The Fundamental Probability Issue: True Blackjack Odds - New Software Calculator. The probability to get a blackjack (natural): 64 / 1326 =.0483 = 4.83%. 2) Let's do now the calculations for arrangements. (The combinations are also considered boxed arrangements; i.e. The order of the elements does not count).

We begin this Blackjack guide with a very important assertion – casino games, hence the name, are designed with a built-in house advantage – a casino's edge in odds over a player at any given bet.

Thus, by stepping into a casino, you know that the odds by default are stacked against you to a certain degree. This means that in the long term you will always lose money, unless you skew the odds to even or in your favor.

Casinos believe that as soon as you enter their premises, it is just a matter of time before all your money becomes theirs. And since they want to keep you around for as long as possible, they will attract you with the so-called comps – complimentary items and services given out by the house to encourage players to gamble.

Casinos will do everything they can to make you feel cozy, valued and inclined to prolong your stay at the tables. These “freebies” they give out depend on the game a person plays, for how long, and of course on the size of his bets. Casinos have staff whose job is to manage the comps and contact players to persuade them to visit and play.

As a casino game, Blackjack also falls under this principle and is designed to transfer the money from your pocket into the house's vault, unless some method of advantage play is used. This is where this guide comes in.

We will present ideas which will can help you shift odds to near-even, and in some cases even slightly in your favor. This will be done in the first section of the guide where we will discuss strategies relating to the basic strategy player.

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Later on we will move to the so-called advantage player, where card counting takes place. Whereas the basic strategy player is on relatively even ground with the house, albeit still behind, the advantage players, hence the name, have an advantage over the casino as soon as the game begins.

Regardless of which type of player you want to become, both require the aforementioned “method of advantage play” – strategies, card counting etc., which help skew the odds out of the casino's favor.

Blackjack is one of the most widely played casino games for several reasons – it has simple rules, it is offered by almost every casino and most importantly – offers the best overall odds for the player, even for the non-advtantage one. It is simply a game that falls under the principles of odds and probabilities and can be beaten through lots of experience, knowledge and skill.

Odds and probabilities

Now, one would wonder how come if the stacks are always stacked against the non-advantage players, who make up most of the player mass, there are still many people going to the casinos. After all, if all these people were constantly losing, they would ultimately become discouraged and the majority will stop playing.

Gamblers hope that on any particular night they might be lucky and the odds fall in their favor. For example, although tossing a coin has a 50% chance to turn heads or tails, when you toss it only 20 times, it might land 14 times on heads and 6 on tails. The even probability of tossing tails or heads is true only when you repeat the exercise enough times to ensure a large enough sample pool.

And because many people get lucky at any given moment, they will earn money, fueling their excitement and luring them back in the casino the next night. And although this causes the house to lose money, the casino relies on the fact that players place millions of bets, which irons out the outcome in the long-term and makes the house profitable. In mathematics, this is known as the law of large numbers.

This rule dictates that the more bets are placed, the closer the casino's odds will come to the artificially created built-in house advantage, thus the more hands (bets) a non-advantage gambler plays (places), the smaller his chances to win become.

Thus, players who do not employ advantage methods will be losing money if they continue to play in the long-term, which allows casinos to continue to operate, while basic strategy and advantage players profit from their efforts.

Calculating the house's advantage in blackjack is difficult due to the huge amount of card combinations and also because not all winning bets have the same payout (for example, a blackjack which is a 21-hand with an ace and a 10-valued card, pays 3:2 in most casinos).

The extent and source of the house's advantage varies in different casinos. In blackjack, for example, it is derived from the fact that when the player busts himself by exceeding the count of 21, the house wins the bet, regardless of whether the dealer would also bust when drawing more cards to complete the hand for other players on the table.

Improving or reducing the house's advantage

The house edge depends on the rules the casino has established for the blackjack table and they are posted and easily visible either on, or near the table.

For example, a casino where dealers stand on a soft 17 (S17), instead of hitting it (H17), favors the players' odds, reducing the house's edge by around 0.2%. Increasing the number of decks also increases the house's edge, and vice versa.

The implementation of other rules such as the allowance or disallowance of resplitting, doubling down after split, double on 9/10/11 or only on 10/11 and so on. Casinos typically aim to boost their advantage but also not to discourage players from joining the game and, thus, seek some form of balance. For example, if they offer one-deck blackjack, they typically forbid doubling on soft hands or after splitting, restrict resplitting and so on.

The table above illustrates the house's edge relative to the different number of decks, considering the following set of rules:

– dealer hits soft 17
– double split is allowed
– resplit to four hands is allowed
– no surrender
– no hitting split aces
– double on any two cards
– original bets only lost on dealer blackjack
– cut-card used

As evident, the house's edge experiences the most dramatic jump when raising the number of decks from one to two and grows progressively slowerr as more decks are added.

Hand-held and shoe games, house edge

Single-deck games belong to the so-called hand-held games. Double-deck games could also be hand-held. Although they are still being offered by some casinos, their peak of popularity has passed. Nowadays, casinos more often host shoe games.

In a shoe game, a card shoe (rectangular box) holds multiple decks of cards. The dealer pulls cards out of the shoe and slides them to the appropriate areas in front of the players. Cards are most often dealt face up, which prohibits the player from touching them. Even if the gambler splits their hand, they don't touch the cards and instead just place their additional bet and the dealer does the splitting.

Only in games where cards are dealt facing down can the player hold his cards, but only in one hand.

Almost always you will see shoe games consist of multiple decks, four and more, and on rare occurrences two. Thus, shoe games will logically favor the house's odds.

You may also encounter tables using the so-called Continuous-Shuffling Machines. These devices hold three or more decks and after a couple of rounds the dealer returns the used cards to the machine and shuffles them with the unused cards. Thus, each shuffle refreshes the shoe, making it impossible to count cards, which is why card counters avoid these games.

As for basic strategy players, CSMs don't have such an impact, but they increase the number of hands played per hour, meaning the player will incur larger money losses (why we will explain later).

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 to bust. 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 16 comes 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 an Ace 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 this playing 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.

Odds Of Busting In Blackjack

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 to your 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 percentage will 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 loss less than following a seat-of-the-pants strategy. 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 more cards, 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 of standing.

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’t like “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 than hitting. 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%. This means 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 net loss 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 the better 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. If not, then hit.

Finally, we have the 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, the combined 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 then surrendering.

Blackjack Winning Percentage

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 will be optimizing your chances of winning more, and losing less, in the long run. It’s the smart way to play blackjack.

Odds Of Winning One Blackjack Hand

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 Blackjack Insider 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