If you do not follow basic blackjack strategy, your odds drop even lower. So assuming you are playing the game to win, why wouldn't you use basic blackjack strategy? It may seem like a huge risk to hit when you have 16 and the dealer is showing a 10, but sticking to the strategy consistently will give you the best odds.
Blackjack Odds of Winning As mentioned previously, the best possible house advantage you'll usually see at blackjack tables is 0.5% or a little bit less, even with a solid understanding of basic blackjack strategy. However, it's theoretically possible for blackjack to actually favor the player with the right rule sets. Blackjack is actually one of the most popular games in the casino and also has some of the lowest odds of all the casino games, except casino craps of course. Generally their edge ranges from 1% to 15% depending on what variation of blackjack you are playing. How to Beat the Casino House Odds. In the context of blackjack, the standard deviation of a single hand you play in a six-deck game is estimated at 1.14. Without any deeper understanding of odds in blackjack, it's easy to believe that hitting on a hand value of 12 would always be the right decision. This is because 12 is a very low value and the fact that more than two-thirds of the cards in the deck (s) would improve the value of it.
Some blackjack players are so preoccupied with mastering perfect basic strategy and card counting that they neglect their money management. In blackjack, just like in any other casino-banked game, managing one's bankroll adequately is of great significance.
Having said that, we would also like to point out bankroll management is powerless when it comes to decreasing the house edge. What it does help with is longevity, or preserving your blackjack bankroll for a longer period of time. No matter how perfect your play is, you are guaranteed to lose your money without discipline and proper bankroll management.
Building a Bankroll – How Much Money Do You Need to Play Blackjack?
Let's start by specifying that your bankroll is the money you have set aside strictly for the purpose of playing blackjack. We suspect you already know this but just to play it safe, we shall say it again – you should never use money you need to cover your day-to-day expenses for playing blackjack, regardless of your level of skill or previous experience.
Our advice is to place your blackjack bankroll in a separate account and withdraw from it when you plan to attack the blackjack tables. Once you finish with the assault, you go back and deposit whatever you have left alongside any winnings you have generated during the session.
You should leave your bankroll alone in the beginning and avoid using it for any non-blackjack-related purchases. Once you succeed in building your bankroll, you can reward yourself by buying something with some of the winnings you have generated.
Table Limits and Session Bankrolls
With this clarification out of the way, we warn you there is no uniform bankroll size that applies to absolutely all blackjack players. The edge skilled players get inevitably manifests itself over the long term. Anything can happen over the course of a single session, a week, or even a few months.
Experiencing short-term losses, even if you are an accurate card counter, is hardly anything unheard of. The bottom line is as a serious blackjack player, you need a bankroll that is large enough to withstand the losses you may incur on a short timescale.
The overall amount you allocate for blackjack play should be broken down into smaller session bankrolls. How much you allocate for a single session is closely linked to what table limits you play.
If there are lots of casinos in your area but you have limited funds for blackjack play at your disposal, the smartest thing to do is scout the different gambling halls and find a table with low enough limits to accommodate your small bankroll. Provided that there is a single casino with high limits in your city, you better wait until you save a sufficiently large bankroll to play such stakes.
Show MoreHide MoreA session bankroll should be at least 50 times the lowest bet at the table. This is the bare minimum, recommended for basic strategy players and flat bettors. Respectively, players who count cards and move their bets with the true count are recommended to put aside at least 100 times their top bets.Thus, if there are $10 tables in your vicinity and you flat bet at this minimum with basic strategy, your session's bankroll should be at least $500. Your max bet should not exceed the amount of $10 under any circumstances. Provided that you are a novice card counter who uses a less aggressive bet spread like 1 to 5, you will need a session bankroll of at least $5,000.
Each number 1 through 5 corresponds to the number of base bets you need to wager when you move with the true count. You put out 5 units or $50 on a count of +5 or higher, 4 units or $40 on a count of +4, and so on. One unit of $10 is wagered on a count of +1 as well as on neutral and negative counts.
Evaluating Your Risk of Ruin
Disciplined players who exercise good money management are well-acquainted with the term 'Risk of Ruin', abbreviated as RoR. For those of you who are not, RoR denotes the probability of a given player losing their entire bankroll.
There are several values you need to take into account when estimating your Risk of Ruin, including your standard deviation, your bankroll in units, and your win rate per every hundred hands. There are free RoR calculators on the web players can use to accurately estimate the likelihood of busting their full bankrolls. Your other option is to use blackjack simulators that can calculate the RoR for you.
We can distinguish between two types of Risk of Ruin, namely session RoR and the RoR for players' full bankroll. The former denotes the likelihood of the player losing their entire bankroll for the session while the latter shows you the probability of busting your overall lifetime bankroll.
To give you an example, let's suppose you have a session bankroll of $2,000, play perfect basic strategy, and flat bet $10 per hand. You have 200 base betting units at your disposal. The software you are using has calculated that you have a session RoR of 18%.
This means that eventually you will end up losing your $2,000 around 18% of the time. And the opposite, your bankroll will increase 82% of the time. Meanwhile, if you cut your bankroll in half to $1,000, or 100 units, your RoR will jump to nearly 32%, which exceeds the tolerable limits. In the other 68% of the time, you will increase the bankroll.
It is important to specify that different players are willing to put up with different RoR percentages. At the end of the day, this is all a matter of individual tolerance. The bottom line is the bigger your bankroll is and the more base betting units you have, the lower your RoR will be.
Understanding Standard Deviation
The term standard deviation (SD) is normally used in mathematical statistics in relation to the distribution of expected results. In blackjack, it denotes the distribution of players' results within a range of probable outcomes.
It tells you how frequently a specific outcome will deviate from your expected average. This is important because it enables you to assess whether you are playing a losing or a winning game as well as to decide how big your bankroll should be for any given session.
It is unrealistic to think you can win each and every blackjack session, even if you are perfect at basic strategy and count cards with great accuracy. A low standard deviation indicates the actual results fall closely within one's expectations.
We shall explain how standard deviation works with a simple coin-flipping example. A coin has a 50% chance of landing on tails and a 50% chance of landing on heads. Yet, you cannot expect the coin to land precisely 50 times on tails and 50 times on heads in every 100 trials, or at least not in the short term. Sometimes it may land only 45 times on tails and 55 times on heads which happens roughly 2/3 of the time or around 68.3%.
Show MoreHide MoreIn the context of blackjack, the standard deviation of a single hand you play in a six-deck game is estimated at 1.14. Thus, you are expected to win or lose roughly 1.14 bet units around 68.3% of the time within one standard deviation, 2.28 betting units will be lost/won 95% of the time within two standard deviations and 3.42 units will be lost/won 99.7% of the time within three standard deviations. The distribution of these results is shown on the so-called Gaussian bell-curves.Knowing their standard deviation enables players to calculate the probability of winning or losing a given number of units over the course of a certain number of hands. You do this by multiplying your standard deviation by the square root of the number of hands you play.
So if your sample size involves 400 hands with a standard deviation of 1.14, you can expect to lose or win √400 x 1.14 = 20 x 1.14 = 22.8 betting units around 68.3% of the time. Respectively, 95% of the time, you can expect results within two standard deviations where you will lose √400 x 2.28 = 20 x 2.28 = 45.6 betting units over the course of 400 hands. And finally within three standard deviations, you will lose √400 x 3.42 = 20 x 3.42 = 68.4 betting units every 400 hands 99.7% of the time.
Standard deviation may be complex to understand if you are a novice but is nevertheless of great importance. You need it when calculating your RoR, which in turn helps you determine the bankroll you need. Do not be intimidated, however, as you can figure out what your RoR is by using a simulator software or one of the online RoR calculators.
House Edge and Hourly Losses
The beauty of using basic strategy is that it reduces the house edge in blackjack to such an extent that you are nearly playing a break-even game. Yet, basic strategy is not powerful enough to completely overcome the built-in casino advantage.
Even if you are perfect at basic strategy, the house edge will inevitably cause a dent in your blackjack bankroll over the long run. This dent, however, will be far more significant if you rely on gut feelings and hunches instead of using the optimal strategy.
Knowing the house edge of a blackjack game helps you calculate the hourly losses you can expect to incur in the long term. Suppose you choose a table with more liberal rules like those offered across Las Vegas Strip casinos where the house edge revolves around 0.36%.
You multiply this percentage by the average number of hands you play per hour and your average bet size. Assuming you are a recreational player who joins mostly full tables and bets $30 per hand on average, you will be able to go through roughly 80 hands per hour.
Therefore, the long-term hourly losses you can expect to see will amount to ($30 x 80 hands x 0.36)/100 = 864/100 = $8.64.You will inevitably arrive at this figure when you get enough playing hours under your belt. By 'enough', we mean tens of thousands of hours as anything can happen in the short run.
Unlike basic strategy players who are practically betting on a negative EV game, skilled and disciplined card counters are able to overcome the house edge. They have an advantage of around 1% at six-deck games with decent rules.
This enables them to grow their bankrolls overtime instead of incurring long-term losses. They calculate their expected hourly winnings with the same formula, i.e. by multiplying their edge by the average bet size and the number of hands they play per hour.
Respectively, an accurate counter who plays heads-up at an empty table with at a 1% advantage and goes through 100 bets of $30 per hour can expect long-term hourly returns of ($30 x 100 hands x 1)/100 = 3,000 / 100 = $30.
Handling Losing Sessions
Variance is inherent to all casino games, including blackjack. All players, no matter how skilled they are, will inevitably end up going through some losing sessions. Knowing how to handle these and when to call it quits is of great significance for preserving your bankroll.
Needless to say, chasing your losses is a terrible idea. The rule of thumb all smart blackjack players should follow is to always leave a table before they have busted their entire session bankroll. The general recommendation is to throw in the towel when you are left with fewer than six betting units.
So if you bet $50 per hand, you must ensure you have at least $300 before you continue playing; if you wager $100, you end the session when you are down to less than $600 and so on.
The reason for this is simple – you need enough money to back up any potential splitting and doubling decisions in line with basic strategy. The bottom line is you should never stay at the table if you are so underbanked that you can no longer exercise the optimal playing decisions. Doing the opposite will ultimately cost you money in the long run.
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
Hollywood slots casino hours. 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.
Best Odds For Blackjack
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.
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.
Blackjack Odds Calculator
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.
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. River rock casino parking map. 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%.
Blackjack Odds Explained
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% |
Standard Blackjack Odds Explained
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.
Odds Of Winning Blackjack
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.
Casino Odds Blackjack
| 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.
Standard Blackjack Strategy Card
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.
