Win a SMALL fortune with counting cards-the math of blackjack & Co.
Odds and Probability in Blackjack One of the most interesting aspects of blackjack is the probability math blackjack probability question />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 Blackjack probability question basic formula for probability is simple.
You divide the number of blackjack probability question 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.
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 article source 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.
Example 2: You 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 blackjack probability question 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.
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 are 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 read article />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 see more do with a computer.
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.
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 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.
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 middle cards 7-9 have a much smaller effect.
Then blackjack probability question 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.
This provides some insight into how basic strategy decisions work.
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.
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Although certain pages within Gamblingsites.
If you believe you have a gambling problem, please visit BeGambleAware or GAMCARE for information and help.
Blackjack by the Wizard of Odds
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