3/28/2022

Blackjack Double Deck Odds

The proper Basic Strategy for a double-deck game closely resembles that of a four- or six-deck game, much more so than a single-deck game. The few differences between a two-deck and six-deck game with the same rules (dealer hits or stands on soft 17, double after split is allowed, etc.) lie mainly in splitting pairs and, since pairs are the. There are two Double Deck Blackjack games offered online, one by Bovada and one by Cryptologic. Both use a similar set of rules, the main advantage of the version we review here is that you can play up to five hands per round, which is why it’s very popular with high rollers and more experienced gamers, that are able to take advantage of it. If you are playing online blackjack, just click the button which says DOUBLE DOWN and your bet will be automatically placed. Double Down Blackjack Strategy. The long-held belief among casual blackjack players is that you always double down a total of 11. There is a good chance you will receive a 10 for a total of 21.

Double deck blackjack follows standard blackjack rules for the most part. Players and dealer are still required to reach a hand total as close to 21 are possible without exceeding 21. Only two major differences occur with double deck blackjack, which includes double down only on hand total of 10 or 11 and the dealer stands on a soft 17.

The double down feature is one of the primary moves in blackjack and one that any blackjack player should become familiar with. To double down is to increase the size of your bet to twice its value. When this happens, you will be dealt one more card and you will have to stand on that particular hand. The double down option gives you the opportunity to make great plays and exponentially increase your winnings potential. While this move does sound cut and dry there are certain subtleties to it and you should not take it lightly. Below, you will find a comprehensive guide about when it is a good idea to double down, as well as the different types of the double down option and the circumstances in which you can use it.


Double Down Variations

Double down comes in a variety of different forms, though some are more commonly seen than others. While you may only be interested in one type, it is a good idea to know the different variations so if you ever come across an unfamiliar type you know what’s going on and how to react.

Standard Double Down

The standard double down feature is the one that you will experience the most often. It is a simple as it sounds, all that happens is that you double the size of your bet and you win or lose depending on the outcome. There is nothing complicated to it, though knowing when to double down is a different matter. Additionally, some blackjack variations restrict your ability to double down only on hard totals of 9, 10, and 11.

Doubling Down on Three Cards

This is among the rarest double down variations that you will find in the gambling world since it pushes the odds in the player’s favor. While rare, it is not unheard of for casinos to allow this. Typically, you are only permitted to double down on your opening hand which consists of two hands. However, there are some establishments that will give you the option of doubling down after hitting. As you can imagine, this allows you to make much better plays that you would normally have the chance to make. Basically, with this double down variation, you have more options and that is never a bad thing.

Doubling Down for Less

Doubling down for less is an option at some land-based casinos and possibly certain online blackjack variations. The idea is that you increase your bet for a lower amount than its original value. For example, your starting wager is $10 and then the game gives you the option to double down for $5. This is the whole premise behind this double down variation and with that said, you should really avoid doubling down for less whenever possible.

The whole idea behind doubling down, in general, is to maximize your potential profit on the back of a strong hand. By doubling down for less, you reduce your winnings potential by a significant margin and this will hurt not only your bankroll but also how long you can keep playing. Furthermore, having standard double down options keeps the odds closer to you, even if still in the favor of the house. However, by giving up the opportunity to increase your bet, you push the advantage further in the casino’s favor and thus, reduce your overall chances of winning.

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Let’s run a simulation. Suppose you have a hard 11 against a dealer’s 10. In this situation, you come out on top 54% of the time when you double down. At $10 per standard bet, assuming traditional double down rules and that you will double down on such hands, you will win $10*2 * 54 = $1,080 in gross winnings and $10*2 * 46 = $920 in losses, which makes for a net profit of $160.

However, when you play with ‘double down for less’ rules, things take a different turn. Assume that you double down for 50% of your original bet ($10 + $5) in the same scenario. Now you have ($10 + $5) * 54 = $810 in gross winnings and ($10 + $5) * 46 = $690 in losses, which makes for a net profit of only $120 or 25% less than you would with standard rules. The profit loss percentage only increases as you reduce the double down amount.

No matter how you split it, doubling down for less is a bad move and you should avoid such tables in favor of those with standard doubling down rules. The only acceptable situation for doubling down for less is when you are low on funds and close to losing what is left of your bankroll. You could make an argument for such cases, yet even then, traditional double down rules will still give you better chances of making it out with something.

Doubling Down on Soft Hands

Something that not many players think about is the effect that an Ace can have on their hand total. As you are aware, the Ace can have a shifting value of 1 or 11, depending on your current total. If your hand is lower than 21, the Ace will count for 11. But if it potentially exceeds 21, the Ace will revert to its 1 value state. For instance, you are dealt a hand of Ace and 3 for a total of soft 14. You choose to hit and receive an 8, for a total of 22. However, since the Ace can also count as 1, your new total is not 22, rather 12.

Something to note is that not all blackjack variations will allow you to double down on soft hands. By their very nature, soft hands are always totals of 13 or more, while certain games only allow you to double down on 9, 10, and 11. With this in mind, choose your game of choice carefully. Granted, where it’s allowed to double on any hand, soft totals could potentially be very profitable.

For example, assuming 4-8 decks are in play and you have a soft 13 (Ace-2) against a dealer’s 5 or 6, you should double down. If this were a hard total, it would be advisable to stand, however, since you will not automatically bust by going over, you should take advantage. The same can be said of a soft 14 (Ace-3). When it comes to soft 15 (Ace-4) and soft 16 (Ace-5), you should always double down against a dealer’s 4, 5, and 6. Having a soft 17 (Ace-6) total is an advantageous position for you, even more so if doubling down is an option. Going into a soft 18 (Ace-7), it is important to take note whether the dealer hits or stands on a soft 17. If they stand, then you should only double down against a dealer total of 3, 4, 5, and 6. However, if they hit a soft 17, then a better approach is to double down against their 2, in addition to the previous totals.

If you hand consists of a soft 19 (Ace-8) or more and the dealer stands on soft 17, you should always stand. But, if they hit a soft 17, you should double down on your soft 19 against their 6. In all other situations, you should either hit or stand.

Doubling Down in Single- and Multi-Deck Games

Doubling down is not the same across multiple variations. When there is a larger number of decks, the odds significantly change as opposed to single-deck versions of the game. Below, we will outline some of the differences between doubling on single-deck and multi-deck variations.

Doubling Down in Single-Deck Variations

If you prefer single-deck blackjack, the conditions under which you want to double down are pretty specific. For example, holding a total of 9 against a dealer’s 2 through 6 is an ideal game state to double down. This is due to the fact that your hand will be made up of low-value cards, leaving all the high-value cards and Aces still in the shoe. Moreover, the dealer will also have the same chance of drawing similar cards, thus increasing their chance to bust. In the event that you hold a total of 8 (2-6; 3-5; 4-4) against a dealer’s 5 or 6, you should take the same action based on the same logic. When holding a hand total of 11 you want to double down, regardless of the dealer’s hand, as the chance to gain the upper hand is prime.

The reason why most of these situations are advantageous in single-deck versions is that doubling down on a low dealer’s total in multi-deck variations is too much risk to sustain long-term plays. All in all, single-deck variations give you more leeway in this regard, provided you know what you are doing.

Doubling Down in Multi-Deck Variations

Single-deck variations are popular but more often than not you will come across games played with 4-8 decks. Given the larger number of multi-hand titles, it is important that you also become familiar with those, as well. There is some slight variation if the dealer hits or stands on a soft 17 but we will get to that also. When holding a 9 against a dealer’s 3 through 6, it is in your best interest to double down. The same is also true when you hold a total of 10 versus a dealer’s 2 through 9. This gives you the best odds at scoring a good hand and getting that larger payout. When you hold a 10 against a dealer’s 2 through 10, you should double down. However, if the dealer hits a soft 17 and they hold an Ace, you should double down in that situation as well.

Doubling Down Tips

Doubling down is a crucial aspect of blackjack, one that has a great effect on your success in the game. But just like it can bring in a lot of profit, it can also ruin your bankroll if you use it carelessly. A double down is a calculated risk, allowing you to benefit from a statistical advantage in any given moment. There is a right time to use any move allowed in the game and it is empirical to learn when the appropriate time for each is. When it comes to doubling down, you are expected to do so in less than half of all possible situations. Therefore, do not expect to make all of your profit from it. Doubling down is a tool that you use when the occasion calls for it and when you stand to make a profit from it. Of course, you should also not expect every time you double down for the game to simply give you money. You will likely lose quite often, but if you play right, you will win more than you lose.

If you take away anything from this article, let it be this:

  • Double down on 9 against dealer’s 3 – 6 total
  • Double down on 10 against dealer’s 2 – 9 total
  • Double down on 11 against dealer’s 2 – 10 total (if dealer hits soft 17 double down on Ace, as well)
  • Double down on soft 13/14 against dealer’s 3 – 6 total (if allowed, otherwise hit)
  • Double down on soft 17/18 against dealer’s 3 – 6 total (if allowed, otherwise stand)

By Ion Saliu, Founder of Blackjack Mathematics

I. Probability, Odds for a Blackjack or Natural 21
II. House Edge on Insurance Bet at Blackjack
III. Calculate Double-Down Hands
IV. Calculate Blackjack Pairs: Strict or Mixed Ten-Cards
V. Free Blackjack Resources, Basic Strategy, Casino Gambling Systems

1.1. Calculate Probability (Odds) for a Blackjack or Natural 21

First capture by the Double deck blackjack oddsWayBack Machine (web.archive.org) Sectember (Sect Month) 1, 2015.

I have seen lots of search strings in the statistics of my Web site related to the probability to get a blackjack (natural 21). This time (November 15, 2012), the request (repeated 5 times) was personal and targeted directly at yours truly:

  • 'In the game of blackjack determine the probability of dealing yourself a blackjack (ace face-card or ten) from a single deck. Show how you arrived at your answer. If you are not sure post an idea to get us started!'

Oh, yes, I am very sure! As specified in this eBook, the blackjack hands can be viewed as combinations or arrangements (the order of the elements counts; like in horse racing trifectas).

1) Let's take first the combinations. There are 52 cards in one deck of cards. There are 4 Aces and 16 face-cards and 10s. The blackjack (or natural) can occur only in the first 2 cards. We calculate first all combinations of 52 elements taken 2 at a time: C(52, 2) = (52 * 51) / 2 = 1326.

We combine now each of the 4 Aces with each of the 16 ten-valued cards: 4 * 16 = 64.

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 calculate total arrangements for 52 cards taken 2 at a time: A(52, 2) = 52 * 51 = 2652.

In arrangements, the order of the cards is essential. Thus, King + Ace is distinct from Ace + King. Thus, total arrangements of 4 Aces and 16 ten-valued cards: 4 * 16 * 2 = 128.

The odds to get a blackjack (natural) as arrangement: 128 / 2652 = .0483 = 4.83%.

4.83% is equivalent to about 1 in 21 blackjack hands. (No wonder the game is called Twenty-one!)

Calculations for the Number of Cards Left in the Deck, Number of Decks

There were questions regarding the number of cards left in the deck, number of decks, number of players, even the position at the table.

1) The previous probability calculations were based on one deck of cards, at the beginning of the deck (no cards burnt). But we can easily calculate the blackjack (natural) odds for partial decks, provided that we know the number of remaining cards (total), Aces and Ten-Value cards.

Let's take the situation heads-up: One player against the dealer. Suppose that 12 cards were played, including 2 Tens; no Aces out. What is the new probability to get a natural blackjack?

Total cards remaining (R) = 52 - 12 = 40

Aces remaining in the deck (A): 4 - 0 = 4

Ten-Valued cards remaining (T): 16 - 2 = 14

Odds of a natural: (4 * 14) / C(40, 2) = 56 / 780 = 7.2%

(C represents the combination formula; e.g. combinations of 40 taken 2 at a time.)

The probability for a blackjack is higher than at the beginning of a full deck of cards. The odds are exactly the same for both Player and Dealer. But - the advantage goes to the Player! If the Player has the BJ and the Dealer doesn't, the Player is paid 150%. If the Dealer has the blackjack and the Player doesn't, the Player loses 100% of his initial bet!

This situation is valid only for one Player against casino. Also, this situation allows for a higher bet before the round starts. For multiple players, the situation becomes uncontrollable. Everybody at the table receives one card in succession, and then the second card. The bet cannot be increased during the dealing of the cards. Hint: try as much as you can to play heads-up against the Dealer!

The generalized formula is:

Probability of a blackjack: (A * T) / C(R, 2)

  • A = Aces in the deck
  • T = Tens in the deck
    • R = Remaining cards in the deck.

    2) How about multiple decks of cards? The calculations are not exactly linear because of the combination formula. For example, 2 decks, (104 cards):

    ~ the 2-deck case:

    C(52, 2) = 1326

    C(104, 2) = 5356 (4.04 times larger than total combinations for one deck.)

    8 (Aces) * 32 (Tens) = 256

    Odds of BJ for 2 decks = 256 / 5356 = 4.78% (a little lower than the one-deck case of 4.83%).

    ~ the 8-deck case, 416 total cards:

    C(52, 2) = 1326

    C(416, 2) = 86320 (65.1 times larger than total combinations for one deck.)

    32 (Aces) * 128 (Tens) = 4096

    Odds of BJ for 8 decks = 4096 / 86320 = 4.75% (a little lower than the two-deck situation and even lower than the one-deck case of 4.83%).

    There are NO significant differences regarding the number of decks. If we round the figures, the general odds to get a natural blackjack can be expressed as 4.8%.

    The advantage to the blackjack player after cards were played: Not nearly as significant as the one-deck situation.

    3) The position at the table is inconsequential for the blackjack player. Only heads-up and one deck of cards make a difference as far the improved odds for a natural are concerned.

    • Axiomatic one, let's cover all the bases, as it were. The original question was, exactly, as this: 'Dealing yourself a blackjack (Ace AND Face-card or Ten) from a single deck'. The calculations above are accurate for this unique situation: ONE player dealing cards to himself/herself. The odds of getting a natural blackjack are, undoubtedly, 1 in 21 hands (a hand consisting of exactly 2 cards).
    • Such a case is non-existent in real-life gambling, however. There are at least TWO participants in a blackjack game: Dealer and one player. Is the probability for a natural blackjack the same – regardless of number of participants? NOT! The 21 hands (as in probability p = 1 / 21) are equally distributed among multiple game agents (or elements in probability theory). Mathematics — and software — to the rescue! We apply the formula known as exactly M successes in N trials. The best software for the task is known as SuperFormula (also component of the integrated Scientia software package).
    • Undoubtedly, your chance to get a natural BJ is higher when playing heads-up against the dealer. The degree of certainty DC decreases with an increase in the number of players at the blackjack table. I did a few calculations: Heads-up (2 elements), 4 players and dealer (5 elements), 7 players and dealer (8 elements).
      • The degree of certainty DC for 2 elements (one player and dealer), one success in 2 trials (2-card hands) is 9.1%; divided by 2 elements: the chance of a natural is 9.1% / 2 = 4.6% = the closest to the 'Dealing yourself a blackjack (Ace AND Face-card or Ten) from a single deck' situation.
      • The chance for 5 elements (4 players and dealer), one success in 5 trials (2-card hands) is 19.6%; distributed among 5 elements, the degree of certainty DC for a blackjack natural is 19.6% / 5 = 3.9%.
      • The probability for 8 elements (7 players and dealer), one success in 8 trials (2-card hands) is 27.1%; equally distributed among 8 elements, the degree of certainty DC of a blackjack natural is 27.1% / 8 = 3.4%.
    • That's mathematics and nobody can manufacture extra BJ natural 21 hands... not even the staunchest and thickest card-counting system vendors! The PI... er, pie is small to begin with; the slices get smaller with more mouths at the table. Ever wondered why the casinos only offer alcohol for free — but no pizza?

    1.2. Probability, Odds for a Blackjack Playing through a Deck of Cards

    The probabilities in the first chapter were calculated for one trial. That is, the odds to get a blackjack in the first two cards. But what are the probabilities to get a natural 21 dealing an entire deck?

    1.2.A. Dealing 2-card hands until the deck is dealt entirely

    There are 52 cards in the deck. Total number of trials (2-card hands) is 52 / 2 = 26. SuperFormula probability software does the following calculation:
    • The probability of at least one success in 26 trials for an event of individual probability p=0.0483 is 72.39%.

    1.2.B. Dealing 2-card hands in heads-up play until the deck is dealt entirely

    There are 52 cards in the deck. We are now in the simplest real-life situation: heads-up play. There is one player and the dealer in the game. We suppose an average of 6 cards dealt in one round. Total number of trials in this case is equivalent to the number of rounds played. 52 / 6 makes approximately 9 rounds per deck. SuperFormula does the following calculation:
    • The probability of at least one success in 9 trials for an event of individual probability p=0.0483 is 35.95%.

    You, the player, can expect one blackjack every 3 decks in heads-up play.

    2. House Edge on the Insurance Bet at Blackjack

    “Insurance, anyone?” you can hear the dealer when her face card is an Ace. Players can choose to insure their hands against a potential dealer's natural. The player is allowed to bet half of his initial bet. Is insurance a good side bet in blackjack? What are the odds? What is the house edge for insurance? As in the case of calculating the odds for a natural blackjack, the situation is fluid. The odds and therefore the house edge are proportionately dependent on the amount of 10-valued cards and total remaining cards in the deck.

    We can devise precise mathematical formulas based on the Tens remaining in the deck. We know for sure that the casino pays 2 to 1 for a successful insurance (i.e. the dealer does have Ten as her hole card).

    Blackjack Double Deck Odds Nfl Week 11

    We start with the most easily manageable case: One deck of cards, one player, the very beginning of the game. There is a total of 16 Teens in the deck (10, J, Q, K). The dealer has dealt 2 cards to the player and one card to herself that we can see exactly — the face card being an Ace. Therefore, 52 – 3 = 49 cards remaining in the deck. There are 3 possible situations, axiomatic one:

    • 1) The player has 2 non-ten cards; there are 16 Teens in the deck = the favorable situations to the player if taking insurance. There are 49 – 16 = 33 unfavorable cards to insurance. However, the 16 favorable cards amount to 32, as the insurance pays 2 to 1. The balance is 33 – 32 = +1 unfavorable situation to the player but favorable to the casino (the + sign indicates a casino edge). In this case, there is a house advantage of 1/49 = 2%.
    • 2) The player has 1 Ten and 1 non-ten card; there are 15 Teens remaining in the deck = the favorable situations to the player if taking insurance. There are 49 – 15 = 34 unfavorable cards to insurance. However, the 15 favorable cards amount to 30, as the insurance pays 2 to 1. The balance is 34 – 30 = +4 unfavorable situations to the player but favorable to the casino. In this case, there is a house advantage of 4/49 = 8%.
      • This can be also the case of insuring one's blackjack natural: an 8% disadvantage for the player.
      • This figure of 8% represents the average house edge regarding the insurance bet. I did calculations for various situations — number of decks and number of players.
    • 3) The player has 2 Ten-count cards; there are 14 Teens in the deck = the favorable situations to the player if taking insurance. There are 49 – 14 = 35 unfavorable cards to insurance. However, the 14 favorable cards amount to 28, as the insurance pays 2 to 1. The balance is 35 – 28 = +7 unfavorable situations to the player but favorable to the casino. In this case, there is a house advantage of 7/49 = 14%. This is the worst-case scenario: The player should never — ever — even think about insurance with that strong hand of 2 Tens!

    Believe it or not, the insurance can be a really sweet deal if there are multiple players at the blackjack table! Let's say, 5 players, the very beginning of the game. There is a total of 16 Teens in the deck (10, J, Q, K). The dealer has dealt 10 cards to the players and one card to herself that we can see exactly — the face card being an Ace. Therefore, 52 – (10 + 1) = 41 cards remaining in the deck. There are many more possible situations, some very different from the previous scenario:

    • 1) The players have 10 non-ten cards; there are still 16 Tens in the deck = the favorable situations to the player if taking insurance. There are 41 – 16 = 25 unfavorable cards to insurance. However, the 16 favorable cards amount to 32, as the insurance pays 2 to 1. The balance is 25 – 32 = –7 favorable situation to the player but unfavorable to the casino (the – sign indicates a player advantage now). In this case, there is a house advantage of 7/41 = –17%. The Player has a whopping 17% advantage if taking insurance in a case like this one!
    • 2) The players have 10 Ten-count cards; there are 6 Teens in the deck = the favorable situations to the player if taking insurance. There are 41 – 6 = 35 unfavorable cards to insurance. However, the 6 favorable cards amount to 12, as the insurance pays 2 to 1. The balance is 35 – 12 = +23 unfavorable situations to the player but favorable to the casino. In this case, there is a house advantage of 23/41 = 56%. This is the worst-case scenario: None of the players should ever even think about insurance with those strong hands of 2 Tens per capita!
    • 3) Applying the wise aurea mediocritas adagio, there should be an average of 3 or 4 Teens coming out in 11 cards; thus, 12 or 13 Tens remaining in the deck. There are 41 – 13 = 28 unfavorable cards to insurance. However, the 12.5 favorable cards amount to an average of 25, as the insurance pays 2 to 1. The balance is 30 – 25 = +5 unfavorable situations to the player but favorable to the casino. In this case, there is a house advantage of 5/41 = 12%. Unfortunately, even if we consider averages, taking insurance is a repelling bet for the player.
      A formula? It would look complicated symbolically, but it is very easy to follow.

      HA = {(R – T) – T*2} / R

      where —

    • HA = house advantage
    • R = cards remaining in the deck
    • T = Tens remaining in the deck.

    • Axiomatic one, buying (taking) insurance can be a favorable bet for all blackjack players, indeed. Of course, under special circumstances — if you see certain amounts of ten-valued cards on the table. The favorable situations are calculated by the formula above.
    But, then again, a dealer natural 21 occurs about 5%- of the time — the insurance alone won't turn the blackjack game entirely in your favor.

    3. Calculate Blackjack Double-Down Hands

    Strictly-axiomatic colleague of mine, writing software leads me into new-ideas territory far more often than not. I discovered something new and intriguing while programming software to calculate the blackjack odds totally mathematically. By that I mean generating all possible elements and distinguishing the favorable elements. After all, the formula for probability is the rapport of favorable cases, F, over total possible cases, N: p = F/N.

    Up until yours truly wrote such software, total elements in blackjack (i.e. hands) were obtained via simulation. Problem with simulation is incomplete generation. According to by-now famed Ion Saliu's Probability Paradox, only some 63% of possible elements are generated in a simulation of N random cases.

    I tested my software a variable number of card decks and various deck compositions. I noticed that decks with lower proportions of ten-valued cards provided higher percentages of potential double-down hands. It is natural, of course, as Tens are the only cards that cannot contribute to a hand to possibly double down. However, the double-down hands provide the most advantageous situations for blackjack player. Indeed, it sounds like 'heresy' to all followers of the cult or voodoo ritual of card counting!

    I rolled up my sleeves and performed comprehensive calculations of blackjack double-downs (2-card hands). The single deck is mostly covered, but the calculations can be extended to any number of decks.

    At the beginning of the deck (shoe): Total combinations of 52 cards taken 2 at a time is C(52, 2) = 1326 hands. Possible 2-card combinations that can be double-down hands:

    • 9-value cards AND 2-value cards: 4 9s * 4 2s = 16 two-card possibilities
    • 8-value cards AND 2-value cards: 4 8s * 4 2s = 16 two-card configurations
    • 8-value cards AND 3-value cards: 4 8s * 4 3s = 16 two-card possibilities
    • 7-value cards AND 2-value cards: 4 7s * 4 2s = 16 two-card configurations
    • 7-value cards AND 3-value cards: 4 7s * 4 3s = 16 two-card possibilities
    • 7-value cards AND 4-value cards: 4 7s * 4 4s = 16 two-card configurations
    • 6-value cards AND 3-value cards: 4 6s * 4 3s = 16 two-card configurations
    • 6-value cards AND 4-value cards: 4 6s * 4 4s = 16 two-card combinations
    • 6-value cards AND 5-value cards: 4 6s * 4 5s = 16 two-card possibilities
    • 5-value cards AND 4-value cards: 4 5s * 4 4s = 16 two-card combinations
    • 5-value cards AND 5-value cards: C(4, 2) = 6 two-card hands (5 + 5 can appear 6 ways).
    • Ace AND 2-value cards: 4 As * 4 2s = 16 two-card combinations
    • Ace AND 3-value cards: 4 As * 4 3s = 16 two-card possibilities
    • Ace AND 4-value cards: 4 As * 4 4s = 16 two-card hands
    • Ace AND 5-value cards: 4 As * 4 5s = 16 two-card possibilities
    • Ace AND 6-value cards: 4 As * 4 6s = 16 two-card hands
    • Ace AND 7-value cards: 4 As * 4 7s = 16 two-card combinations.
    • Total possible 2-card hands in doubling down configuration: 262. Not every configuration can be doubled down (e.g. 4+5 against Dealer's 9 or A+2 against 7).
    • We look at a double down blackjack basic strategy chart. Some 42% of the hands ought to be doubled-down (strongly recommended): 262 * 0.42 = 110. That figure represents 8% of total possible 2-hand combinations (1362), or a chance equal to once in 12 hands.
    • The chance for double-down situations increases with an increase in tens out over the one third cutoff count. The probability for a natural blackjack decreases also — one reason the traditional plus-count systems anathema the negative counts. But what's lost in naturals is gained in double downs — and then some.
    • A sui generisblackjack card-counting strategy was devised by yours truly and it beats the traditionalist plus count systems hands down, as it were.
    • Be mindful, however, that nothing beats the The Best Casino Gambling Systems: Blackjack, Roulette, Limited Martingale Betting, Progressions. That's the only way to go, the tao of gambling.

    4. Calculate Blackjack Pairs: Strict or Mixed Ten-Cards

    The odds-calculating software I mentioned above (section III) also counts all possible blackjack pairs. The software, however, considers pairs to be two cards of the same value. In other words, 10, J, Q, K are treated as the same rank (value). My software reports data as this fragment (single deck of cards):

    Mixed Pairs: All 10-Valued Cards Taken 2 at a Time

    Evidently, there are 13 ranks. Nine ranks (2 to 9 and Ace) consist of 4 cards each (in a single deck). Four ranks (the Tenners) consist of 16 cards. Total of mixed pairs is calculated by the combination formula for every rank. C(4, 2) = 6; 6 * 9 = 54 (for the non-10 cards). The Ten-ranks contribute: C(16, 2) = 120. Total mixed pairs: 54 + 120 = 174. Probability to get a mixed pair: 174 / 1326 = 13%.

    Strict Pairs: Only 10+10, J+J, Q+Q, K+K

    But for the purpose of splitting pairs, most casinos don't legitimize 10+J, or Q+K, or 10+QBlackjack double deck odds poker, for example, as pairs. Only

    Double Deck Blackjack Odds

    10+10, J+J, Q+QDouble, K+K are accepted as pairs. Allow me to call them strict pairs, as opposed to the above

    Blackjack Double Deck Odds Explained

    mixed pairs.

    There are 13 ranks of 4 cards each. Each rank contributes C(4, 2) = 6 pairs. Total strict pairs: 13 * 6 = 78. Probability to get a mixed pair: 78 / 1326 = 5.9%.Total strict pairs = 78 2-card hands (5.9%, but...).

    However, not all blackjack pairs should be split; e.g. 10+10 or 5+5 should not be split, but stood on or Doubledoubled down. Only around 3% of strict pairs should be legitimately split. See the optimal

    Blackjack Double Deck Odds Poker

    split pairs

    Blackjack Double Deck Odds Calculator

    black jack strategy card.

    5. Free Blackjack Resources, Basic Strategy, Casino Gambling Systems

    • Blackjack Mathematics Probability Odds Basic Strategy Tables Charts.
    • The Best Blackjack Basic Strategy: Free Cards, Charts.
      ~ All playing decisions on one page — absolutely the best method of learning Blackjack Basic Strategy (BBS) quickly (guaranteed and also free!)
    • Blackjack Gambling System Based on Mathematics of Streaks.
    • Blackjack Card Counting Cult, Deception in Gambling Systems.
    • The Best Blackjack Strategy, System Tested with the Best Blackjack Software.
    • Reality Blackjack: Real, Fake Odds, House Advantage, Edge.

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