Probability Blackjack Hands

In a game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack. (Round your answers to four decimal places.) (a) If a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack? In a freshly shuffled deck (standard 52 cards), what is the probability that neither of you are dealt a blackjack. Blackjack being 2 cards adding to 21 i.e. A c e + 10, J, Q, o r K (or vice versa as order does not matter). The farthest I've really come is that the odds of the first player getting dealt a blackjack is 128 2652.

1. Blackjack Hand Chart
2. Probability Blackjack Hands Rule
3. Probability Blackjack Hands Svg

By Henry Tamburin
No other hand makes blackjack players feel queasy than the dreaded 16. Players hate to hit the hand because they are afraid tobust. So many chicken out and stand no matter what the dealer shows. Others opt for the surrender option if it’s available figuring losing half a bet is better then losing it all. If your 16comes as a pair of 8’s most players are reluctant to split if the dealer shows a 9, 10, or ace because they are afraid of losing two bets instead of one. Then there is the 16 made up with anAce counted as 11 (i.e., soft 16). So what’s a player to do when he gets a 16?

First, let’s focus on a hard 16. That’s a hand that does not contain an Ace or if it does the Ace counts as one. Some examples of a hard 16 would be 10-6 or 5-7-4 or 7-8-Ace.

The correct basic playing strategy for hard 16 is to stand when the dealer shows a small card (2 through 6) and hit when the dealer shows a high card (7, 8, 9, 10, or Ace). Following thisplaying strategy will not guarantee that you will win every time but that you are more likely to lose less in the long run.. Let me explain.

Suppose you are dealt a 10-6 and the dealer shows a 7 upcard.

If you hit you win on average 30% of the time and lose 70%.

If you stand you will on average win 26% and lose 74%.

Note that you improve your chances of winning the hand by 4% if you hit rather than stand. But the dealer is still an overwhelming favorite to beat you because he will win 70% of the hands toyour 30%. But is it better to win 26% of the time by standing or 30% of the time by hitting? You should hit because it will increase your chance of winning by 4%, not much, but every percentagewill help you in the long run when you play blackjack.

So the bottom line with a hard 16 is this. Even by following the basic strategy, you will lose more hands than you win but in the long run, you will lose less than following a seat-of-the-pantsstrategy. Losing less on hands where you are the underdog is just as important as winning more when you are the favorite.

What if your 16 consists of three or more cards like 5-7-4? Normally the basic strategy ignores the composition of the hand. However, if you have a hard 16 hand consisting of three or morecards, then you should stand when the dealer has a 10 showing. The reason is that you have consumed a few of the small cards that you need if you were to draw. This tips the odds in favor ofstanding.

Some casinos allow players to surrender. This means you give up the opportunity to play out your hand and automatically lose half your bet. Even when surrender is offered, most players don’tlike “giving up” without a fight. So they rarely surrender. That’s unfortunate because surrendering a hard 16 when the dealer shows a 9, 10, or Ace will save you more money in the long run thanhitting. In fact, surrender is always the best option when your chance of winning a hand is less than 25%. Take the hand of hard 16 against a 10. If we hit our chance of winning is 23.4%. Thismeans the dealer’s chance of beating us is 76.6%. If we played a hundred hard 16’s against the dealer 10 with those probabilities, we would end up winning about $23 and losing $77 for a netloss of $54 on average. By surrendering on every hand our net loss would be $50. Get the point? You are better off losing $50 then $54 which is why surrendering a hard 16 against a 10 is thebetter play because you will save $4.

If you happen to be dealt a soft 16 (like Ace-5), you should never surrender and you should never stand. Your first option is to double but only if the dealer shows a weak 4, 5, or 6 upcard. Ifnot, then hit.

Finally, we have a pair of 8’s. The correct basic strategy play is to always split the 8’s no matter what the dealer shows. Even though you will lose money on both 8’s when you split, thecombined loss, in the long run, will be less than the amount you will lose by playing the one hand as a 16. Splitting 8’s against a dealer 10, by the way, is also a slightly better play thensurrendering.

No question that 16 is a lousy blackjack hand. Unfortunately, it’s one of the most frequent hands you are going to be dealt in blackjack. But, by following the above playing strategy you willbe optimizing your chances of winning more, and losing less, in the long run. It’s the smart way to play blackjack.

Henry Tamburin has been a respected casino gambling writer for the past 50 years. He is the author of the Ultimate Blackjack Strategy Guide and was editor of the BlackjackInsider newsletter. You can read his latest articles on blackjack, video poker, and his personal playing experiences at https://www.888casino.com/blog/writers/henry-tamburin

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.

Blackjack Hand Chart

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.

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.

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.

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