Blackjack, also known as twenty-one,among all casino games is the one card game known to be the easiest for a novice to learn, play and win.
Card counting is a casino card game strategy used primarily in the blackjack family of casino games to determine whether the next hand is likely to give a probable advantage to the player or to the dealer. Card counters are a class of advantage players, who attempt to reverse the inherent casino. Free Practice Card Counting Blackjack What many people don’t know is that playing with a good and fair deposit bonus gives you a much, much higher.
Unlike most other “games of chance,” such as Roulette or Craps, everything that happens at a Blackjack table is influenced by preceding events, so a player who remembers what has occurred can apply that knowledge for a winning advantage.
Besides a good memory, it is useful for a Blackjack player to have a clear knowledge of the rules of the game and a good grasp of Blackjack basic strategy.
Blackjack has many variations so it is appropriate to begin by mastering the most common version, before progressing to more complicated forms.
THE BIBLE OF BLACKJACK – Beat the Dealer!
Edward O. Thorp is the father of blackjack card counting, and in Beat the Dealer he reveals the revolutionary point system that has been successfully used by professional and amateur blackjack players for two generations.
From Las Vegas to Monte Carlo, the tables have been turned and the house no longer has the advantage at blackjack,
Containing the basic rules of the game, proven winning strategies, how to overcome casino counter measures and spot cheating. Beat the Dealer is the bible of blackjack. Perforated cards included in the book are a convenient way to bring the strategies into the casino. Read Beat the Dealer.
Blackjack – Begin with the Basics
Blackjack is a game for two or more participants, one of them being the dealer (bank or house), whom the other players will try to beat. The game uses a standard deck of 52 cards and begins with the players making their initial wagers. Players who bet are called “in” and receive two cards each, as does the dealer.
Those who do not bet are “out” for the hand. The value of each card dealt is the number on its face for all cards 2 through 10. Face cards—the King, Queen and Jack—each have a value of ten.
Aces may have a value of either one or eleven, so an Ace plus a three, for example, can be counted as either four or fourteen. The object for each player is to draw cards that total higher than the dealer’s cards without going over 21.
Once the initial cards have been dealt, one of the dealer’s two cards is turned over, facing up for all to see. If that card has a value of ten, the dealer will take a peek at the other card (the so-called “hole card”) and turn it over if it is an Ace.
That means the dealer has exactly 21 and all players lose their bets except those who were also dealt a “natural blackjack,” i.e., an Ace plus a card valued at ten. Players with blackjacks simply “push” (draw or tie) and get their original bets back.
If the dealer’s hole card is not an ace, then play resumes, with players given four options in turn. They may “hit” by taking another card, “stand” by staying with what was dealt, “split” by making two new hands out of a matched pair, or “double down” by increasing the original bet and drawing just one more card.
In the latter case, the player must stay with whatever comes up and may not draw again.
Sometimes available is a fifth option known as “surrender.” That means you can quit the hand by surrendering half of your bet. Another special circumstance is when the dealer is showing an Ace. You may buy “insurance” for half the amount of your initial wager.
If the dealer comes up with a natural blackjack, you will keep everything you bet. If the dealer has anything else, you lose the insurance portion of your bet and play continues.
In turn, each player may draw cards, trying to improve the dealt hand until either going “bust” (a total of over 21) or deciding to stand. The dealer, on the other hand, must play according to fixed rules. Splitting, doubling, surrendering and insurance are not available for the dealer.
The dealer must draw until the hand is valued at 17 or more, and then must stand. No more cards may be taken. Players who have not busted win their bets whenever their hands come closer to 21 than the dealer’s without going over, or if the dealer busts.
Specific Examples and Payouts in Blackjack
If the dealer holds two 9s, for instance, that is a value of 18, and the dealer may not draw any more cards. A player facing the dealer’s 18 must hold cards valued at 19, 20 or 21 in order to win, such as a pair of Jacks, or an Ace plus an 8, or a 4+5+10. Beating the dealer pays even money: one unit won for every unit bet.
As mentioned, an Ace plus a face card or 10 creates a natural 21—a so-called “blackjack”—which is the best two-card hand possible. When it wins, blackjack pays 3-to-2, or 1.5 units for every unit bet.
Other combinations of three or more cards may also total 21, such as three 7s or a 6+7+8 or a 2+4+5+10, etc. However, when they win, they pay only one unit per unit wagered.
If the values of the dealer’s cards and the player’s cards are identical, the hand is declared a “push” (tie or draw). The bet is neither won nor lost.
Any combination of cards which totals more than 21, such as a 5+8+9, is called a bust. The player who busts is out for the rest of the hand and the wager is immediately lost.
When a player “doubles down” to take just one more card, all of the units bet are lost if the hand busts. If the hand wins, it is paid out at one unit for every unit wagered. Some house rules allow doubling down on any two cards.
Some allow doubling down for less than two times the initial wager. Others permit doubling only on cards valued at ten or eleven.
When a player “splits” a matched pair to create two hands, an amount equal to the initial wager must be placed on the newly formed hand. Each hand then receives an additional card and play continues. Opportunities to stand, hit, split or double down are offered in turn on the new hands.
Some house rules permit splitting of Aces only once, or the drawing of only one card after splitting Aces. Some permit unlimited splitting of any pairs. But for natural blackjacks occurring on split hands, the payout is always 1-to-1. The 3-to-2 payout applies only to the original two cards dealt.
In most Blackjack games, a player with a natural blackjack can take “insurance” against a dealer’s Ace by requesting “even money.” That means the hand will pay 1-to-1 instead of 3-to-2, no matter whether the dealer has 21 or not. If even money is not taken and the dealer has 21, the result is a push.
Hands containing an Ace that can be counted as either one or eleven are called “soft.” A hand with an Ace and a six, for example is a “soft 17.” Some house rules require a dealer to stand on soft 17; others require the dealer to draw.
Either way, the dealer does not have a choice. The dealer’s hand must count an Ace as eleven, unless it would result in a bust, in which case the Ace must count as one.
Variations of Blackjack
Blackjack as it is played today is a relatively new game. Its origins are obscure, but it certainly can trace it roots to the mid-18th century and a French game called vingt-et-un or “twenty-one.” This game probably derived from trente-et-un, or “thirty-one,” a slower game with several betting rounds played as early as 1464.
Vingt-et-un did not catch on quickly outside France, so it was made more enticing by Americans who offered 10-to-1 payouts for the Ace of spades drawn with a Jack of clubs or spades on the first two cards. This new game of “Blackjack” soon became popular on the riverboats and in the private gaming parlours of the Wild West.
In the United States, Blackjack evolved into several unique forms, the most enduring of which are Vegas Downtown Blackjack, Vegas Strip Blackjack, and Atlantic City Blackjack.
In the Downtown version, two decks of 52 cards are used; the dealer must hit soft 17; you can double down on any two cards and after a split; and you can split any two cards valued at ten, such as a King and a Queen.
In the Strip version, four or six decks of 52 cards are used; the dealer stands on any 17; and splits are allowed up to three times, for four hands in total. Atlantic City, meanwhile, is like the Strip version, but it uses eight decks of 52 cards and Aces can only be split once.
Among the many current variations of the game outside the United States, European Blackjack is a single-deck game with no hole card and therefore no peeking and no insurance.
It allows doubling down only on values of nine, ten or eleven; unlimited splitting of pairs; unlimited draws on split Aces; the dealer stands on soft 17; and 10s do not count for natural blackjacks—only face cards do.
How to get a job at netflix watching movies. Spanish Blackjack, an eight-deck game played with a hole card, has some different rules.
A player’s blackjack or 21 beats a dealer’s blackjack or 21; the dealer must hit soft 17; any two cards valued at ten may be split; and bonus payments are offered on certain counts totaling 21, such 2-to-1 for any six-card 21, 3-to-1 for any seven-card 21, and 3-to-1 for a 7+7+7 or 6+7+8 all in spades.
As if those were not enough, how about some truly exotic forms?
Double Exposure Blackjack uses eight decks and has no hole card; it shows both of the dealer’s cards up, while paying 1-to-1 on natural blackjacks. SuperFun 21 Blackjack allows surrender at any time, even after drawing cards; it pays 1-to-1 on natural blackjacks and lets the player’s blackjack win against the dealer’s natural.
Big Five Blackjack, Triple Sevens Blackjack, No Bust Blackjack…one expert has said there are no fewer than 113 kinds of Blackjack currently played in the world’s casinos and online.
Most of these games derive from the standard version, altering the odds, payoffs and dealer’s play to create new possibilities. So before you play any form of Blackjack, it is an excellent practice to read the rules carefully. It could very easily affect how you play and win.
Playing by the Book at Blackjack
It is unlikely that Edmond Hoyle (1672-1769) ever played any form of Blackjack other than one quite similar to the original French vingt-et-un. Nevertheless, his enduring book “Rules of Games” laid the foundation for playing card games for centuries to come.
By the 1946 edition, it had set forth the basic strategy for winning blackjack play, which has remained virtually unchanged despite the many attempts to modify the game since then.
Regarding hitting or standing, according to Hoyle, the player should stand on seventeen or higher, just like the dealer does. For any total less than seventeen, count Aces as one. If the dealer is showing a 2 through 6, stand on any hand valued at thirteen or higher.
If the dealer is showing a 7 through 10 or an Ace, hit when holding thirteen through sixteen. No matter what the dealer shows, hit on twelve or under. (Note: Later authors have advised standing on twelve when the dealer shows 4, 5 or 6.)
When it comes to doubling down, always do so when holding eleven, unless the dealer is showing an Ace. Double down on ten whenever the dealer is not showing a 10 or an Ace.
Do not double down on other totals. (Note: Again, later authors suggest doubling on nine against the dealer’s 2 through 7, and doubling on any soft hand except the A+9 against the dealer’s 4, 5 or 6.)
As for pairs, Hoyle says always split Aces and 8s and never split 10s, 5s or 4s. Only split other pairs if the dealer is not showing a 7 through 10 or an Ace. (Note: Against a dealer’s 7, some later authors say the proper play is to split 2s, 3s, or 7s, and 9s should be split against a dealer’s 8 or 9.)
Hoyle never addressed the questions of insurance or surrender, which probably didn’t exist in his day, but most experts say insurance is a bad bet, unless taking even money for a natural blackjack—a guaranteed win. Surrender is always a losing strategy; even you if guess correctly, you still give up half your wager.
When you are just starting out, it is not a good idea to stray too far from Hoyle’s basics. If you are playing in a land-based casino, other players can become very upset by “non-standard play,” such as splitting tens or drawing to fourteen against a dealer showing a 6.
When in doubt, you can always ask the dealer, “What does the book say about this situation?” They are well trained in standard play, and most pit bosses do not mind at all if the dealer tells you what the most common choice would be.
Before you play for real money, you might want to try dealing some hands of your own at home using a single 52-card deck. Get used to the types of situations that come up. Take your time and learn how to play “by the book.”
You can then extend this practice to free play online or by using a Blackjack simulation on your computer. The more you practice, the easier it will become. Master the basic strategy and you will soon be ready to start winning for real.
Improving the Odds – Blackjack Basic Strategy
Besides making it easy for you to know how to play in any situation, blackjack basic strategy is also absolutely necessary in order to reduce the house advantage. Although Blackjack is basically an even money game, paying 1-to-1 on most bets, it would be a mistake to think of the odds of winning as 50:50. Here’s why:
Let’s suppose your strategy was to play exactly the same way the dealer plays. You would never double or split. You would never take insurance or surrender. You would always hit till you reach seventeen or higher. On the face of it, you might think you would perform just as well as the dealer.
But the truth is that you would still lose more often than the dealer would. That’s because you must draw before the dealer does. If you bust, you lose your entire bet before the dealer ever takes a card. For that reason alone, you will lose hands that you would have won when the dealer busts. You have to be “in” to win.
American stage magician John Scarne (1903~1985) was one of the first to calculate the house edge at blackjack caused by these “simultaneous busts.” He found that the dealer will bust once every 3.57 hands, or 28% of the time. The same would be true of the player. The probability of the dealer and player busting on the same hand is .28 x .28 or 7.84%.
However, Scarne also had to factor in the effect of the player getting paid 3-to-2 on a blackjack. When he did so, he discovered that the true house advantage reduces to 5.9%. That means the player can expect to experience a net loss roughly once every 17 hands, if all hands are played in exactly the same way as the dealer plays.
Playing the basic strategy actually helps reduce the number of times the player busts. It falls from 28% to just 17%. This brings the house advantage down to.17 x .28 or 4.76%. Instead of busting every 17 hands, the player will bust once every 21 hands.
Again, the player receives 3-to-2 for natural blackjacks, plus additional bonuses on doubling down and splitting pairs at the optimum time. This will drop the house edge to as little as 1%, or a net loss of once every 100 hands, not 17 or 21. The importance of sticking to basic strategy cannot be over-emphasized.
Blackjack Betting Progressions
One aspect of the game of Blackjack that you have absolute control over is how much to bet on any given hand. If, by using basic strategy, you can reduce the house advantage to almost zero, it should be possible to win in the short term by playing standard betting progressions.
The Martingale system, doubling up after a loss, can be applied to Blackjack in the same way it is used for even money bets at Roulette. You begin by betting one unit. If you win, set aside your profit (one unit) and start a new series, betting a single unit.
If you lose, double your wager (two units) and bet again. Continue doubling in this manner until you win, then set aside your profit (one unit) and begin again.
In centuries past, Martingale was thought to be a perfect gambling system. Any win in a series of bets will recover all of the previous losses and yield a profit of one unit. However, the system has some serious drawbacks, especially when playing blackjack.
The biggest problem is streaks. If you win seven times in a row, your total profit will be seven units. But if you lose seven times in a row, your accumulated loss will be 127 units. Martingale will require you to wager 128 units on the next hand. That means your total stake will be 255 units in an attempt to win just one single unit.
Even if you are willing to take such a risk, another problem is that you may reach the table limit and be unable to double your bet after another loss.
A table with a $5 minimum, for example, will commonly have a maximum of $500. Your progression will automatically cap out and fail if you lose seven times in a row, because your next bet would have to be $620.
A third concern when playing Martingale at Blackjack is the effect of splits. You have to decide before you make your first bet exactly how you will factor such occurrences into your play.
Will you split a pair of Aces, as basic strategy dictates, when the situation comes up after five straight losses? If you win one of the splits and lose the other, will you continue your progression as if it were a push?
Doubling down is less of a concern, because you can simply follow a policy of never doing so. But remember, if you do not double down when you should, you are not following basic strategy and the house odds will improve accordingly.
Advanced Blackjack Strategy
Besides Martingale, other even money betting progressions, such as Labouchereor d’Alembert, can be applied to Blackjack with short term success, although they, too, fall afoul of streaks, limits and splits.
But Blackjack, unlike Roulette or Craps, is a game directly affected by previous events. Knowing this, great minds of the 20th century set about devising a strategy that takes into account the cards that are removed from the deck(s) during play.
In 1956, an article by Roger Baldwin entitled “Optimum Strategy in Blackjack” was published in the Journal of the American Statistical Association. A professor of mathematics at UCLA, Edward O. Thorp, read the article, tested it in real play, and found it lacking, even though it claimed to lower the house edge from 2% down to just 0.62%.
Using an IBM 704 computer, Thorp analysed the game of Blackjack more rigourously than it had ever been studied before. He determined ways of reducing the house advantage to a mere 0.21%, and then he hit upon a way of keeping track of cards that could actually turn the tables in the player’s favour.
At the center of Thorp’s strategy was a simple a priori concept. When the deck contains a lot of high-value cards, a dealer who must draw to 17 is more likely to bust. Therefore, a player who keeps track of how many high-value cards have been removed from the deck can know, with considerable accuracy, when the odds have shifted and when to make larger bets.
Confident in the potential rewards of this approach, Thorp tested this theory in actual play. With $10,000 gathered from supporters, he tried out his strategy at the tables of Las Vegas and rather easily doubled his bankroll.
Then, in 1962, Thorp published his findings in a book called Beat the Dealer, which revolutionised the way Blackjack is played.
Blackjack Card Counting
Thorp’s major contribution to the game of Blackjack is the Plus Minus Strategy, or so-called “card counting.” In its simplest version, players are advised to keep track of low cards (2, 3, 4, 5, and 6) by giving each one they see a value of +1. Concurrently, they are told to count high cards (10, Jack, Queen, King and Ace) as -1. All other cards (7, 8, and 9) have no value.
As the cards are dealt, the player silently counts each card as it shows, adding or subtracting values and maintaining a total. This total will indicate when the deck is rich or poor in terms of high cards. Small cards removed from the deck favour the player, and the count become positive. Large cards removed favour the house, and the count becomes negative.
Knowing when the deck is rich (positive count) or poor (negative count) affects play in two ways. At the beginning of a hand, you want to increase your bet for a rich deck, or decrease it for a poor one. For example, when playing with a single deck, bet just one unit when the count is +1 or lower, and bet two units if it is +2 or higher.
When playing with multiple decks, you should adjust this procedure accordingly, i.e., +4 or lower and +5 or higher for four decks, and +6 or lower and +7 or higher for six decks, etc.
Then, when the hand is played, you want to adjust your play—drawing, doubling down and splitting—with the knowledge of how a rich or poor deck will impact your hand. If the count is negative, you know the deck has a lot of small cards, so you might choose not to double down on a nine, for example, against a dealer’s 2 through 6.
Since Thorp’s method first appeared, many have attempted to improve upon it. Some advocate keeping track of fives. Some track Aces separately.
But no matter what card counting approach you take, one thing remains constant: it is not as easy as it might seem. Card counting requires a great deal of concentration, excellent recall, and flawless mastery of basic play.
Blackjack Team Game
In the 1970s, Harvard MBA Ken Uston was recruited by a team of Blackjack players located in San Francisco. Using an advanced “point count” system based on Thorp’s strategy, the team members would place minimum bets at a number of tables, keeping the count until a rich deck was found. They would then signal Uston, who would join the table and bet the maximum.
The team reportedly made millions of dollars at the tables of Atlantic City, Reno and Las Vegas. But eventually, a casino surveillance operation caught on to their cooperative efforts. Thereafter, Uston was banned from play.
In the 1990s, a group of MIT students duplicated the efforts of Uston’s team, with even greater success in keeping their collusion secret. Their success was revealed in Ben Mezrich’s 2002 book, Bringing Down the House, which was later made into a movie called “21” with Kevin Spacey.
Casinos are well aware of attempts to count cards and form teams. They are not at all concerned about a few friends or a married couple playing together at a table, but if they suspect players of a team effort to count cards and take advantage of the quality of the deck, they will waste no time in banning them from the tables.
As private businesses, casinos have the right to refuse service to anyone, with or without reason.
Casinos also have other countermeasures they can use to thwart card counters and team play. Frequent shuffling of the cards will reduce the occurrence of rich and poor decks. Changing table minimums and maximums can make steady winning difficult. Not allowing new players to sit in mid-deck is another tactic they employ.
And of course, there is always the constant distraction of free alcoholic beverages. Casinos know that it is very difficult to count cards when drunk. For this reason, professional player Lawrence Revere, author of Playing Blackjack as a Business, advises adopting one cardinal rule: “I do not drink when I work.”
Cheating at Blackjack
Card counting is certainly not cheating, nor is it illegal, even though most casinos seem to treat it as such. It is simply a strategy that takes away the house edge. However, there are several ways in which dealers and players have attempted to get a little more edge than the rules allow, and these are strictly against the law.
Dealers handle all of the cards, so they have the greatest opportunity to cheat. Marking a deck with tiny, almost indiscernible pin pricks or ink dots is one.
Dealing from the bottom of the deck in a single deck game or dealing “seconds” from a shoe are other common ones. In the latter, the dealer leaves the top card in the deck in place and instead deals the card beneath it—the second card.
Blackjack Switch Card Counting Sheet
Rest assured that legitimate casinos keep a close watch over their employees for cheats. The game already has a built-in advantage for the house, so there is no incentive for dealers to cheat against the players. A dealer willing to risk his/her job by cheating is probably working with an accomplice who is a player.
On the other side of the table, players may try to mark cards by creasing the corners or cutting tiny slits into the edges with their fingernails.
Players with fast hands may also try to “palm a card,” hiding it under their cupped fingers or sliding it up a sleeve to be used later. Another way in which players try to cheat is by playing two separate hands and switching cards between them.
As you might guess, it is extremely difficult to cheat and not get caught, especially with so many watchful eyes surrounding the table, from the dealer to the pit boss and surveillance managers. Since it is quite possible to win without cheating, it’s a wonder that people still try, but they do, and invariably they get caught.
One variation of the game that turns all of the rules and strategies upside-down is tournament Blackjack. In tournament play, the object is to beat the other players at the table, not necessarily the dealer. The game begins with a buy-in, typically $25 or so. The player then receives tournament chips, usually valued at $500 worth, with which to play.
Switch Card Issue Number
Each table in the tournament will have six or seven players, who will play a fixed number of hands, typically 25, from a six deck shoe.
Although a casino dealer will shuffle and deal the cards, a marker called the “button” is used to indicate where the deal begins, and it moves from player to player each hand, as if the deal were being passed clockwise from one player to the next each hand.
Players may wager a minimum of $10 up to a maximum of $300. In all other aspects, play is the same as it would be when vying against the house. The object, however, is to amass more winnings than any other player at the table.
When a number of elimination rounds are played, the top two winners at each table move on to the next round, while everyone else drops out.
Eventually, a final table is formed, and those who reach the last round are guaranteed a percentage of the entry fees collected. For example, the top chip winner might get half the fees collected, second place a quarter, third place an eighth, etc.
Tournament Blackjack strategy can be quite different from standard play. For example, a player may start out betting the maximum in an attempt to establish a big lead quickly, or else slow play until the deck seems rich. Quite often, players will base their bets on what others at the table are wagering to keep pace with the chip leaders.
If a player can survive to the last four or five hands without going broke or falling too far behind, it may require some risky betting to make it to the next round.
It is not uncommon to see a player split a pair of tens or fives, draw a card to a natural blackjack, or double down on 18, if that is the only way to end up among the qualifiers. It is a very different version of the game, indeed.
Playing Blackjack Online
Before playing Blackjack on the Internet, it is a good idea to do a search to see if the web site you have chosen is trusted or blacklisted. Watchdog groups keep an eye out for any operators whose games are unfair—i.e., they do not post results consistent with a random play or else fail to pay out legitimate winnings. Obviously, you should play only at sites you can trust.
Once you have selected a site, you will want to choose a variation of the game that you fully understand. Most games of Blackjack are similar to the ones mentioned earlier.
If the game doesn’t pay 3-to-2 on a natural blackjack, you probably want to avoid it. Also, seek out versions of the game that allow you the most options when it comes to splitting and doubling down.
Once you are certain that you understand the online game’s rules and are satisfied that the odds are fair, you will probably want to play a some hands using the “for fun” mode, without risking any real money.
See how the game plays. If something doesn’t seem quite right or you are not comfortable, just leave and try another site. There are certainly plenty to choose from.
Since most Blackjack games online are individual, not multiplayer, you will not have to worry about other players making bad choices ahead of you or behind you. You can control the pace of play. You can consult your books and strategy charts if you like.
You can even use reference software to assist you. It is quite different from the land-based casino environment, where such aids are not allowed at the table.
If you have chosen to play at an online casino that offers bonus cash, be sure to check whether playing Blackjack games will qualify for bonus redemption.
Many web sites disallow so-called “even money games” from promotional play. As always, it is best to avoid any unpleasant surprises by reading the terms and conditions carefully before you play.
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Four Poker is a new poker variation invented by Roger Snow and marketed by Shufflemaster. The game is similar to Three Card Poker but as the title suggests, four cards are used instead of three. Also, there is no dealer qualifying hand and the player can raise up to three times his ante. However, the dealer gets one extra card to form his best hand.
- Two initial bets are available: The Ante and the Aces Up.
- All players get five cards each and the dealer gets six cards. One of the dealer cards is placed face up, and five face down.
- Players making the Ante bet must decide to fold or raise.
- If the player folds he forfeits his Ante bet. He may or may not forfeit his Aces Up bet, depending on casino rules. It shouldn't matter because if the player has a paying Aces Up bet, he shouldn't be folding anyway.
- If player raises, then he must raise at least the amount of the Ante and at most, three times the Ante.
- The player keeps his best four cards and discards one.
- Following is the ranking of hands from lowest to highest: high card, pair, two pair, straight, flush, three of a kind, straight flush, four of a kind.
- After all decisions have been made, the dealer will turn over his cards and select the best four out of six.
- The player's hand shall be compared to the dealer's hand, the higher hand winning.
- If the dealer's hand is higher, then the player shall lose the Ante and Raise.
- If the player's hand is higher or equal then the Ante and Raise shall pay one to one.
- If the player has at least a three of a kind, then he shall also be paid a Bonus, regardless of the value of the dealer's hand. Two different pay tables are available for the Bonus, as displayed below, and are based on the ante bet. Pay Table 1 is the only one I know of to be actually used.
- Another bet is available (similar to the Pairplus in Three Card Poker), based only on the player's four card hand, called the Aces Up. Seven pay tables are available as indicated below. The only one I know of to be actually used is pay table 5.
Bonus Pay Table
|Hand||Table 1||Table 2|
|Four of a kind||25||30|
|Three of a kind||2||2|
Aces Up Pay Table
|Hand||Table 1||Table 2||Table 3||Table 4||Table 5||Table 6||Table 7|
|Four of a kind||50 to 1||50 to 1||50 to 1||50 to 1||50 to 1||50 to 1||50 to 1|
|Straight flush||40 to 1||40 to 1||30 to 1||30 to 1||40 to 1||40 to 1||40 to 1|
|Three of a kind||9 to 1||7 to 1||9 to 1||7 to 1||8 to 1||8 to 1||7 to 1|
|Flush||6 to 1||6 to 1||6 to 1||6 to 1||5 to 1||6 to 1||5 to 1|
|Straight||4 to 1||5 to 1||4 to 1||5 to 1||4 to 1||4 to 1||4 to 1|
|Two pair||2 to 1||2 to 1||2 to 1||2 to 1||3 to 1||2 to 1||3 to 1|
|Pair of aces or better||1 to 1||1 to 1||1 to 1||1 to 1||1 to 1||1 to 1||1 to 1|
Of these pay tables for the Aces Up side bet, number five is the most popular. The only exceptions that I'm aware of are an unconfirmed report that that Tulalip in Washington uses pay table 4 and the Grand Casino Hinckley in Minnesota uses pay table 1.
The following return table is based on optimal player strategy under the 2-20-25 Ante Bonus pay table. The lower right cell shows a house edge of 2.79%.
Return Table Based on Optimal Strategy
|Four of a Kind||3||Win||40,182,878,736||0.000240||+29||0.006960|
|Four of a Kind||3||Lose||18,594,576||0.000000||+21||0.000002|
|Three of a Kind||3||Win||3,675,379,352,400||0.021951||+6||0.131703|
|Three of a Kind||3||Lose||103,559,138,928||0.000618||-2||-0.001237|
The average final bet under optimal strategy is 2.142342 units, making the element of risk, -0.027879/2.142342 = 1.30%. The standard deviation, relative to the original bet, is 2.71.
A simple strategy to this game, first proposed by Stanley Ko, is as follows.
- Raise 3X with a pair of tens or higher.
- Raise 1X with a pair of twos to nines.
- Fold all other.
According to the second edition of 'Beyond Counting' by James Grosjean, this 'simple strategy' results in a house edge of 3.396%.
The following intermediate strategy was created to balance power and simplicity by our own JB.
- Pair of Aces or better: Bet 3X
- Pair of Js, Qs, Ks: Bet 3X if dealer's upcard is lower than your pair or matches a rank in your hand, otherwise bet 1X
- Pair of 9s, 10s: Bet 1X if dealer's upcard outranks your pair, otherwise bet 3X
- Pair of 8s: Bet 3X if dealer's upcard is a 2, otherwise bet 1X
- Pair of 3s, 4s, 5s, 6s, 7s: Bet 1X
- Pair of 2s or AKQ: Bet 1X if dealer's upcard matches a rank in your hand, otherwise fold
- All other: Fold
Against the 2-20-25 Ante Bonus pay table, the house edge is 2.8526% and the element of risk is 1.3233%.
I'm proud to present the following advanced strategy, also created by my sidekick JB.
- Pair of Aces or better: Bet 3X
- Pair of Ks: Bet 3X, except bet 1X against an Ace and you don't have an Ace nor 4.
- Pair of Js or Qs: Bet 3X, except bet 1X if the dealer's card outranks pair your pair rank and does not match a singleton in your hand.
- Pair of 9s or 10s: Bet 3X, except bet 1X if dealer card outranks your pair rank.
- Pair of 8s: Bet 1X, except bet 3X against a 2
- Pair of 4s thru 7s: Bet 1X
- Pair of 3s: Bet 1X, except fold against a Jack if your highest kicker is a 10 or lower
- Pair of 2s or AKQ: Fold, except bet 1X if dealer card matches a rank in your hand
- AKJT: Fold, except bet 1X against a Jack
- AKJ9 or lower: Fold
Against the 2-20-25 Ante Bonus pay table, the house edge is 2.8498% and the element of risk is 1.3216%. Here is a house edge comparison of various known strategies.
- Simple: 3.396%
- Intermediate: 2.853%
- Advanced: 2.850%
- Optimal: 2.788%
To put it another way, here are the cost of errors:
Blackjack Switch Card Counting Games
- Simple: 0.606%
- Intermediate: 0.065%
- Advanced: 0.062%
- Optimal: 0.000%
Aces Up Analysis
The next table shows the probability of each hand and the return under pay table five of the Aces Up side bet. The lower right cell shows a house edge of 3.89%.
Return for Aces Up Pay Table 5
|Four of a kind||624||0.00024||50||0.012005|
|Three of a kind||58656||0.022569||8||0.180552|
|Pair of aces||81096||0.031203||1||0.031203|
The next table shows the house edge according to all four Aces Up pay tables.
Aces Up House Edge
|Pay Table||House Edge|
Note: There is also a similar game called Crazy Four Poker.
I would like to recognize:
- JB for the analysis of the optimal strategy.
- Stanley Ko for the simplified strategy.
- James Grosjean for the unpublished advanced strategy.