Jump to content

Blackjack

From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by 66.236.143.130 (talk) at 15:47, 4 August 2008 (Five card charlie). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Blackjack (also known as Twenty-one, Vingt-et-un (French for Twenty-one), or Pontoon) is the most widely played casino banking game in the world.[1] Much of blackjack's popularity is due to the mix of chance with elements of skill, and the publicity that surrounds card counting (calculating the probability of advantages based on the ratio of high cards to low cards). The casino version of the game should not be confused with the British card game Black Jack (a variant of Crazy Eights).

History of blackjack

Blackjack's precursor was vingt-et-un ("twenty-one"), which originated in French casinos around 1700, and did not offer the 3:2 bonus for a two-card 21.

When 21 was first introduced in the United States it was not very popular, so gambling houses tried offering various bonus payouts to get the players to the tables. One such bonus was a 10-to-1 payout if the player's hand consisted of the ace of spades and a black Jack (either the Jack of clubs or the Jack of spades). This hand was called a "blackjack" and the name stuck to the game even though the bonus payout was soon abolished. As the game is currently played, a "blackjack" may not necessarily contain a jack or any black cards at all.

How to play blackjack

The hand with the highest total wins as long as it doesn't exceed 21; a hand with a higher total than 21 is said to bust or too many. Cards 2 through 10 are worth their face value, and face cards (jack, queen, king) are all worth 10. An ace's value is 11 unless this would cause the player to bust, in which case it is worth 1. A hand in which an ace's value is counted as 11 is called a soft hand, because it cannot be busted if the player draws another card.

Each player's goal is to beat the dealer by having the higher, unbusted hand. Note that if the player busts they lose, even if the dealer also busts. If both the player and the dealer have the same point value, it is called a "push", and neither player nor dealer wins the hand. Each player has an independent game with the dealer, so it is possible for the dealer to lose to some players but still beat the other players in the same round.

Example of a Blackjack game. The top half of the picture shows the beginning of the round, with bets placed and an initial two cards for each player. The bottom half shows the end of the round, with the associated losses or payoffs.

The minimum/maximum bet is printed on a sign on the table and varies from casino to casino and table to table. Very rarely do casinos offer minimum bets less than $5 (except during promotions). After initial bets are placed, the dealer deals the cards, either from one or two hand-held decks of cards, known as a "pitch" game, or more commonly from a shoe containing four or more decks. The dealer gives two cards to each player including themself. One of the dealer's two cards is face-up so all the players can see it, and the other is face down. (The face-down card is known as the "hole card". In European blackjack, the hole card is not actually dealt until the players all play their hands.) The cards are dealt face up from a shoe, or face down if it is a pitch game.

In American blackjack, if the dealer's face-up card is an ace or a ten-value, the dealer checks their hole card to see if they have a blackjack. This check occurs before any of the players play, but after they have been offered insurance (if the face-up card is an ace). If the dealer has blackjack, all players lose their initial bets, except players who also have blackjack, who push. (In some American casinos, the dealer does not actually check the hole card until after the players have all played. At that time, if the dealer turns out to have blackjack, all players who did not have blackjack lose their bets, and players who increased their bets by doubling or splitting lose only the original bet, and have the additional bets returned to them; thus, the end result is precisely as if the dealer had checked the hole card before playing.)

A two-card hand of 21 (an ace plus a ten-value card) is called a "blackjack" or a "natural", and is an automatic winner (unless the dealer has blackjack as well, in which case the hand is a push). A player with a natural is usually paid 3:2 on his bet. Some casinos pay only 6:5 on blackjacks; although this reduced payout has generally been restricted to single-deck games (Current Blackjack News, Pi Yee Press).[citation needed] This reduced payout for a natural increases the house advantage over a player by as much as 1000 percent. The move was decried by longtime blackjack players[2].

Player decisions

The player's options for playing his or her hand are:

  • Hit: Take another card.

  signal: (handheld) scrape cards against table; (face up) touch finger to table

  • Stand: Take no more cards, also "stick" or "stay".

  signal: (handheld) slide cards under bet; (face up) move hand horizontally

  • Double down: Increase the wager to a maximum of double the original bet and take exactly one more card. For example, if the player's original bet was $25, the player could increase the bet by up to an additional $25, for a new total bet of up to $50. Increasing the wager to less than twice the original bet is called "double down for less", and is not always permitted.

  signal: place additional chips next to (not on top of) original bet, make "one finger" sign

  • Split: Double the wager and have each card be the first card in a new hand. This option is available only when both cards have the same rank or, depending on the locality, value.

  signal: place additional chips next to (not on top of) original bet, make "two fingers" sign

  • Surrender: Forfeit half the bet and give up the hand. This option is not always available.

  signal: make 'chopping' motion over bet (signal is rare, usually just done verbally)

Hand signals are required in most casinos, so that in case of a dispute, a video record exists of the player's decisions.

The player's turn is over after deciding to stand, doubling down to take a single card, or busting. If the player busts, he or she loses the bet even if the dealer goes on to bust.

After all the players have finished making their decisions, the dealer then reveals his or her hidden hole card and plays the hand. House rules say that the dealer must hit until he or she has at least 17, regardless of what the players have. In some casinos a dealer must also hit a soft 17 (a combination of cards adding up to either 7 or 17, such as an ace and a 6).

If the dealer busts then all remaining players win. Bets are normally paid out at the odds of 1:1. Players who push (tie) with the dealer receive their original bet back.

Rules variations

Each blackjack variation has its own set of rules, strategies and odds. It is advised to take a look at the rules of the specific variation before playing. Many countries have legal acts and laws which determine how a casino game of blackjack must be played. Not all rules are posted. The player has to ask, either beforehand or when the situation occurs. Over 100 variations exist.[3]

Dealer soft 17

In fact, there are two slightly different dealer strategies. In the "S17" game, dealer stands on all 17s. In the "H17" game, dealer hits on soft 17s; of course, he stands on hard 17s. (In either case, the dealer has no choice; he must or must not hit.) The H17 game is substantially less favorable to the player. Which game is customary depends on locality. Las Vegas Strip rules are about equally split.

Number of decks

All things being equal, fewer decks are more favorable for the player. (This is true for basic strategy players, even without card counting.) In fact, all things are not equal; multi-deck games almost always have otherwise better rules than single-deck games.

Late surrender

The player may "give up" and get back half his bet, before taking any other action. (In some places, this is posted, "surrender is available", while in other places, it is available, but it is not posted.) In some cases (15 vs. ten, 16 vs. 9, 16 vs. ace), this is slightly favorable. In one important case (16 vs. ten), it is definitely favorable.

Resplit to nn

(In other words, the option to split exists for a two-card hand from a split the same as the first two cards.) The simplest rule is "resplit infinite"; this means that the player may continue to split so long as he receives same-value cards and is willing to put up the additional bet. More typically, the rule is "resplit to four." These rules are practically identical, since even four hands is fairly unusual.

Resplit aces

In general, after splitting aces, the player gets only one card even with the above rule. With this rule in effect, an exception is made: if the second card is an ace, the player can resplit. (Of course, this is always favorable.)

Double after split

In other words, the option exists to double for a two-card hand from a split the same as the first two cards. Generally, the player should play a hand after a split the same as the first two cards. However, this rule does slightly change which hands should be split in the first place.

Double on 10 or 11 only

Often called "Reno" rules. (Also seen is "double on 9, 10, or 11 only".) It is annoying to many players because doubling soft hands is considered part of the game.

European no-hole-card rule

In some places, the dealer does not receive a hole card, but if the dealer is later found to have blackjack, the player loses only his original bet but not any additional bets (doubles or splits). This has the same advantage as the usual game and it should not be considered "European no-hole-card rule".

Altered payout for natural

In some places, a natural pays 6:5 or even 1:1. This is the most unfavorable variation, increasing the house edge significantly more than any other player restriction.

Dealer wins ties

This is catastrophic to the player, though rarely used in standard Blackjack. It is sometimes seen in "blackjack-like" games.

Five card charlie

With this rule, the player always wins when five cards have been drawn without busting. In general casino and video blackjack varients either eliminate this rule or change it to a seven card win.

Insurance

If the dealer's upcard is an Ace, the player is offered the option of taking Insurance before the dealer checks his 'hole card'.

The player who wishes to take Insurance can bet an amount up to half his original bet. The Insurance bet is placed separately on a special portion of the table, which usually carries the words "Insurance Pays 2:1". The player who is taking Insurance is betting that the dealer was dealt a natural, i.e. a two-card 21 (a blackjack), and this bet by the player pays off 2:1 if it wins. It is called insurance because it, in effect, can protect the original bet if the dealer has a blackjack. If you bet the full half of the original bet, you win the same amount of the player's Blackjack wager. In this case, if insurance is taken and the player doesn't have blackjack but dealer does, no money is lost. Of course the dealer can end up not having blackjack and the player can still win or lose the blackjack bet, and the insurance bet is forfeit.

Insurance is a bad bet for the non-counting player who has no knowledge of the hole card because it has a house edge of 2% to 15%, depending on number of decks used and visible 10-cards [4]. Essentially, taking insurance amounts to betting that the dealer's hole card is a ten or face card. Since in an infinite deck, 4/13 of the cards are tens or face cards, an unbiased insurance wager would actually pay 9:4, or 2.25:1; since the bet only pays 2:1, the house has a strong advantage. However, if the player has been counting cards, he may know that more than a third of the deck is ten-value cards, in which case insurance becomes a good bet.

If a player has a natural (an ace and a ten or face-card) and the dealer is showing an ace, the dealer usually asks the player "Even money?" instead of offering insurance. If the player accepts the offer, he is immediately paid 1:1 for his natural, regardless of whether the dealer has blackjack. Thus, accepting "even money" has exactly the same payout as buying insurance: if the dealer does not have blackjack, the player would forfeit the insurance bet and win 3:2 on the natural, thus receiving a net payout equal to the original bet; if the dealer does have blackjack, the player would push on the natural and win 2:1 on the insurance wager, again receiving a net payout equal to the original bet. Since taking "even money" is equivalent to buying insurance, it is likewise a bad choice for the player, unless he has been counting cards and knows the deck has an unusually high proportion of ten-value cards.

In casinos where a hole card is dealt, a dealer who is showing a card with a value of Ace or 10 may slide the corner of his or her facedown card over a small mirror or electronic sensor on the tabletop in order to check whether he has a natural. This practice minimizes the risk of inadvertently revealing the hole card, which may give the sharp-eyed player a considerable advantage.

Score Player buys insurance Player does not buy insurance
Dealer: blackjack
Player: no blackjack
Player loses the original bet, but wins 2:1 on his insurance bet, which was 1:2 of the original bet.
Losses and gains even out to 0.
Player loses 1:1.
Dealer: no blackjack
Player: wins
Player wins the original bet, but loses the insurance money.
The player wins 1:2 of the original bet.
Player wins 1:1.
Dealer: no blackjack
Player: same as the dealer
Player loses the insurance money.
The player loses 1:2 of the original bet.
Player pushes.
No loss or gain: 0.
Dealer: no blackjack
Player: loses
Player loses the original bet, and loses the insurance money.
The player loses 3:2 of the original bet.
Player loses 1:1.
Even money
Dealer: blackjack
Player: blackjack
Blackjacks even out, but the player wins 2:1 on the 1:2 of the insurance money.
The player wins 1:1 of the original bet.
Player pushes.
No loss or gain: 0.
Dealer: no blackjack
Player: blackjack
Player wins the original bet at 3:2, but loses the insurance bet of 1:2.
The player wins 1:1 of the original bet.
Player wins 3:2 of the original bet.

Blackjack strategy

Basic strategy

Because blackjack has an element of player choice, players can reduce casino advantage by playing optimally. The complete set of optimal plays is known as basic strategy. There are slight variations depending on the house rules and number of decks.

Your hand Dealer's face-up card
2 3 4 5 6 7 8 9 10 A
Hard totals
17-20 S S S S S S S S S S
16 S S S S S H H SU SU SU
15 S S S S S H H H SU H
13-14 S S S S S H H H H H
12 H H S S S H H H H H
11 Dh Dh Dh Dh Dh Dh Dh Dh Dh H
10 Dh Dh Dh Dh Dh Dh Dh Dh H H
9 H Dh Dh Dh Dh H H H H H
5-8 H H H H H H H H H H
Soft totals
2 3 4 5 6 7 8 9 10 A
A,8 A,9 S S S S S S S S S S
A,7 S Ds Ds Ds Ds S S H H H
A,6 H Dh Dh Dh Dh H H H H H
A,4 A,5 H H Dh Dh Dh H H H H H
A,2 A,3 H H H Dh Dh H H H H H
Pairs
2 3 4 5 6 7 8 9 10 A
A,A SP SP SP SP SP SP SP SP SP SP
10,10 S S S S S S S S S S
9,9 SP SP SP SP SP S SP SP S S
8,8 SP SP SP SP SP SP SP SP SP SP
7,7 SP SP SP SP SP SP H H H H
6,6 SP SP SP SP SP H H H H H
5,5 Dh Dh Dh Dh Dh Dh Dh Dh H H
4,4 H H H SP SP H H H H H
2,2 3,3 SP SP SP SP SP SP H H H H

The above is a basic strategy table for 3 or more decks, dealer stands on soft 17, double on any 2 cards, double after split allowed, dealer peeks for blackjack, and blackjack pays 3:2. Key:

S = Stand
H = Hit
Dh = Double (if not allowed, then hit)
Ds = Double (if not allowed, then stand)
SP = Split
SU = Surrender (if not allowed, then hit)

Most Las Vegas strip casinos hit on soft 17. This rule change requires a slightly modified basic strategy table -- double on 11 vs A, double on A/7 vs 2, and double on A/8 vs 6. Most casinos outside of Vegas still stand on soft 17.

Card counting

Basic strategy provides the player with the optimal play for any blackjack situation based on millions of hands played in the long run. However in the short run, as the cards are dealt from the deck, the remaining deck is no longer complete. By keeping track of the cards that have already been played, it is possible to know when the cards remaining in the deck are advantageous for the player.

Card counting creates two opportunities:

  • The player can make larger bets when he or she has the advantage. For example, the player can increase the starting bet if there are many aces and tens left in the deck, in the hope of hitting a blackjack.
  • The player can use information about the remaining cards to improve upon the basic strategy rules for specific hands played. For example, with many tens left in the deck, the player may double down in more situations since there is a better chance of making a strong hand.

Virtually all card counting systems do not require the player to remember which cards have been played. Rather, a point system is established for the cards, and the player keeps track of a simple point count as the cards are played out from the dealer.

Depending on the particular blackjack rules in a given casino, basic strategy reduces the house advantage to near 0 with some single-deck games, and less than one percent in a multi-deck game.[5] Card counting, if done correctly, can give the player an advantage, typically ranging from 0 to 2% over the house.[6] To counter card counting, many casinos switched from a single deck to multiple decks, with the cards dealt out of a container known as a "shoe".

In most US jurisdictions, card counting is legal and is not considered cheating.[7] However, most casinos have the right to ban players, with or without cause, and card counting is frequently used as a justification to ban a player. Usually, the casino host will simply inform the player that he or she is no longer welcome to play at that casino. Players must be careful not to signal the fact that they are counting. The use of electronic or other counting devices is usually illegal.

See also: Martingale (betting system)
See also: MIT Blackjack Team

Composition-dependent strategy

Basic strategy is based on a player's point total and the dealer's visible card. A player's ideal decision may depend on the composition of his hand, not just the information considered in the basic strategy. For example, a player should ordinarily stand when holding 12 against a dealer 4. However, in a single deck game, the player should hit if his 12 consists of a 10 and a 2; this is because the player wants to receive any card other than a 10 if hitting, and the 10 in the player's hand is one less card available to cause a bust for the player or the dealer.[8]

However, in situations where basic and composition-dependent strategy lead to different actions, the difference in expected value between the two decisions will be small. Additionally, as the number of decks used in a blackjack game rises, both the number of situations where composition determines the correct strategy and the house edge improvement from using a composition-dependent strategy will fall. Using a composition-dependent strategy only reduces house edge by 0.0031% in a six-deck game, less than one tenth the improvement in a single-deck game (0.0387%).[9]

Shuffle tracking

Techniques other than card counting can swing the advantage of casino blackjack towards the player. All such techniques are based on the value of the cards to the player and the casino, as originally conceived by Edward O. Thorp. [citation needed] One technique, mainly applicable in multi-deck games, involves tracking groups of cards (aka slugs, clumps, packs) during the play of the shoe, following them through the shuffle and then playing and betting accordingly when those cards come into play from the new shoe. This technique, which is admittedly much more difficult than straight card counting and requires excellent eyesight and powers of visual estimation, has the additional benefit of fooling the casino people who are monitoring the player's actions and the count, since the shuffle tracker could be, at times, betting and/or playing opposite to how a straightforward card counter would.[10]

Arnold Snyder's articles in Blackjack Forum magazine brought shuffle tracking to the general public. His book, The Shuffle Tracker's Cookbook, mathematically analyzed the player edge available from shuffle tracking based on the actual size of the tracked slug. Jerry L. Patterson also developed and published a shuffle-tracking method for tracking favorable clumps of cards and cutting them into play and tracking unfavorable clumps of cards and cutting them out of play. [11] [12] [13] Other legal methods of gaining a player advantage at blackjack include a wide variety of techniques for hole carding or gaining information about the next card to be dealt.

Variants

Pontoon is an English variation of blackjack with significant rule and strategy differences. However, in Australia and Malaysia, Pontoon is an unlicensed version of the American game Spanish 21 played without a hole card; despite the name, it bears no relation to English Pontoon.

Spanish 21 provides players with many liberal blackjack rules, such as doubling down any number of cards (with the option to 'rescue', or surrender only one wager to the house), payout bonuses for five or more card 21s, 6-7-8 21s, 7-7-7 21s, late surrender, and player blackjacks always winning and player 21s always winning, at the cost of having no 10 cards in the deck (though there are jacks, queens, and kings).

21st Century Blackjack (also known as "Vegas Style" Blackjack) is commonly found in many California card rooms. In this form of the game, a player bust does not always result in an automatic loss; there are a handful of situations where the player can still push if the dealer busts as well, provided that the dealer busts with a higher total.

Certain rules changes are employed to create new variant games. These changes, while attracting the novice player, actually increase the house edge in these games. Double Exposure Blackjack is a variant in which the dealer's cards are both face-up. This game increases house edge by paying even money on blackjacks and players losing ties. Double Attack Blackjack has very liberal blackjack rules and the option of increasing one's wager after seeing the dealer's up card. This game is dealt from a Spanish shoe, and blackjacks only pay even money.

The French and German variant "Vingt-et-un" (Twenty-one) and "Siebzehn und Vier" (Seventeen and Four) don't include splitting. An ace can only count as eleven, but two aces count as a Blackjack. This variant is seldom found in casinos, but is more common in private circles and barracks.

Chinese Blackjack is played by many in Asia, having no splitting of cards, but with other card combination regulations.

Another variant is Blackjack Switch, a version of blackjack in which a player is dealt two hands and is allowed to switch cards. For example, if the player is dealt 10-6 and 5-10, then the player can switch two cards to make hands of 10-10 and 6-5. Natural blackjacks are paid 1:1 instead of the standard 3:2, and a dealer 22 is a push.

In Multiple Action Blackjack the player places between 2 or 3 bets on a single hand. The dealer then gets a hand for each bet the player places on a hand. This essentially doubles the number of hands a single dealer can play per hour. Splitting and Doubling are still allowed.

Recently, thanks to the popularity of poker, Elimination Blackjack has begun to gain a following. Elimination Blackjack is a tournament format of blackjack.

Many casinos offer optional side bets at standard blackjack tables. For example, one common side-bet is "Royal Match", in which the player is paid if his first two cards are in the same suit, and receives a higher payout if they are a suited queen and king (and a jackpot payout if both the player and the dealer have a suited queen-king hand). Another increasingly common variant is "21+3," in which the player's two cards and the dealer's up card form a three-card poker hand; players are paid 9 to 1 on a straight, flush or three of a kind. These side bets invariably offer worse odds than well-played blackjack.

In April of 2007 a new version of Blackjack, called Three Card Blackjack™ was approved for play in the State of Washington. Three Card Blackjack ™ is played with one deck of 52 cards. In Three Card Blackjack the players place an ante bet. The players and dealer are then dealt 3 cards each. The players make the best blackjack (21) hand they can using 2 or all 3 cards. If the player likes their hand they make a play bet that is equivalent to their ante bet. The dealer must qualify with an 18 or better. If the dealer qualifies and the player beats the dealer, the player is paid 1-1 on both the Ante and Play bets. If the dealer does not qualify, the player is paid 1-1 on their Ante bet and their Play bet pushes. There is no hitting and no busting. At the same time that the player makes the Ante bet, they have the option of making an Ace Plus bet. If the player has 1 Ace in their hand of 3 cards, they get paid 1-1. An Ace and any 10 or Face Card pays them 3-1. An Ace and any two 10's or Face cards is paid 5-1. Two Aces pays 15-1 and Three Aces pays 100-1.

Blackjack Hall of Fame

In 2002, professional gamblers around the world were invited to nominate great blackjack players for admission into the Blackjack Hall of Fame. Seven members were inducted in 2002, with new inductees every year afterwards. The physical hall of fame is located at the Barona Casino in San Diego, California. Members include Edward O. Thorp, author of the 1960s book Beat the Dealer which proved that the game could be beaten with a combination of basic strategy and card counting; Ken Uston, who popularized the concept of team play; Arnold Snyder, author and editor of the Blackjack Forum trade journal; Stanford Wong, author and popularizer of the "Wonging" technique of only playing at a positive count, and several others.

Notes

  1. ^ Scarne's New Complete Guide to Gambling, p. 342
  2. ^ ♠Las Vegas SUN: Taking a hit: New blackjack odds further tilt advantage toward the house
  3. ^ QFIT.com 100+ Blackjack variations
  4. ^ Blackjack Insurance Exceptions
  5. ^ Rules & House Edge Table
  6. ^ Theory of Blackjack, p. 5
  7. ^ Theory of Blackjack, pp 6-7
  8. ^ "The Wizard of Odds". Fine points of basic strategy in single-deck blackjack. {{cite web}}: Unknown parameter |accessmonthday= ignored (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help)
  9. ^ "The Wizard of Odds". Total Dependent and Composition Dependent Basic Strategy in Blackjack. {{cite web}}: Unknown parameter |accessmonthday= ignored (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help)
  10. ^ Shuffle Tracking Counts
  11. ^ The Gambling Times Guide to Blackjack; Gambling Times Incorporated, Hollywood, CA; © 1984; Page 110; ISBN 0-89746-015-4 Shuffle-Tracking An Easy Way to Start ]
  12. ^ Break the Dealer; by Jerry L. Patterson and Eddie Olsen; Perigee Books; A Division of Penguin Putnam; © 1986; ISBN 0-399-51233-0 Shuffle-Tracking; Chapter 6, Page 83]
  13. ^ Blackjack: A Winner’s Handbook; by Jerry L. Patterson; Perigee Books; A Division of Penguin Putnam; © 1990; ISBN 0-399-51598-4 Shuffle-Tracking; Chapter 4, Page 51]

Sources

  • Beat the Dealer : A Winning Strategy for the Game of Twenty-One, Edward O. Thorp, 1966, ISBN 978-0-394-70310-7
  • Blackbelt in Blackjack, Arnold Snyder, 1998 (1980), ISBN 978-0-910575-05-8
  • Blackjack: A Winner’s Handbook, Jerry L. Patterson, 2001, (1978), ISBN 0-399-52638-8
  • Ken Uston on Blackjack, Ken Uston, 1986, ISBN 978-0-8184-0411-5
  • Knock-Out Blackjack, Olaf Vancura and Ken Fuchs, 1998, ISBN 978-0-929712-31-4
  • Luck, Logic, and White Lies: The Mathematics of Games, Jörg Bewersdorff, 2004, ISBN 978-1-56881-210-6, 121-134
  • Million Dollar Blackjack, Ken Uston, 1994 (1981), ISBN 978-0-89746-068-2
  • Playing Blackjack as a Business, Lawrence Revere, 1998 (1971), ISBN 978-0-8184-0064-3
  • Professional Blackjack, Stanford Wong, 1994 (1975), ISBN 978-0-935926-21-7
  • The Theory of Blackjack, Peter Griffin, 1996 (1979), ISBN 978-0-929712-12-3
  • The Theory of Gambling and Statistical Logic, Richard A. Epstein, 1977, ISBN 978-0-12-240761-1, 215-251
  • The World's Greatest Blackjack Book, Lance Humble and Carl Cooper, 1980, ISBN 978-0385153829

Regulation in the United Kingdom

Blackjack calculators