Gambling Odds Blackjack

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Unlike other casino card games, blackjack has a low house edge and allows players to increase their bets when the odds are in their favor. When these factors are combined with a good blackjack strategy, players can make money. What many people don’t know Odds I Blackjack is that playing with a Odds I Blackjack good Odds I Blackjack and fair deposit bonus gives you Odds I Blackjack a much, much higher chance of leaving the games with a profit, and bonuses are by far the biggest cost of any online casino.

Blackjack is one of the few casino games which are actually beatable, or at least in theory. This is because unlike most of the other games available on the casino floor, blackjack is a game of dependent trials rather than being based on independent trials. Games like roulette, craps, and slots rely on pure chance for their outcomes since subsequent results are independent of previous ones.

Blackjack is unlike these games because the composition of the shoe or deck changes constantly as cards are being dealt. Since this is a game of dependent events, previously dealt cards can impact the odds of future outcomes. Here the advantage is a variable rather than a constant – it sways back and forth between the dealer and the player as the deck or shoe composition changes.

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Furthermore, the structure of the game is such that certain card denominations favour the dealer while others work to the benefit of the players. This is not the case in games like roulette and slots where the advantage of the house remains constant regardless of what outcomes have previously occurred.

Well-versed blackjack players can recognize the instances when they hold the advantage and make the most of them. However, before you can do this, you must arrive at a proper understanding what blackjack probability and odds are.

The Basic Concept of Probability

Before you dive in the deep end, you must understand what probability is in the first place. Simply put, this is a branch of mathematics that measures the events’ likelihood of occurring. In the context of gambling, probability measures the likelihood of occurrence of random events that belong to a particular set.

In gambling, these sets normally feature a fixed number of random events like the 36 possible permutations for dice rolls or the 37 numbers that could possibly hit during any round in single-zero roulette games.

Calculating blackjack probabilities is a bit more difficult due to the higher number of possible hand combinations within the set, even more so when multiple decks are in play. Smart gamblers can determine whether a given wager will win or lose in the long run by analyzing its payout (the casino odds) in relation to its actual chances of winning (true odds).

To calculate the likelihood of something happening, you can use the basic probability formula, which is P(E) = n(E)/n(S), where P(E) stands for the probability of the event occurring, n(E) reflects the number of ways said event can occur in, and n(S) corresponds to the overall number of possible events within a fixed set.

In the context of gambling, probability is calculated by dividing the number of winning outcomes by the total number of outcomes within a respective set. Let’s examine several simpler examples to make things easier for gambling novices.

Example №1 – The Coin Flip

Each coin flip can result in one out of two possible outcomes, heads or tails. It follows that the probability of landing tails, for example, is equal to P(tails) = 1(tails) / 2(S), or 1/2. Therefore, the likelihood of getting tails is the same as that for landing heads or 0.5, which, in essence, corresponds to 50%.

Example №2 – The Dice Roll

A standard dice has only six sides, which restricts the total number of possible outcomes to six (1, 2, 3, 4, 5, or 6). However, you can get no more than one result per roll, so the probability of rolling any one of these numbers is the same (assuming the dice is not loaded) and equal to 1/6, or P(winning number) = 1(winning number) / 6(S) = 0.166. This corresponds to roughly a 16.6% chance of occurrence.

Example №3 – Any One Individual Number in Roulette

All individual numbers in roulette share exactly the same probability of occurring during any given round of play. It matters not how many times the zero, for instance, has hit. It still stands the same chances of hitting on the next round as the other 36 numbers. Since the set of possible outcomes in single-zero roulette is limited to 37, the zero’s probability of winning is equal to P(zero) = 1 (zero) / 37(S) = 0.0270, or 2.70%.

Example №4 – Drawing the Ace of Diamonds from a Deck of Cards

Suppose you want to determine the likelihood of pulling the ace of diamonds out of a standard card deck. The pack contains 52 cards when the jokers are removed but there is only one ace of diamonds. Respectively, the probability of procuring this ace is P(ace of diamonds) = 1(ace of diamonds) / 52 (S) = 0.0192, or 1.92%.

How Is Probability Mapped?

In random games of independent trials, such as roulette and craps, each possible outcome stands equal chances of occurring during any given round as the rest. Regardless of how many times a specific roulette number has previously occurred, it still has the same odds of appearing on the next round.

This is not the case in blackjack, though. The cards that have left the deck influence the odds of the cards that are yet to be dealt. For example, if you take a single deck and remove the aces of all four suits, the probability of drawing an ace from the remaining pack would be nil.

The probability of events’ occurrence is normally mapped on the so-called probability line. You can see what it looks like below. The closer an event is to the zero, the less probable it is to occur and vice versa. Events in the rightmost spectrum of the probability line are more likely to happen. If a given event has a probability of 1, it is 100% sure to happen. The opposite is true for events whose probability is 0, i.e. they will never occur.

The Probability Line

0________0.25_________0.50________0.75_________1

Probability and Expected Value

Probability is also linked to expected value. In the context of gambling, the expected value (EV) reflects the amount a gambler can expect to lose or win with the same wager over the course of many, many rounds.

The EV of most gambling games is negative because of the built-in house edge. The casino will inevitably return less money to players compared to the overall amount they have collectively wagered. You can calculate the EV of a bet with the following formula: [(Pw x payout) – (Pl x amount lost per wager)]. Pw stands for “the probability of winning” whereas Pl corresponds to “the probability of losing”.

For example, the EV of a European roulette player who wagers $10 on the zero (or any other individual number) would be [(1/37 x $350) + (36/37 x (-$10)] = 9.4594 + (-9.7297) = -0.2703. The EV is a reflection of the house edge and surely enough, 2.70% is the advantage the casino holds over players in single-zero roulette.

Converting Probability to Odds

Odds can also be used for the purposes of expressing probability. There are two types of odds blackjack players can distinguish between, true odds and casino odds. The true odds reflect the actual mathematical probability of a given outcome occurring. The casino odds correspond to the payouts players receive for their winning wagers.

With casino games, including blackjack, there are discrepancies between the true and casino odds. Players are mispaid at shorter odds, which gives the house its edge. True odds are different from probability in that they are expressed as a ratio between the number of winning outcomes and the number of losing outcomes.

Meanwhile, the casino odds reflect the ratio between the amount won and the amount staked. The overall amount won is always less than the overall amount staked in the long run. Here are several examples for further clarification.

• The odds of the zero hitting on a single-zero roulette wheel are 1 to 36 because there is only one zero and 36 other possible outcomes/numbers.
• The odds of drawing the ace of diamonds from a full deck are 1 to 51 because there is only one ace of this suit and 51 other cards.

You may notice casinos typically display the odds of winning bets in reverse. This is because the casino is basically betting against you and rooting for you to lose. When expressed this way, these are the odds against the players winning.

Thus, the first part of the ratio reflects how many units you will be paid per one wagered unit. In roulette, the payout for a single number is 35 to 1, which is to say you get $35 for every dollar you wager. As you can see, the payout is one unit short because the true odds are 36 to 1 rather than 35 to 1.

As for the conversion from probability to odds, it is rather straightforward. Here is another simple example so you can see how it works. The probability of a coin flip resulting in heads is 0.50, or 50%. The odds for heads will then be converted in the following manner:

Odds (heads) = 0.50 / (1 – 0.50) = 0.50 / 0.50 = 1/1 = 1 to 1

The Probability of Receiving Blackjacks

Now that you have gained a rudimentary understanding of how odds and probability work, we shall try to apply this knowledge to the game of 21. The hand blackjack borrows its name from is easily the most important hand in the entire game since it comes with a boosted payout of 3 to 2 (or 1.5 times your winning bet). By contrast, all other winning hands pay out at even-money odds or 1 to 1.

Given the higher expected value of this hand, we thought you might be interested in figuring out what the probability of a blackjack occurring is. To calculate this for a game that plays with a single deck, you should multiply your probability of drawing a ten by that of drawing one of the four aces.

There are a total of 16 ten-value cards since we count in the 10, J, Q, and K of diamonds, spades, clubs, and hearts. Therefore, the probability of drawing an ace is equal to 4 in 52 when you draw from a full deck whereas that of pulling out a ten next is 16 in 51.

The number of cards in the second case has dropped by one to account for the missing ace. We must also multiply the probabilities by two to account for the two different card permutations, (A/Ten) and (Ten/Ace).

Therefore, the likelihood of pulling a blackjack from a single deck is P(BJ) = P (ace) x P(10, K, Q, J) x 2 = (4/52 x 16/51) x 2 = 0.04826, or approximately 4.83%. It follows that blackjacks in single-deck games will occur once per every 21 hands, on average (20.7 hands if you insist on absolute accuracy).

One interesting peculiarity here is that the percentage for blackjacks slightly drops with each deck you introduce into the game. For comparison, the probability of a player pulling out a blackjack in a game that plays with eight decks is P(BJ) = P(ace) x (10, K, Q, J) x 2 = (32/416 x 128/415) x 2 = 0.04745, or 4.75%.

This slight decrease in blackjack probabilities is due to the effect of card removal. The latter is less pronounced in games that use multiple decks. It is worth emphasizing that these percentages correspond to an average. They become accurate over the course of tens of thousands of played hands. You should not be too quick to accuse the house of cheating if you do not get dealt a blackjack even once in 100 rounds.

The Probability of the Dealer Pushing with the Player’s Blackjack

Sometimes it would happen so that a player receives a blackjack only to push with the dealer who also turns out to have obtained this powerful hand. When this happens, the player receives their original bet back rather than getting the coveted 3 to 2 payout. The question arises what is the likelihood of a blackjack push occurring in a single-deck game.

Let’s continue with our previous example to figure it out. Assuming that you have already obtained your blackjack, the dealer’s probability is 3 in 50, because one of the four aces has already been dealt to your hand next to a ten.

Thus, the number of remaining aces drops to 3 and that of the ten-value cards decreases to 15 whereas the overall number of remaining cards is now 50. It follows that the probability of a dealer blackjack is P(DBJ) = P(ace) x P(10, K, Q, J) x 2 = (3/50 x 15/49) x 2 = 0.03673. Therefore, the dealer and the player will push with blackjacks roughly 3.67% of the time, or once per every 27 player blackjacks on average.

You can subtract this percentage from 100% to determine the likelihood of the dealer not pushing with your natural as follows: 100% – 3.67% = 96.33%. One key thing to bear in mind here is that the dealer and the player initially have equal chances of obtaining this powerful hand.

However, the player loses even money (1 to 1) to the dealer’s blackjack whereas the dealer pays for player blackjacks at higher odds of 3 to 2 (or 1.50 to 1). Thus, the player extracts more expected value from blackjacks than the dealer does. Said value can be estimated with the following formula: (PBJ x NDBJ x Payout) + (DBJ x NPBJ x Payout) where:

PBJ stands for the player’s probability of getting a blackjack (0.0483)

NDBJ stands for the probability of the dealer not having a blackjack (0.9633)

DBJ stands for the probability of the dealer having a blackjack (0.0483)

NPBJ stands for the probability of the player not having a blackjack (0.9633)

The payout for a player blackjack is 1.5x the player’s wager

The payout the dealer collects from the player when beating them is 1 to 1, i.e. the player is one unit down or -1

Therefore, when we enter these probabilities and payouts in the formula, it will run as follows: (0.0483 x 0.9633 x 1.5) + (0.9633 x 0.0483 x -1) = 0.06979 + (-0.04652) = 0.02327. In other words, the edge players obtain from blackjacks and their higher payouts stands at roughly 2.33%.

The trouble is blackjacks are not the only hands that occur in this game, not to mention the rest of the rules are tweaked so that the house can maintain a constant advantage over blackjack players.

At some tables, there is also a reduction in the payouts for blackjacks (6 to 5, or 1.2x your initial bet), which has a dramatic effect on the value this hand gives to players. In some variations, blackjacks even pay at odds of 1 to 1, which makes them no different than any other hand in the game. Check the calculations below to see what happens to the EV you extract from your blackjacks in such cases.

EV for Player Blackjacks with 6 to 5 Payouts

(0.0483 x 0.9633 x 1.2) + (0.9633 x 0.0483 x -1) = 0.05583 + (-0.04652) = 0.00931, or 0.93% in EV for the player

EV for Player Blackjacks with Even Money Payouts

(0.0483 x 0.9633 x 1) + (0.9633 x 0.0483 x -1) = 0.04652 + (-0.04652) = 0, or no EV for the player at all. This is why you should never play at tables that offer you reduced payouts for your naturals.

Dealer Probabilities in Blackjack

We previously tackled the probability of the dealer getting a blackjack. Let’s proceed with the likelihood of them busting when starting their hand with different upcards. The chances of the dealer busting are higher whenever they start with lower cards 2 through 6.

Cards with pip values of 4, 5, or 6 are the worst for the dealer as they yield the highest bust rates. This could be at least partially attributed to the fact that the dealer plays under fixed rules.

Unlike players who can stand on any total they want, the dealer must always draw to at least 16 and stand on totals of 17 or above. Basic strategy recommends more aggressive play against dealers with 5s and 6s because of the higher bust rates these two small cards yield (approximately 43% and 42%).

Players are more likely to achieve successful splits and double downs under such circumstances. Respectively, if the player gets stuck with stiff hands 12 through 16, they would stand rather than risk going over 21 themselves when the dealer has a 5 or a 6. The bust rates for the other upcards of the dealer are listed below.

The Concept of the House Edge

Most games on the casino floor are set up in favour of the house. They have a negative expected value and players will inevitably lose in the long run. The longer you engage in a negative-EV game, the higher your chances of registering losses.

Blackjack is different from other casino games because it can become a positive expectation game, provided that you know how to count cards. This would allow you to identify the spots when you have an advantage over the dealer and extract more earnings from profitable situations.

With that said, blackjack players cannot eliminate the house edge by relying on basic strategy alone. The latter reduces it dramatically but is powerless when it comes to eliminating it.

Another interesting aspect about blackjack is that here the casino advantage is the cumulative result from all playing conditions, including the dealer’s standing position, the payouts for blackjacks, the number of decks, the peek rule or its absence, and so on.

For instance, a six-deck game with late surrender, double after split, doubling on any two cards, and a peeking dealer who stands on soft 17 has a house edge of 0.36%. By contrast, a single-deck blackjack variation without surrender, double after a split, doubling on 10 and 11 only, no peek, and a dealer who hits soft 17 will have a slightly higher house edge of 0.38%.

The house edge reflects the amount the house collects in relation to the overall amount wagered at a given table. If you play a blackjack game with a 0.36% house edge and use basic strategy, you will be down roughly $0.36 for every $100 you have wagered over the long haul. Due to this, players are recommended to always scout for the blackjack tables that yield the lowest house edges and the highest expected return, respectively.

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Blackjack, unlike other gambling games is not considered a game of chance, it is one that you can win if you start applying some knowledge. Unlike many other games where the result depends on player luck only, this game provides probabilities depending on the player decisions. Therefore, in order to win you have to know what your probabilities are now and how and when to increase them.

Before we take a look at player and dealer blackjack odds, we should consider all the parameters that affect the odds in the game.

Blackjack Rules Variations

Blackjack variations were created to entertain players and provide them with a chance to win more money on side bets. Each rule variation affects the house edge, some rules making a big, others making a minor difference. Most common rule variations can be found at our House Edge Calculator in the «Rules» window. Now, let's take a closer look at the rules and see how they affect the odds in the game.

NOTE: The rules chosen in the table below are most favorable for the player.

Number of decks

The first thing a player should consider when choosing a table is the number of decks used in the game. The more decks there are - the less odds the player has. (See the table - Probabilities – Number of decks)

Dealer hits or stands on soft 17

The main rules of the game are usually written on the table felt and it may say either dealer hits or stands on soft 17. If according to the rules dealer hits soft 17, the game gives the house a 0.2% extra edge.

Rules for doubling

This rule is sometimes called the 'Reno' rule, which restricts doubling only to certain hand totals. Double 9 - 11 affects the house edge increasing it by 0.09% (8 decks game) and 0.15% (1 deck game). Double 10-11 increases the house edge by 0.17% (8 decks game) and 0.26% (1 deck game).

Doubling after Split

If the casino allows a player to double after he splits a pair, the player will get a further edge of around 0.12%.

Resplitting

Most casinos allow players to split again after he/she splits a pair and is dealt another card of the same rank. However, if the casino does not, this means the odds favor the house. As the best hands for splitting are a pair of Aces and 8s, there may be a special rule for Splitting Aces. If the casino allows the player to re-split Aces, the player gets a 0.03% extra edge. Moreover, in most cases if the player splits Aces, the casino will deal only one card per hand and that's it. Allowing players to hit on a hand of Split Aces gives the player an edge of 0.13%. We do not consider this rule in our calculator due to the fact it is almost never used, especially online.

• 1 deck of cards (house edge 0.17%)
• Doubling allowed on any cards
• Doubling allowed after Split and after Hit (player edge 0.12%)

• Early surrender is preferable
• Dealer stands on soft 17 (player edge 0.2%)
• Resplitting any cards allowed (player edge 0.03%)

Extra Rules Affecting Blackjack Odds

European No-Hole-Card Rule

Some blackjack variations are played with a hole card that is dealt to the dealer only after all the players have played their hands. This rule affects player strategy when playing against dealer up 10 or an Ace. In a typical hole-card game the player would know whether the dealer has a Blackjack or not before he makes any decisions. In this game, however, the player is risking a lot more if he decides to double or split. This rule adds 0.11% to the house advantage. However, there may be some casinos that allow the player to push on all the additional bets (doubling down and splitting pairs) if the dealer happens to have Blackjack.

Another Payouts on Blackjack

The classic payout on player Blackjack is 3 to 2. However, some casinos change the payout to increase the house edge. The payout on blackjack thus may vary from 1:1 to 6:5. As a Blackjack hand frequency is approximately 4.8% (see the table Two Card Hand Frequency), the payout of 1:1 will increase house edge by 2.3% and the payout of 6:5 - by 1.4%. The first rule (1:1) is only rarely found , while the second (6:5) can be found at some tables with a single deck blackjack game. The payout on Blackjack is generally written on a table felt.

Best tip
for odds seekers

The easiest way to choose the game with the highest odds is to play blackjack with no extra special rules. Do not forget where your basic odds are hidden - chance to Split, Double Down and get a 3 to 2 payout on Natural.

Dealer wins Ties

Another disadvantage for the player is when the rules of the game say that dealer wins all ties. This rule is almost never used in the classic games, though it can be found in some blackjack variations.

Insurance

The Insurance bet is a casino trick that gives the house a huge edge. The main factor why many players take this bet lies in the fact it costs only half of the original one. However, when the player takes Insurance every time he plays the game, the house edge may raise up to 7%. Added to all the other rules the casino sets on the game and you will see why probabilities are worth learning if you want to quit winners.

Side Bets

All blackjack games that offer side bets seem to be the biggest attraction for blackjack lovers. However, if you consider blackjack odds on these bets, you will notice that no matter how big the jackpot is (as in progressive blackjack rules) or how great the payout is for the pair (as in perfect pairs rules), the odds still favor the house and you are not likely to win.

Blackjack Probabilities charts

The quantity of decks increases the house advantage with each extra deck added to the game. Look for games with the smallest number of decks. However, some games offering a chance to play with 1 deck may only still provide low player odds due to low payouts on Blackjack and other rules. Be sure to check them before you play.

The table on the left describes how often the following hands can appear. The hands are the first two-cards dealt to the player. The frequency stands for the average number of times dealt per deck of cards. As you can see, the most frequent hands dealt are the 'Decision hands' that demand knowledge of blackjack strategy.

Las Vegas Sports Gambling Odds

In this table you can see the probability of going bust on any hand if the player decides to Hit. This means that with 0% you can never go bust when hitting a hand of 11 or less. As you can see, the table is for hard hand totals as you will 100% bust if you Hit on a hand of hard 21.

You probably already know that in blackjack small cards in the deck favor the dealer while big ones favor the player. In this table you can see that removing 2s from the deck adds a 0.40% of advantage to the player, while if 10's are taken out - the odds are 0.51% for the house.

Nfl Football Gambling Odds Online

Blackjack probabilities are calculated due to different parameters, including the dealer up card. The table on the left depicts how likely it is that dealer will go bust with certain up cards and what the player odds are in this very situation. For example, the highest player odds are when the dealer shows a 6, as he is most likely to go bust with this hand. The lowest player odds are when the dealer's up card is a 10 or an Ace.