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.

• Blackjack Is It Possible To Win 7
• How To Play Blackjack And Win
• How To Win Blackjack Online

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.

You can't expect to win at blackjack every time you play. That's because it has a house edge which ensures that the casino has an advantage in the long run.

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.

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.

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.

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.

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.

Here’s an example.

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.

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.

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.

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.

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.

In this article you'll find:

• A basic Blackjack cheat sheet for beginners
• An overview of the best Blackjack strategies to play online
• Useful online Blackjack tips to increase your chances of winning

Let's face it - we've all looked for the best and the most effective strategy to win at blackjack.

More than once.

As a huge fan of Blackjack, I tried countless betting strategies.

I won big, I lost big. Luckily, all of this experience helped me to understand one thing: moderation is the key.

After all I've been through, I want to share my knowledge with you.

My goal is to maximize your winnings and to minimize your losses.

At the end of the day, we are all on the same boat:

We just want to beat the dealer and bring home as much money as possible.

Even though a fool proof blackjack strategy doesn't exist, the info below can help you play smart and win more.

Blackjack Is It Possible To Win 7

Losing all your savings won't get you anywhere and will only make you hate casinos.

So, let's make the best out of your blackjack casino experience and help each other to you win more.

After all, the most important thing is to have fun. And the more you know, the more fun blackjack gets.

Check Out This Blackjack Cheat Sheet

First things first. Even though the most important thing that keeps you from losing big is money management - and as a poker player I assume you are A PRO at this - you also have to know the basic tactics to deal with cards effectively.

As you know, there are a few decisions you can take depending on your cards and the dealer's open card.

These decisions are:

• Stand
• Hit
• Double
• Split
• Surrender

Sometimes, all it takes is basic logic.

Like you don't want to hit (ask for an additional card) if you have a 20, and you don't want to stand if you have only a 3.

However, things are not always that simple.

That's why our experienced team prepared a detailed blackjack chart to show you how to play every hand at blackjack.

Use it to know when it is recommended to hit, to stand, or to do something else.

Yes, you can use this basic blackjack strategy table when you play online blackjack for real money.

Whether you play virtual or live dealer games, you can (or better, you should) base your blackjack play on what's indicated on this blackjack cheat-sheet.

Alternatively, you can use this downloadable Blackjack basic strategy chart.

Key:
S = Stand
H = Hit
Dh = Double (if not allowed, then hit)
Ds = Double (if not allowed, then stand)
SP = Split
SU = Surrender (if not allowed, then hit)

Now that you have a basic understanding the different blackjack actions (which you can practice HERE for free), let's move to the best blackjack betting strategies.

A Conservative Blackjack Strategy: Win Little by Little

If you're a beginner, I completely understand your fear of high stakes.

I also wouldn't want to lose a fortune on my very first game.

Or on my second. And third one.

That would discourage me from playing blackjack ever again - or even visiting Las Vegas.

That's why I suggest you to use a conservative approach when it comes to betting in blackjack.

The main idea is this:

Raise your bet every time you win.

This strategy is based on the idea that wins and losses come in streaks.

You might lose five times in a row, but then, miraculously, win three consecutive bets.

I know, I know, blackjack is a game of chance, and the outcome is random.

BUT

My long-term experience says that there is a pattern. I just can't explain it logically.

Just look at some random sequences made with the probability theory in mind.

Usually, you can see some sort of streaks, and this can be applied to blackjack too.

So, all you need to do is raise your stakes little by little - but only when you win.

You can use our list of the best casinos to play blackjack online and test this strategy for free. Don't forget to use our strategy charts when learning how to win.

An Aggressive Approach to Blackjack: the Martingale Strategy

Now we're talking.

The Martingale blackjack strategy is my favourite.

This is a blackjack system that helps me win often - but only when I have a lot of money to invest on my games.

If you don't have at least $500 to gamble online - don't use it.

If you do - keep reading and get ready to have fun.

The Martingale strategy is completely different from the conservative blackjack approach.

You have to be brave to use this one.

It basically goes like this:

You double your bet… every time you lose.

Now that sounds like a downer.

How can you ever win if you keep losing - and losing more and more as you keep playing?

Listen.

Even if you lose lots of money on several consecutive losses, everything changes when you win.

As you've been doubling your bets, the one that brings you victory makes your bankroll grow to the point of covering the amount you lost before that happened.

However, there's one thing to keep in mind. One very important thing.

Once you go over your initial bankroll, STOP.

The Martingale blackjack strategy doesn't work when it comes to long gaming sessions.

There have been cases when I lost all my money, and that happened because I was greedy.

The best approach is to play blackjack often and stop immediately when you get some extra cash.

This way, you will benefit greatly in the long run and won't be left penniless at the end of the day.

You are very likely to win at least one hand per round of blackjack - and that's all you need when applying the Martingale blackjack strategy.

Just keep in mind that you need a big initial bankroll for this one.

You need to have enough money to keep doubling the bet until you finally beat the odds.

If you feel like it, you can practice this strategy on different blackjack variants to see, which one works best for you.

In case your betting limits are low - don't worry. The next blackjack strategy guide is for you.

1-3-2-6 Blackjack Betting System

The 1-3-2-6 blackjack betting strategy doesn't sound like the most exciting thing ever - especially after you've read about the Martingale strategy - but it can still help you a lot.

Most importantly, it doesn't require to have an enormous bankroll, so that's a plus.

So, what do the numbers in the title of the strategy stand for?

Your bets after you win a hand of blackjack.

In other words, you trigger this system after you win - and cut it once you lose.

This way, you won't lose all your money at once.

Once again, this blackjack strategy is based on the idea that winnings come in streaks.

Also, it gives you a systematic approach to your bets. You don't make your bets randomly and that gives you control over the game. Everything goes as planned - step by step.

How To Play Blackjack And Win

Let's take a look at an example of the 1-3-2-6 blackjack strategy.

Say, your initial bet is $10. If you won blackjack game four times in a row, your betting pattern would look like this:

$10-$30-$20-$60

Of course, let's not forget that you would immediately cut this sequence if you lost.

You would then return to your original $10 and wait for another win.

You might ask, does 1-3-2-6 blackjack strategy really work?

Well, it helps.

It helps you manage your bets, not to overspend, and gives you an advantage when you hit a hot streak.

Even if your winnings might look like rookie numbers at the beginning, you'll have an advantage in the long run.

You can play blackjack for free at this Casino to see if this strategy works for you in reducing the house edge.

How to Win More at Blackjack: A Few Important Tips

Even though we all want to win at blackjack every time we play, it's impossible.

Luckily, you can maximize your winnings and make blackjack odds more favorable with a few simple tips that are as important as an effective blackjack betting strategy.

So, here's what you need to do to be a successful blackjack player:

• Say NO to insurance. Blackjack insurance is probably the worst thing that could happen to this casino game. It's useless, money-draining, and should be thrown out the window immediately. Don't use it!
• Keep the house edge in mind. You can't expect to win at blackjack every time you play. That's because it has a house edge which ensures that the casino has an advantage in the long run. The best method to avoid the house edge is to stop playing as soon as you win extra money.
• Check the rules of blackjack every time you play. It comes as no surprise that such a popular game like blackjack has tons of different variations. Each of them has slightly different rules. Check them out before you make your first bet.
• Choose 3:2 over 6:5 payout. Some casinos decide to cheat a little and make the payout 6:5 instead of the usual 3:2. Playing at such a casino means that you won't win as much as you should. Avoid casino sites, mobile casinos, and live casinos with bad payouts for blackjack players.

And now it's time to test all these best blackjack strategies in real life.

How To Win Blackjack Online

Also, use these tips and study the blackjack action strategy table. After a short while, you'll find yourself winning more and more.

However, the most important method to win at blackjack game is, once again, moderation.

No blackjack strategy will help you if you waste your winnings playing blackjack all day long.

You must quit as soon as you make even the smallest profit, or otherwise everything will go to waste.

If you play small, your winnings will accumulate, and you'll win big in the long run.

And that's the most important thing of all.

Finding a trustworthy room to play online poker can be a monumental burden. That's all the more true if you're just looking for a place to play poker for free. We've listed five of the best play-money poker sites to enjoy and help hone your skills.