2.2 The Rule of Blackjack. Number cards count as their natural value; the jack, queen, and king (also known as “face cards” or “pictures”) count as 10; aces are valued as either 1 or 11 according to the player’s choice. If the hand value of player exceeds 21 points, it busts, and all. Blackjack: Finding Expected Values of Games of Chance with Cards In this video we learn about games of cards, and how to calculate probabilities. We look at the game of Blackjack and calculate the. Acronym for expected value. A phrase that the player may state or the dealer may ask, if the player has a blackjack and the dealer has an ace as an up-card. If the player agrees to even money he will be paid the amount of his wager before the dealer checks his hole-card. This is essentially the same thing as the player insuring his blackjack. The part of the card that matters when playing Blackjack is its number value. For the actual numbered cards, you can gather that their card value is equal to the actual number they represent. Cards 2 through 10, no matter the suit, represent that number. Face cards, whether it’s.

Blackjack’s biggest allure lies in its simplicity. The rules of this classic casino staple are easy to comprehend, or at least if one is playing the game in its purest form. You play against the house and your purpose is to get a hand total that is as close to 21 as possible without exceeding it. If your total is higher than the dealer’s, you receive a payout, if not, you lose. It really is as simple as this.

The enormous popularity this casino mainstay enjoys worldwide has caused dozens of blackjack variations to pop up over the years. Some of those have only minor rule deviations while others are so odd that it almost feels like you are playing an entirely different game, so much so that at BlackjackExpert.com we have dedicated separate pages to some of these variations.

Rule deviations make the game all the more exciting, presenting players with more winning opportunities but it is also important to recognize that some adjustments are there for the simple purpose of giving the house a higher edge. Because of this, it is important to differentiate between the variations that work to your advantage and those that are in the casino’s favor. Continue reading to learn all the fine points of blackjack rule variations and why do they matter.

Common Rule Variations

The thing about casino games, including blackjack, is that they are always slightly rigged against the player so that the house can extract advantage and profit from its tables. This is not to say the casino is cheating you out of your money. There are various legal ways for the house to gain an edge over players and the simplest of them is by enforcing various adjustments to the rules that have a direct effect on the odds. Some of these adjustments actually work in your favor improving your odds while others are designed to hurt your long-term chances of winning.

For those of you who are not familiar with what the term “house edge” refers to, this is the built-in percentage the house collects from each bet made at its tables in the long run. The house edge in blackjack fluctuates wildly but it is safe to say it generally ranges between 0.50% and 1.00% when you follow basic strategy to the tee, making 21 one of the games with the lowest casino advantage.

So for example, if you join a blackjack table with a 1.00% house edge, bet $10 per hand, and play about 60 hands per hour, your action would amount to $600 per hour. Respectively, you are expected to lose $6 on average to the house over the course of time. This is not to say you will not turn a profit over the short term but the more hands you play, the closer you will inch to these expected results.

The house can improve its long-term edge by adjusting some of the basic rules of play at the blackjack tables. The most common rule deviations pertain to the number of decks in play, the dealers’ standing totals, the payouts on naturals, to splitting pairs, and doubling down. We cover all these rule variations in further depth below.

Number of Decks in Play

Blackjack usually plays with one to eight full decks of cards, but deck penetration and the depth of dealing also do matter, especially if one is counting cards. There is a general consensus among skilled blackjack players that fewer decks give the house the lowest advantage. The casino edge increases proportionately to the number of decks in play. From this, it follows that the most profitable tables are the ones using a single deck of cards.

The reason for this is quite simple – the number of decks affects your opportunities to profit from double downs as well as your odds of getting dealt blackjacks. You can easily figure out the probability of obtaining naturals when you know the number of cards in play.

For the purpose, you multiply the odds of receiving an ace by the odds of being dealt a ten-value card. A full deck contains 52 cards and respectively, there are only 4 aces and 16 cards that are assigned a value of ten.

We use the following formula: Pb = n(ace) x n(ten-value cards) x 2 where n indicates the number of aces and ten-value cards, and Pb corresponds to the probability of being dealt a blackjack. The result is then multiplied by 2 as we also take into account the order in which the cards are dealt, which can be either ace/ten or ten/ace.

Therefore, the calculations for a single-deck game run in the following manner: Pb = (4/52) x (16/51) x 2 = 0.04826 x 100 = 4.82%. We multiply by 100 to obtain the figure in the form of a percentage. Also, the overall number of cards in the second brackets is reduced to 51 instead of remaining 52 because you have supposedly already drawn one card, the ace.

We can use the same formula to calculate the probability of receiving a blackjack when multiple decks are in use. Respectively, the likelihood of getting naturals in a six-deck game will be Pb = (24/312) x (96/311) x 2 = 0.04748 x 100 = 4.74%. The difference of 0.08% appears minuscule but when it comes to gambling, things unfortunately do add up in the long run.

The smaller your chances of receiving blackjacks at a given table, the more the house edge increases because it is the naturals that give players the best value in this fascinating game. In a single-deck game where you use perfect basic strategy, the house edge is -0.013% whereas eight decks give the casino an advantage of 0.57%

Dealer Standing Rules

If you are reading this, you probably already know that blackjack dealers make no decisions whatsoever when playing their hands because they need to abide by fixed rules. The house gains an edge over players by forcing them to act on their hand before the dealer acts on theirs. However, the rules the dealer follows also bear consideration because can vary, sometimes even from table to table in the very same casino.

The general consensus in the blackjack community is that tables where the dealers stand on all totals of 17 are the best ones to play at. You may come across blackjack tables whose dealers are required to hit soft totals of 17. This gives the casino an extra 0.22% edge over you. Dealers who hit soft 17s have a higher probability of improving their totals to 18, 19, 20, or 21 as opposed to their colleagues who stand on all 17s. Luckily, the dealers’ standing rules are clearly written on the baize of the tables, making it easy to figure out which games to avoid.

Payout Variations

We already talked about how blackjacks are the most valuable hands in this game. This is so because naturals pay out at higher odds than regular winning hands which only offer you even money. So instead of profiting from a hand that occurs more rarely, you are paid the same amount you would receive for any other winning total.

Any table with a reduction in the casino odds of blackjacks is not worth your time and especially, your money. Always shoot for the games where naturals return at a rate of 3 to 2 and your net profits amount to one and a half times your original stake. A blackjack payout of 6 to 5 is a no go.

Beware of variations like Blackjack Switch, for example, where the dealer pushes with you on totals of 22 instead of going bust. There is no need to clarify that the tables where the dealers take all ties are also to be avoided.

Pair Splitting and Doubling Rule Variations

Doubling down and splitting are two of the most important betting actions at the blackjack table for the simple reason they help you to extract more value in favorable situations. Casinos would often resort to rule modifications to prevent this from happening. You may come across tables where doubling down is restricted only to some totals, usually, 9, 10, and 11. This cripples your chances of increasing your profits, boosting the odds in favor of the house by 0.20%. Being able to double on any total gives you more flexibility in making the right decisions should you detect a favorable situation.

The same applies to splitting pairs of equal cards. It is in players’ best interest to be able to resplit to up to four hands. Just imagine the following hypothetical situation where you get a pair of aces, which you are advised to always split. If you are dealt one more ace on each split card, you have four hands starting with an ace and this improves your chances of obtaining a winning hand total. One such thing would occur on rare occasions, which is why it improves the house’s odds with 0.05% only but it still counts.

However, there are tables where the players are permitted to split pairs of ten-value cards only if they are of the same kind, two queens, for example. Remember these restrictions are detrimental to your long-term expected value.

The optimal rules would allow you to double down following a split. You pour more money into the action but this also increases the amounts you win. For instance, you start with a $10 bet and get dealt a pair of kings. You split those placing an additional wager of $10. You double down on both cards and receive aces on each king, winning a total of four hands for an overall profit of $50. This certainly is a satisfactory result for a wager that started off at $10.

Early vs. Late Surrender

The ability to be able to surrender potentially losing hands and forfeit half of your initial stake is of essential importance for your expected return. There is even a separate variation called Blackjack Surrender and it is the game of choice of many expert blackjack players. However, there is a clear distinction between early and late surrender, and it is the former that gives you better odds.

Simply put, early surrender enables you to admit defeat before your dealer has peeked for a natural. Needless to say, this saves you money. When late surrender is in force, you still can give up on your hand at the cost of half of your original wager, but you can do so only after the dealer has checked for a blackjack when showing an ace.

Of course, if the dealer indeed has a natural, you do not get to surrender anything because you lose right away. Hunt for tables with early surrender since this improves your edge by 0.39%. Let us warn you in advance, though – these variations are as rare as hen’s teeth, even more so if you play online.

Charlie Rules

The Charlie rules are great for blackjack players because they stipulate that once you draw a given number of cards without going bust, your hand is an automatic winner no matter what total the dealer obtains after you have acted. When playing live, you should feel free to inquire whether or not a Charlie rule applies at the table and if yes, for what number of cards. In randomly generated games, this is clearly written in the respective variations’ rules, which, it goes without saying, you must always go through in advance.

The reduction of the house edge in the presence of a Charlie rule is minuscule but as a blackjack player, you should learn to never look away from favorable rule variations. Casinos offer even-money payouts on seven-card Charlies which reduces the house advantage by 0.01%. On rare occasions, you will encounter tables with the six-card or five-card Charlies in force, which take away 0.16% and 1.46% from the house’s edge.

Why Rule Variations Affect Decision Making in Blackjack

Blackjack is one of the select few games where players can gain the upper hand through optimal decision making. The most common way to achieve this is either through advanced techniques like card counting or through using a basic strategy. The latter relies on the knowledge of your starting hand and the one card your dealer is showing. It helps you make optimal decisions under the assumption these three cards have already been dealt out from the shoe or deck and therefore, will not make another appearance before the reshuffle.

If you want to improve your chances of winning at blackjack, you should start with mastering basic strategy. That being said, you should not be too quick to memorize the first basic strategy chart you come across over the internet and follow it to the tee because the different rules also lead to variations in basic strategy. Some of the things you need to take into account include the rules on surrendering, splitting, and doubling, the deviations in dealers’ fixed rules, and the number of decks the game is played with.

Following a basic strategy designed for multiple-deck play at a single-deck blackjack table takes away some of your edge. Even a fraction of a percent matters in the long term so the best way to start would be to master basic strategy and then vary it in accordance with the rules that apply to the particular blackjack game you are playing. Once you put in a sufficient amount of practice, it would be much easier to vary your basic strategy depending on rule modifications.

Common Blackjack Variations at Online Casinos

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Now that we explained the most typical rule variations and why do they matter, we believe it is time to acquaint you with some of the most common blackjack variations you can find online or offline. Some of these improve your odds of winning, others reduce them but all are equally enticing.

Atlantic City Blackjack

When the first casinos in Atlantic City opened doors, they attracted the action of thousands of advantage players with the flexible rules at their blackjack tables. Card counters thrived in Atlantic City whose casinos did not persecute them as severely as their Sin City counterparts. Since gambling is regulated by the local New Jersey Casino Control Commission, all casinos in Atlantic City would offer the same rules at their blackjack tables, hence the name of this variation.

Atlantic City Blackjack is a multiple-deck game which uses eight full packs of 52 cards each. The dealers must stand on all totals of 17, soft or not, and peek for naturals on both aces and ten-value cards. Doubling down is possible on all totals, with players having the option to split to a total of four hands. One card is dealt on split aces and you have the option to double down after a pair is split. Naturals offer the standard payout of 3 to 2 but most importantly, you can surrender after the dealer has checked for a blackjack.

Vegas Strip Blackjack

Vegas Strip Blackjack ranks as one of the most favorable variations of 21. It typically plays with four full decks of cards. The objective of the player remains the same but some of the rules that distinguish it from other blackjack varieties are that the dealers are required to peek for naturals and must stand on soft totals of 17. A natural would usually offer the best payout of 3 to 2 although some venues at the Strip would host tables with a decreased payout of 6 to 5 on blackjack hands.

You can double down on any total your heart desires, even after you have split pairs. While we are on the topic of pairs, Vegas Strip Blackjack enables you to split to up to four hands, unless the pair consists of aces which cannot be resplit. You can receive only one card per split ace. You can split even pairs of ten-value cards that are unlike, like queen-jack, for example. This variation should not be mistaken for Vegas Downtown Blackjack which uses only two full decks and requires the dealer to hit soft totals of 17.

European Blackjack

European Blackjack dominates gambling establishments across the Old Continent and is easy to distinguish since it does not use hole cards. This is actually rather detrimental to players because it eliminates both the necessity of a peek rule and the insurance side bet. Both of these protect you against the dealer’s potential naturals, so you get the picture.

Unlike the previous two variations, European Blackjack plays with two full decks and the dealer initially gets only one face-up card. Once all participants in the coup have made their decisions on how to play their hands, the dealer draws more cards to complete theirs for a total that should be no less than 17.

Things tend to get downhill from this moment on, with very rigid doubling and splitting rules. Doubling down is possible but only on two-hand totals of 9, 10, and 11. Only one split per pair is allowed, but if you get dealt unlike ten-value cards you can forget about splitting. Blackjack awards you a payout of 3 to 2.

Double Exposure

Double Exposure appeared for the first time in Sin City’s Vegas World casino back in October 1979. The game was originally named Zweikartenspiel but everyone called it Double Exposure. The name caught up and this is how the game is known to this day. You have probably guessed where the name originated from – in this variation the dealer has both their cards exposed, which helps with decision making and is especially great for advantage players.

This may come off as a major surprise but Double Exposure is actually one of the variations to give the house the biggest edge in blackjack. The rules have been modified unfavorably, of course, as a means of counterbalancing the edge you get by seeing both cards of the dealer. The games utilizes six regular decks and the dealer takes all ties with the exception of those with naturals, in which case you two would push. Double after splitting is out of the question at these tables and you have the option to split a single time only. But it actually gets worse – you receive even money for your naturals.

Perfect Pairs

Blackjack Expected Value Table

Perfect Pairs is one of those blackjack variations you must try at least once in a lifetime, especially if you are seeking to profit from your side bets. The rules coincide with those in classic blackjack, as in fact the only difference here is the option to place a side wager on the proposition that your starting hand will consist of specific pairs. The more “perfect” the pair is, the bigger the payout you are entitled to. Do have in mind the house holds a ghastly advantage on these side bets that reaches 11% so you only stand a chance of profiting from those if you are counting cards or shuffle tracking.

Other than that, the game is usually played with four decks but the number may vary. Doubling down is permitted on all totals but on the downside, you are prohibited from splitting pairs consisting of aces. When a side bet is made, the dealer would pay out if it wins at the very start of the coup. There are three pairs that pay when a side bet is in place. Mixed pairs are of the smallest value and are likely to occur more often so they pay out 5 to 1. Colored pairs are rarer and return a payout of 10 to 1 whereas the perfect pairs (two suited cards of equal numerical value) offer the highest payout of 30 to 1.

Pontoon

Pontoon is easily one of the most fascinating blackjack variations out there. We will explain about the variation that plays in accordance with the British rules, where no cards are removed from the deck.

Here one full deck is normally in use. The betting actions are largely the same as those in classic blackjack but are given different names. You “stick” to your original hand total which means to decline additional cards. Requesting more cards is called “twisting”. Also, you can pay extra to draw more cards to improve four-card totals, with the option to buy up to three times but never after twisting. In Pontoon, the players are required to twist until they obtain a total of 15 or above.

One of the biggest allures of the game is the increased payout of 2 to 1 for naturals, which are pretty much the same as blackjacks but are called pontoons in this instance. Do not be too quick to rejoice, however, since here no hole cards are in play and the dealer receives both their cards facing down. Respectively, there is no way for you to insure your hands against pontoons.

The second best hand in Pontoon is the five-card trick which is pretty much a five-card Charlie with a fancy name that pays out 2 to 1. Next in line is the regular 21 consisting of three or four cards giving you this total for an even-money payout. In you break 21, you bust, similarly to regular blackjack. Note that here the dealer takes all ties, including those with pontoons.

Card Values Blackjack

All Blackjack Variations

Blackjack Games with Progressive Jackpots

More and more players are turning to online blackjack and the reason is not only to avoid heat on behalf of landbased casino personnel. They also do it because online they have the wonderful opportunity to play progressive blackjack variations. The more players wager on the progressive variation, the higher the jackpot becomes. Certain conditions must be met to become eligible for winning the pot, though, starting with the optional side bet you need to make. This is like an ante that is immediately added to the pools.

In one of the most common progressive variations, the one designed by Microgaming, you are awarded additional payouts for hands consisting of sevens, with cards of the same suits offering you some of the largest prizes. However, the largest prize of all is the progressive pot which is awarded for obtaining hands consisting of three sevens of diamonds.

Expected Value Poker Formula

To conclude it all, we would like to warn you that the house edge on progressive games is typically increased to counterbalance their massive winning potential, so the pot would have to escalate to a specific amount before one such game can give you a positive expected value.