get to the expected results.
If you changed the equation slightly, you could play this
game at a profit. Suppose you only paid him $4 every time he
won. You’d have him at an advantage, wouldn’t you?
- He’d win an average of $4 once every six rolls
- But he’d lose an average of $5 on every six rolls
- This gives him a net loss of $1 for every six rolls.
You can reduce that to how much he expects to lose on every
single roll by dividing $1 by 6. You’ll get 16.67 cents.
On the other hand, if you paid him $7 every time he won, he’d
have an advantage over you. He’d still lose more often than he’d
win. But his winnings would be large enough to compensate for
those 5 losses and then some.
The difference between the payout odds on a bet and the true
odds is where every casino in the world makes its money. The
only bet in the casino which offers a true odds payout is the
odds bet in craps, and you have to make a bet at a disadvantage
before you can place that bet.
Here’s an actual example of how odds work in a casino. A
roulette wheel has 38 numbers on it. Your odds of picking the
correct number are therefore 37 to 1. A bet on a single number
in roulette only pays off at 35 to 1.
You can also look at the odds of multiple events occurring.
The operative words in these situations are “and” and “or”.
- If you want to know the probability of A happening AND
of B happening, you multiply the probabilities. - If you want to know the probability of A happening OR of
B happening, you add the probabilities together.
Here are some examples of how that works.
Example 1:You want to know the probability that you’ll draw an ace of
spades AND then draw the jack of spades. The probability of
drawing the ace of spades is 1/52. The probability of then
drawing the jack of spades is 1/51. (That’s not a typo—you
already drew the ace of spades, so you only have 51 cards left
in the deck.)
The probability of drawing those 2 cards in that order is
1/52 X 1/51, or 1/2652.
You want to know the probability that you’ll get a blackjack.
That’s easily calculated, but it varies based on how many decks
are being used. For this example, we’ll use one deck.
To get a blackjack, you need either an ace-ten combination,
or a ten-ace combination. Order doesn’t matter, because either
will have the same chance of happening.
Your probability of getting an ace on your first card is
4/52. You have four aces in the deck, and you have 52 total
cards. That reduces down to 1/13.
Your probability of getting a ten on your second card is
16/51. There are 16 cards in the deck with a value of ten; four
each of a jack, queen, king, and ten.
So your probability of being dealt an ace and then a 10 is
1/13 X 16/51, or 16/663.
The probability of being dealt a 10 and then an ace is also
16/663.
You want to know if one or the other is going to happen, so
you add the two probabilities together.
16/663 + 16/663 = 32/663.
That translates to approximately 0.0483, or 4.83%. That’s
about 5%, which is about 1 in 20.
You’re playing in a single deck blackjack game, and you’ve
seen 4 hands against the dealer. In all 4 of those hands, no ace
or 10 has appeared. You’ve seen a total of 24 cards.
What is your probability of getting a blackjack now?
Your probability of getting an ace is now 4/28, or 1/7.
(There are only 28 cards left in the deck.)
Your probability of getting a 10 is now 16/27.
Your probability of getting an ace and then a 10 is 1/7 X
16/27, or 16/189.
Again, you could get a blackjack by getting an ace and a ten
or by getting a ten and then an ace, so you add the two
probabilities together.
16/189 + 16/189 = 32/189
Your chance of getting a blackjack is now 16.9%.
This last example demonstrates why counting cards works. The
deck has a memory of sorts. If you track the ratio of aces and
tens to the low cards in the deck, you can tell when you’re more
likely to be dealt a blackjack.
Chances Of Winning 5 Blackjack Hands In A Row
Since that hand pays out at 3 to 2 instead of even money,
you’ll raise your bet in these situations.
The House Edge
The house edge is a related concept. It’s a calculation of
your expected value in relation to the amount of your bet.
Here’s an example.
5%.
Expected value is just the average amount of money you’ll win
or lose on a bet over a huge number of trials.
Using a simple example from earlier, let’s suppose you are a
12 year old entrepreneur, and you open a small casino on the
street corner. You allow your customers to roll a six sided die
and guess which result they’ll get. They have to bet a dollar,
and they get a $4 win if they’re right with their guess.
Blackjack Winning Percentage
Over every six trials, the probability is that you’ll win
five bets and lose one bet. You win $5 and lose $4 for a net win
of $1 for every 6 bets.
Your house edge is 16.67% for this game.
The expected value of that $1 bet, for the customer, is about
84 cents. The expected value of each of those bets–for you–is
$1.16.
That’s how the casino does the math on all its casino games,
and the casino makes sure that the house edge is always in their
favor.
With blackjack, calculating this house edge is harder. After
all, you have to keep up with the expected value for every
situation and then add those together. Luckily, this is easy
enough to do with a computer. We’d hate to have to work it out
with a pencil and paper, though.
What does the house edge for blackjack amount to, then?
It depends on the game and the rules variations in place. It
also depends on the quality of your decisions. If you play
perfectly in every situation—making the move with the highest
possible expected value—then the house edge is usually between
0.5% and 1%.
If you just guess at what the correct play is in every
situation, you can add between 2% and 4% to that number. Even
for the gambler who ignores basic strategy, blackjack is one of
the best games in the casino.
Expected Hourly Loss and/or Win
You can use this information to estimate how much money
you’re liable to lose or win per hour in the casino. Of course,
this expected hourly win or loss rate is an average over a long
period of time. Over any small number of sessions, your results
will vary wildly from the expectation.
Here’s an example of how that calculation works.
- You are a perfect basic strategy player in a game with a
0.5% house edge. - You’re playing for $100 per hand, and you’re averaging
50 hands per hour. - You’re putting $5,000 into action each hour ($100 x 50).
- 0.5% of $5,000 is $25.
- You’re expected (mathematically) to lose $25 per hour.
Here’s another example that assumes you’re a skilled card
counter.
- You’re able to count cards well enough to get a 1% edge
over the casino. - You’re playing the same 50 hands per hour at $100 per
hand. - Again, you’re putting $5,000 into action each hour ($100
x $50). - 1% of $5,000 is $50.
- Now, instead of losing $25/hour, you’re winning $50 per
hour.
Effects of Different Rules on the House Edge
The conditions under which you play blackjack affect the
house edge. For example, the more decks in play, the higher the
house edge. If the dealer hits a soft 17 instead of standing,
the house edge goes up. Getting paid 6 to 5 instead of 3 to 2
for a blackjack also increases the house edge.
Luckily, we know the effect each of these changes has on the
house edge. Using this information, we can make educated
decisions about which games to play and which games to avoid.
Here’s a table with some of the effects of various rule
conditions.
| Rules Variation | Effect on House Edge |
|---|---|
| 6 to 5 payout on a natural instead of the stand 3 to 2 payout | +1.3% |
| Not having the option to surrender | +0.08% |
| 8 decks instead of 1 deck | +0.61% |
| Dealer hits a soft 17 instead of standing | +0.21% |
| Player is not allowed to double after splitting | +0.14% |
| Player is only allowed to double with a total of 10 or 11 | +0.18% |
| Player isn’t allowed to re-split aces | +0.07% |
| Player isn’t allow to hit split aces | +0.18% |
These are just some examples. There are multiple rules
variations you can find, some of which are so dramatic that the
game gets a different name entirely. Examples include Spanish 21
and Double Exposure.
The composition of the deck affects the house edge, too. We
touched on this earlier when discussing how card counting works.
But we can go into more detail here.
Every card that is removed from the deck moves the house edge
up or down on the subsequent hands. This might not make sense
initially, but think about it. If you removed all the aces from
the deck, it would be impossible to get a 3 to 2 payout on a
blackjack. That would increase the house edge significantly,
wouldn’t it?
Here’s the effect on the house edge when you remove a card of
a certain rank from the deck.
| Card Rank | Effect on House Edge When Removed |
|---|---|
| 2 | -0.40% |
| 3 | -0.43% |
| 4 | -0.52% |
| 5 | -0.67% |
| 6 | -0.45% |
| 7 | -0.30% |
| 8 | -0.01% |
| 9 | +0.15% |
| 10 | +0.51% |
| A | +0.59% |
These percentages are based on a single deck. If you’re
playing in a game with multiple decks, the effect of the removal
of each card is diluted by the number of decks in play.
Looking at these numbers is telling, especially when you
compare these percentages with the values given to the cards
when counting. The low cards (2-6) have the most dramatic effect
on the house edge. That’s why almost all counting systems assign
a value to each of them. The middle cards (7-9) have a much
smaller effect. Then the high cards, aces and tens, also have a
large effect.
The most important cards are the aces and the fives. Each of
those cards is worth over 0.5% to the house edge. That’s why the
simplest card counting system, the ace-five count, only tracks
those two ranks. They’re that powerful.
You can also look at the probability that a dealer will bust
based on her up card. This provides some insight into how basic
strategy decisions work.
| Dealer’s Up Card | Percentage Chance Dealer Will Bust |
|---|---|
| 2 | 35.30% |
| 3 | 37.56% |
| 4 | 40.28% |
| 5 | 42.89% |
| 6 | 42.08% |
| 7 | 25.99% |
| 8 | 23.86% |
| 9 | 23.34% |
| 10 | 21.43% |
| A | 11.65% |
Perceptive readers will notice a big jump in the probability
of a dealer busting between the numbers six and seven. They’ll
also notice a similar division on most basic strategy charts.
Players generally stand more often when the dealer has a six or
lower showing. That’s because the dealer has a significantly
greater chance of going bust.
Summary and Further Reading
Odds and probability in blackjack is a subject with endless
ramifications. The most important concepts to understand are how
to calculate probability, how to understand expected value, and
how to quantify the house edge. Understanding the underlying
probabilities in the game makes learning basic strategy and card
counting techniques easier.