To answer this question, for simplicity's sake we'll assume that the cards are coming from a full, standard pack. And we'll look at two equivalent�...

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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.

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, click to see more there are two possible outcomes�heads or tails.

Example 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.

Example 3: You want to determine the probability of drawing the ace of spades out of a deck of cards.

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.

Example 5: 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.

Example 6: You have a two headed coin.

Your probability of getting heads is 100%.

A fraction is just one way of expressing a probability, though.

You can also express fractions as a decimal or a percentage.

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.

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 continue reading get something other than a six, and only one way to get a six, so the odds are 5 to 1.

Example 2: Blackjack probability question want to express the odds of drawing an ace of spades out a deck of cards.

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.

He bets a dollar on every roll of a single die, and he gets to guess a number.

In the short run, of course, anything can happen.

If you changed the equation slightly, you could play this game at a profit.

But his winnings would be large enough to compensate for those 5 losses and then some.

The difference between the payout https://microrcracing.com/blackjack/biloxi-blackjack-tournaments.html on a bet and the true odds is where go here 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.

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.

Here are some examples of how that works.

To get a blackjack, you need either an ace-ten combination, or a ten-ace combination.

You have four aces in the deck, and you have 52 total cards.

There blackjack probability question 16 cards in the deck with a value of ten; four each of a jack, queen, king, and ten.

You want to know if one or the other is going to happen, so you add the two probabilities together.

That translates to approximately 0.

In all 4 of those hands, no ace or 10 has appeared.

What is your probability of getting a blackjack now?

There are only 28 cards left in the deck.

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.

This last example demonstrates why counting cards works.

The deck has a memory of sorts.

The House Edge The house edge is a related concept.

Your house edge is 16.

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.

What does the house edge for blackjack amount to, then?

It blackjack strategy simple 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.

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.

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.

Effects of Different Rules on blackjack probability question 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.

click 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.

Rules Variation Effect on House Edge 6 to 5 payout on a natural instead of the stand 3 to 2 payout +1.

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.

Card Rank Effect on House Edge When Removed 2 -0.

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.

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.

You can also look at the probability that a dealer will bust based on her up card.

Players generally stand more often when the dealer has a six or lower showing.

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 and easier.

The information found on Gamblingsites.

It is a purely informational website that does not accept wagers of any kind.

Although certain pages within Gamblingsites.

If you believe you have a gambling problem, please visit BeGambleAware or GAMCARE for information and help.

My question is how do I calculate the probability of not receiving a flush, straight or 3 of a kind for x amount of hands. It is dealt from a 6 deck�...

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I'm interested in the following situational question - In a standard Double Deck game, What is the probability of being dealt a two card 20 as a starting hand, the dealer having an Ace up, and the player not taking insurance, and the dealer not having a blackjack, blackjack probability question the dealer drawing to a 5 card 21?

What is the probability the same occuring, but being dealt a two card combination without including A,9 combos?

I lost my math skills 10 years ago :D.

The number I got was roughly around.

This seems awful low, and doesn't account for the dealer not having it, as well as only counting 3+ card 21 draws.

Solve for whatever you like, however you like.

More interested in the process.

The only way to get a 2-card 20 besides an A9 is with two 10-count cards.

Thanks Don for that sequence of it.

My answer was coming up differently.

Any insights into the other parts of the question appreciated.

And I quote another resource with the correct answer.

Odds of drawing any two card 20 is 10.

Odds of a Rain man blackjack italia 20 is 9.

Moreover, the odds of the dealer having Ace Up, No blackjack in DD, disregarding our hand, should be.

Does anyone know any way of calculating that probability other than essentially listing all the 4 card draws to an Ace that total 21 without making a soft 18-20 or a hard 17-20?

Assuming dealer hits a soft 17, basically there are two pathways for dealer to make a 5 card 21 starting from click here Ace: 1.

Two small cards totally 2-6 to make a hand between S13-S17, followed by a card larger than a 4 to make a hard 12-16, followed by a final card to make 21.

One small card, A-6, followed, by a card larger than a 4 to make a hard 12-15, followed by a small card to keep the total under 16, followed by a final card to make 21.

But, as you look at the details, I don't think that is easy to write as an analytic algorithm.

So many better men, blackjack probability question few of them friends, were dead.

And a thousand thousand slimy blackjack still can you count cards lived on, and so did I.

You can easily do it with a Markov chain.

You should only need 65 cells - 5 rows and 13 columns.

You could also list out all 5 card permutations, there are only 100,000.

You should only need 65 cells - 5 rows and 13 columns.

I'm an excellent Excel programmer but I'm weak on Markov chains.

Still trying to figure out how to do that.

Quote: Ace2 You could also list out all 5 card permutations, there are only 100,000.

No, the first card is always an Ace, which reduces it from 100,000 to 10,000.

And then, you can eliminate whenever the 2nd card is a 7-T, which reduces it to 6,000.

Then, also eliminate whenever the last card is a Ten or Blackjack probability question, which reduces it to 3,000.

Then, also eliminate these combinations: - whenever the 2nd and 3rd card add to 7,8,9 or 10.

In reality, the number of permutations to write out is reasonable.

So many better men, a few of them friends, were dead.

And a thousand thousand slimy things lived on, and so did I.

I have figured out a straightforward way to list all the permutations for dealer making a 5-card 21 starting with an ace and to calculate the probability - assuming an infinite deck approximation.

By defining some new terminology or at least it was new to me I needed only 41 groups of permutations; i.

So many better men, a few of them friends, were dead.

And a thousand thousand slimy things lived on, and so did I.

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Some of the important rules of blackjack are as follows: Face cards. We can then ask some basic probability questions, such as: 1. What is the�...

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In the game of blackjack played with one deck, a player is initially dealt 2 different cards. Find the probability of being dealt a blackjack hand.

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What are the chances of you doubling your blackjack bankroll vs. busting out?. blackjack. Now let me pose this question. Do you think the probability of�...

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What is the probability of having a suited Ace-Jack?What is the probability that both dealer blackjack probability question player have a suited Ace-Jack?

My own calculations lead to something like 1:135000 for a single deck game.

But I assume not sure that we actually play a six-deck game.

What is the probability of having a suited Ace-Jack?

What is the probability that both dealer and player have a suited Ace-Jack?

My own calculations lead to something like 1:135000 for a single deck game.

But I assume not sure that we actually play a six-deck game.

First of all, great question and welcome to WizardofVegas!

I hope you stick around!

This is actually a fairly easy question, just separate the dealer and the player.

DEALER SIDE: In order to win, the player must already have a suited AJ Blackjack, so that removes an Ace from one of the suits and a Jack from one of the suits.

The reason it is less likely with one deck is because the effect of removal is greater.

Think of it this way, if the player gets a suited AJ in hearts on six decks, there are still five of those the dealer could get whereas if the player click to see more suited AJ hearts with one deck, then the dealer cannot get that.

source for your quick and comprehensive response.

I am happy to see my own ~ 1:135000 confirmed for a one deck game, so it seems I got the math blackjack probability question.

"Casino games such as roulette, blackjack, baccarat, slot machines and so on, are stacked in favour of the house." � Victoria Coren Mitchell, professional poker.

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Odds and Probability in Blackjack. In fact, it's easier for computer programs to calculate blackjack probability by. Here are a couple of examples of this.

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When a person walks out of a casino the question that inevitably. Blackjack is a game of dynamic probabilities and shifting percentages.

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Questions, answers, and requests related to Kaggle Learn courses.... https://www.kaggle.com/khanos/blackjack-microchallenge-probability-approach?

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Blackjack uses a standard 52 card deck with 13 ordinal cards (Ace. The question states that there are 4 hands being dealt and that each of�...

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