Blackjack - Blackjack Variants

Yes, however the edge would actually be less for the basic strategy player in a live casino. This is because in a live casino the dealer will generally deal until a certain point is reached, finish that hand, and then reshuffle. If the deck is rich in small cards (good for the dealer) when the cut card or shuffle point is reached then more cards are likely to be dealt than if the deck were rich in big cards at the shuffle point (good for the player). The effect over thousands of hands is that a disproportionately high number of small cards are dealt which is directly related to a lower player return on investment. The effect is not huge but it is mathematically better to play with the same rules at an online casino as opposed to a physical casino.

For more on this topic, please see my blackjack appendix 10 on the cut-card effect.

For the benefit of others, let me explain that in European blackjack the dealer does not check if he has a blackjack until all players have finished playing their hands. If the dealer does have a blackjack and a player doubled or split, then the player will lose his entire bet. In the United States, the player can lose no more than the original bet if the dealer has blackjack. As you pointed out, online casinos that use Microgaming software follow the European rule. However, Microgaming casinos also play a single-deck game and let you draw to split aces which is unlike the European rules. To make a long story short, please see my European basic strategy.

My blackjack appendix 6 has a full strategy for early surrender.

The house edge in this game is 0.51%.

I'm going to assume that eight decks are used and that the bonuses are not applicable if the dealer has a blackjack. Using the Blackjack Count Analzyer I get a player advantage of 1.4% with a $5 bet. Unfortunately, this advantage is not available at greater bet sizes as the comparable benefit of the bonuses decreases and the additional fee for bets of $25 or over. With a $24 bet the house edge is 1.4%, and with a $25 bet it is 3.3%. This certainly is a very interesting game. If you play it let me know how you do.

I have actually seen these rules when I went to Helsinki in 1986. Without a doubt, the worst blackjack rules I have ever seen.

To answer your question, my blackjack house edge calculator says the house edge is 0.54%, before considering the rule that ties lose on 17-20. My list of rule variations says the effect of losing on 17-20 ties is 8.38% in the house's favor. So, the overall house edge would be 8.92% (ouch!).

Dealing to the bottom of the deck would not help the basic strategy player but greatly benefits the counter. There would be no changes to the basic strategy. However, this game may be of interest to card counters. Vegas World (now the Stratosphere) in Las Vegas used to have such a game but I don't think card counters ever took it seriously because of other adverse rules like a blackjack only paying even money.

Please see my page on rummy, which is the blackjack variant popular in Costa Rica.

Since you asked I added a blackjack strategy for European blackjack to my site. I also discussed this topic in one of my recent newsletters.

According to my blackjack house edge calculator, the house edge before the 6-card Charlie rule and the 3-2 on blackjack after splitting, is 0.34% with perfect strategy.

My list of rule variations says that the 6-card Charlie rule is worth 0.16%, and a 3-2 paying blackjack after splitting aces is worth 0.19%. It still doesn't pay to split tens. So, the overall house edge is 0.34% - 0.16% - 0.19% = -0.01%. In other words, a player advantage of 0.01%.

Assuming six decks, and the dealer hits on soft 17, if the dealer is forced to play out every hand them my blackjack appendix 2B says the probability of the dealer busting is 28.58%. However, in a head-to-head game where the dealer doesn't bother to draw cards if the player has a blackjack or busts first, then my blackjack appendix 4 says the probability of busting is 24.36%.

Yes, I've seen that bet in Tunica. I address it in my blackjack appendix 8. I agree that side bet would seem very countable.

At the time you asked this they still paid 3-2 on blackjacks. Before considering the rule about doubling on 3 or 4 cards, and the six-card Charlie, the my blackjack house edge calculator says the house edge is 0.50%. My list of rule variations says that doubling on 3 or 4 cards is worth 0.23%, and the six-card Charlie rule is worth 0.16%. So, the overall house edge is 0.50% - 0.23% - 0.16% = 0.11%.

However, since you wrote they changed their rules to pay 2 to 1 on suited blackjacks and 1 to 1 on all other blackjacks. This increases the house edge by 1.13%, to 1.24%. They still have the sign stating it is the "World's most liberal blackjack," which is patently untrue, if you interpret the word "liberal" to mean lowest house edge.

According to Basic Blackjack by Stanford Wong, this rule adds 0.2% to the player's expected return. Wong also indicates some strategy deviations under this rule on pages 60-61.

Since you wrote I analyzed one version of California no-bust blackjack. However, that set of rules has since disappeared. It seems every casino in the L.A. area has their own rules and it is hard to keep up. With the fee to play, it is a lousy bet anyway, unless you're banking. Sorry I can't be of more help.

I’ve seen these things at the Las Vegas club, only they cut off two decks out of six I believe. It is a deceptive way to appear to be using fewer decks than are actually involved. Mathematically speaking the house edge would be the same as for the total number of decks in the shuffle machine. Penetration does not matter for the non-card counter. Thus it would not matter whether a machine or a human being cut off two decks from a six-deck shoe, the cards were taken from a six-deck shoe either way.

For those who don’t know what you’re talking about, Triple Action Blackjack is a blackjack variant in which the dealer plays out three different hands, all starting with the same up card. The player makes three bets and his one hand is played against the three dealer hands individually. The strategy for this game is exactly the same as conventional blackjack.

(1) It depends what happens if the dealer does have a blackjack. If the player is guaranteed to lose no more than the original wager then it doesn’t matter if the dealer takes a second card or not. If the player stands to lose the total amount bet after doubling or splitting and the dealer gets a blackjack then that works to the dealer’s advantage. (2) I don’t have to simulate this because the number of players makes no difference.

The reason you double with 2-4 cards and hit with 5 or more is because a hand of 6-cards automatically wins, and a 5 card total of 21 pays 2-1. However these incentives do not apply after doubling. Once the player already has four cards there is a stronger incentive to hit as opposed to double. I nice count strategy has been introduced in the green chip section at bj21.com.

Yes, this is a sucker bet, especially with a 10 showing. This is equivalent to taking insurance. The casinos here always offer "even money" in this situation and both dealer and other players will treat you like a fool if you decline it. However the expected value of a blackjack when the dealer has an ace showing is 1.04 units, better than the 1.00 units you’ll get by taking the even money. So unless you’re a card counter and know the remaining deck to be 10-rich then always decline even money. I’m glad my basic strategy helped you win.

There is a common misconception that a continuous shuffler is equivalent mathematically to an infinite deck game. It is not. If the first card dealt is an ace, for example, the probability that second card is an ace is slightly less than 1/13, because one ace has already been removed from the shoe. As I have explained in great detail in my blackjack appendix 10 a continuous shuffler actually lowers the house edge marginally compared to a cut card game. However the dealer never stops to shuffle so you are being exposed to more hands per hour, so expect to lose more per hour. I doubt very much they allow early surrender at the Mohegan Sun, if they did the player would have an edge of 0.28%. Assuming you really meant late surrender the house edge is coincidentally 0.28%, according to Blackjack Edge software.

This increases the house edge by 1.39%! This is by far the worst blackjack game in Vegas.

Everybody is asking me this. At this time I haven’t worked out the odds yet. Until I do you’re on your own. Since this web site isn’t making me much money I have to give priority to paying consulting work.

This is a popular new gimmick here in Vegas. Many casinos here have prominent signs saying "Single Deck" blackjack. However on a much smaller sign it says "Blackjack pays 6 to 5." Aside from the 6-5 rule the house edge would be 0.05%. However the 6-5 on blackjacks costs the player an additional 1.39%, for a total house edge of 1.44%. This is by far the worst blackjack game in city and I urge you to avoid it.

Mathematically speaking this is the same as playing from an eight deck game. Players have been known to be fooled, incorrectly thinking these are double deck games. For card counting purposes the penetration is 50 out of 416, or 12.02%.

The strategy for Multiple Action Blackjack is the same as regular blackjack. By standing on 16 against an 8 your chances of a total loss are less. However the safe thing to do is not always the right thing to do. Hitting will result in a greater chance of winning 2 or all 3 hands. Think of it as playing the same hand three times in a row. What is right for one hand is right for three hands, or any number.

Thank you for the kind words. Much like multi-play video poker the house edge is the same for multiple action blackjack as regular blackjack, assuming the same rules. It is true that if the player has blackjack he wins on all three hands. However if the player has a 16 he has to play it on all three hands. Overall everything balances out.

I have seen this rule at the casino in Montreal as well. Yes, this is a good opportunity for player collusion, where the seated player bets small and makes sacrificial plays for the big bettor in back. Basic Blackjack by Stanford Wong goes into great depth on this topic. There are lots of changes to the splitting strategy, for example the seated player should always split twos and then the back bettor should play both hands against a 4 to 6, otherwise play only one. Using Wong’s full strategy reduces the house edge by 0.2%.

The player should be more aggressive hitting in Blackjack Switch because a dealer 22 results in a push. Much of the value in standing in regular blackjack is realized when the dealer busts. In Blackjack Switch many of those wins are turned into a push, making hitting a better play in comparison.

I’ve never heard of this rule before. According to my analysis, being allowed to double after splitting aces decreases the house edge by 0.08%. However not allowing resplitting any pair, compared to resplitting to four hands, increases the house edge by 0.06%. So the combination of the two rules decreases the house edge by 0.02%. Following is the basic strategy of when to double after splitting aces, assuming 4 to 8 decks and the dealer stands on soft 17:

Soft 12 to soft 16: double against anything
Soft 17: double against 2 to 9
Soft 18: double against 3 to 6
Soft 19 to 21: never double

Using a random number generator _is_ the same as working like a slot machine. Online blackjack, slot machines, and video blackjack all use random number generators.

It is a Nevada state law that an electronic game with representations of cards or dice must be based on fair odds. So the game should be fair with odds the same as in a hand dealt game having the same rules.

What I meant was that images of cards on the screen had to be statistically fair. For example if you took a tally of each card observed in the initial hand of video poker or video blackjack you would see the distribution approaching a flat line over time, much as you would in a hand dealt game. However there is no law that the standard rules of blackjack must be followed. The machine can legally offer horrible rules like the player losing on ties. The only caveat is that the theoretical return must be at least 75%.

Here it is. I assumed the dealer stands on soft 17 and double after a split is allowed. I assumed an infinite number of decks for the sake of simplicity. Any differences between this strategy and 8 or fewer decks would be very borderline. The house edge assuming infinite decks is 9.36%.

This is a great rule! Only losing one-third of your $3 bet by surrendering adds 2.25% to your expected return. You didn’t tell me the other rules but if we assume a house edge of 0.5% before the surrender rule then the player edge afterward would be 1.75%. Here are the hands you should surrender on based on a six deck game (hit or stand on soft 17 doesn’t matter).

• Player 6 against 10.
• Player 12 or 13 against dealer 9, 10, ace.
• Player 14 or 17 against dealer 8, 9, 10, or ace.
• Player 15 or 16 against dealer 7, 8, 9, 10, or ace.

The only hand you would normally split that favors surrendering is 8,8 against a 10. This advice only holds true for a $3 bet. The value of surrendering diminishes as the odd-numbered bet gets higher.

Yes! If you count sevens as -12 and all other cards as +1 then the odds on the side bet swing to the player’s advantage with a true count (running count divided by remaining decks) of 5 or greater. According to my simulations in six-deck game with no three-card guarantee and 75% penetration the true count is 5 or greater 23.2% of the time and the player advantage at these times averages 27.3%. In the game with a three-card guarantee the average advantage goes up to 29.1%.

Assuming you are right that they don’t take your double/split bet on a dealer blackjack then make no changes to the U.S. basic strategy.

A new game trial period permit was required. This is opposed to a "variation" permit, which is less expensive. For a new game the cost is $3000, I had to fill out lots of forms, including an employment and residence history going back 20 years. The waiting time was six months, which was shorter than what I was expecting.

My blackjack appendix 7 can be used to approximate the answer to this question. Adding the ace would favor the player by 0.005816/24 = 0.00024. Removing a two would favor the player by 0.003875/24 = 0.000161. So the total effect would be 0.000404, or a decrease in the house edge of 0.04%.

No. If splitting is the right play you should do it every time, and if not never. So this rule is moot if you play properly.

Thanks for the kind words. You are right, if the expected value is less than -1 then you should opt to take the double down surrender. As you said if the expected value for standing in my blackjack appendix 9 is less than -0.5 you should surrender, because you are betting two units. I would only add to your strategy that if the dealer hits a soft 17 then you should also surrender 17 against an ace.

Thanks for playing it. Yes, Ties Win Blackjack was a good choice for this promotion. The probability of a full win is 43.314%, a half win is 8.75%, and a loss is 47.936%. So the probability of any win is 52.064%. The probability of five consecutive wins is 0.52064⁵ = 3.825%. Flat betting this results in an extra 3.825% of return for the player. The house edge normally is 0.247%, so the player advantage under this promotion would be 3.5785%. However I find no mention of this promotion on the casino web site and given my usual 2-3 week delay to answer e-mail it is probably over.

For Las Vegas why not use my own blackjack survey at the Wizard of Vegas. For the rest of the United States and Canada, I highly recommend Stanford Wong's Current Blackjack News. That will tell you the exact blackjack rules at almost every casino in both countries.

I’ve actually seen those rules when I went to Helsinki in 1986. I was only 20 at the time and I’m embarrassed to say I actually played the game, because I still underage in the U.S., and was still years away from becoming the Wizard. In fact it would have been the first legal game of blackjack I ever played. Meanwhile there was a single-zero roulette table right next to it.

I assume the dealer stands on soft 17 in both cases. It is my understanding that double after a split is allowed in Sweden but not Finland. Assuming that I get a house edge of 5.99% in Sweden and 8.93% in Finland. Here are the basic strategy charts.

And I thought the rules in Finland were bad. I’m assuming that ties lose. It wouldn’t make any sense for ties to push, which would be better than a win. So if ties lose, wins lose half, and blackjacks pay 11 to 2 the house edge would be 51%!

Isn’t there a commandment in the bible about stealing? I show the house edge of that game is 9.3% (ouch!). Here is the appropriate basic strategy for this variation of Ties Lose Blackjack. See column #110 for the version where the player can double on soft hands.

Thanks. The probability of getting at least one joker in two cards dealt from a 314-card shoe is 1-(combin(312,2)/combin(314,2)) = 1.27%. So the probability is 1.27% of turning an average hand into an automatic winner. If we assume an average hand has an expected value of −0.005 then the value of the first rule is 0.0127*(1-(-0.005)) = 1.28%. You can see from my blackjack section that the five-card Charlie rule is worth 1.46%. Assuming the cards are shuffled after every hand, or you are forced to flat bet, then given the choice as a player I would pick the five-card Charlie rule. However, the joker rule would be very easy to exploit further. The greater the ratio of jokers to cards in the shoe the more you should bet. With at least 50% deck penetration, this should easily be enough to make it the better rule.

Wow! According to my calculations this results in a player advantage of 6.4%. I’m assuming that the rule applies after doubling and splitting. Here is the basic strategy for that rule.

The reason is players make more mistakes in Blackjack Switch.

My blackjack appendix 4 shows the probability of a net win, loss, and draw in blackjack are 40.59%, 42.69%, and 12.44% respectively, assuming Atlantic City rules. The probability of a win, not counting ties is 40.59%/(40.59%+46.97%) = 46.36%. The probability of three consecutive wins, skipping ties, is 0.4636³ = 9.96%. Assuming six decks, blackjack paying 2 to 1 is worth an extra 0.02267. So this gives the player 0.0996*0.02267 = 0.002258. The house edge is usually higher than that, but it is a nice reduction. All this assumes you are flat betting. If you could bet more on the "on fire" hands you could destroy them with a house edge of 1.5% to 2.0%, depending on the specific rules.

First the dealer wins ties and now this. Finland has got to be the world leader for unusual and lousy blackjack rules. Here is your basic strategy.

Assuming six decks, no dealer hole card, dealer stands on soft 17, no surrender, double after split allowed, and resplitting aces allowed, I get a house edge of 1.86%.

For the benefit of other readers, the blackjack rules are as follows.

• 8 decks
• Dealer stands on soft 17
• Dealer always peeks for blackjack
• Double on hard 8 to 11 only
• Double after split allowed
• Shuffle after every hand
• Aces may not be split. All other matching ranks may be split only once.
• Suited blackjack pays 2 to 1
• A 5-card 21 automatically wins and pays 2 to 1

I get a house edge of 0.02% under these rules. Following is the basic strategy.

Regarding the other games, the 2.75% commission on the banker bet in baccarat results in a house edge of 0.03%. The roulette and video poker have zero house edge.

The bet limits are £5-£50 in blackjack, baccarat, and roulette, and the coinage is £1 in video poker, with a max bet of five coins.

Thank you for this information. It is good to know there is at least one normal blackjack game in Finland.

In a six-deck shoe, the probability of such a blackjack is 2 × (6/312) × (12/311) = 0.001484. I’m going to assume that if the dealer has a blackjack also, then the hand is a push. That said, the probability of the dealer not getting blackjack, given that the player did, is 1 - 2 × (23/310) × (95/309) = 0.954379. So the probability of winning such a blackjack is 0.001484 × 0.954379 = 0.001416. The value of an additional 8.5 units whenever that happened is worth 8.5* 0.001416 = 1.2039%. Assuming otherwise liberal Vegas Strip rules, with a house edge of 0.28%, the player edge with the 10 to 1 rule would be 0.92%.

The house edge of this game is 1.30% or 1.33%, as shown in my survey of Las Vegas blackjack rules, depending on whether the number of decks is five or eight. The odds are better in ANY game where blackjack pays 3 to 2. If you were to play this game, which you shouldn’t, you should still always stand on blackjack. Personally, I think the "World’s Most Liberal Blackjack" claim on the marquee is false advertising.

For the benefit of other readers, the full set of rules is:

• Single deck.
• Dealer stands on soft 17.
• Winning blackjack pays even money.
• Player may double any first two cards.
• No double after split.
• Player may resplit to four hands, including aces.
• No draw to split aces.
• No surrender.
• Six-card Charlie (player unbusted six cards automatically wins).
• Cards shuffled after every hand.
• If game runs out of cards, all unbusted player hands automatically win.

The house edge using total-dependent basic strategy is 2.13%. I ran a 7-player simulation, using total-dependent basic strategy, and the average number of cards used per round was 21.65, with a standard deviation of 2.72. In almost 190 million rounds played, the most cards ever used was 42, which happened 7 times.

It is my educated opinion that even with computer perfect composition-dependent strategy the player would still realistically never see the last card. You could cut down the house edge much more using composition-dependent strategy, according to all the cards seen as you go along. However bucking 2.13% house edge to start with, you’ll never get anywhere near break-even, regardless of how hard you try.

Yes, you do. I’m told by Shufflemaster that to meet the definition of a slot machine, one player’s actions can not affect the other players, as is the case in live blackjack. To get around this law, each player and the dealer are dealt cards from a unique six-deck shoe. So, you are in control of your own fate, but not that of the other players or the dealer. I understand that the game is programmed with six-deck shoes. According to my simulations, using separate shoes for the player and dealer adds 0.06% to the house edge.

That is not true about pushing or losing more than half the time. From my blackjack appendix 2 you can see that when the dealer has a 20 the possible outcomes are as follows, after the dealer peeks for blackjack, and based on six decks.

Dealer gets 17-19 or busts: 59.4%
Dealer gets 20: 36.8%
Dealer gets 21: 3.8%

So, the player will push or lose only 40.6% of the time. The value of a 20 against a dealer 10 is prob(win)-prob(loss) = 59.4% - 3.8% = 55.6%. That is more than the 50% you get by invoking the automatic half win, so you should decline the option. I address this option in my blackjack appendix 8, under the title casino surrender.

For the same reason, you should also decline “even money” when you have a blackjack against a dealer ace. In both cases two birds in the bush ARE worth more than a bird in hand.

If you are wagering $5, not including the 50-cent fee, that increases the house edge by 9.09%! The general formula for the increase is c/(b+c), where b=bet, and c=commission. Assuming 60 hands an hour, the commission will cost you $30 an hour (ouch!).

For the benefit of other readers, the Oklahoma casinos are much like those in the Los Angeles area, where players take turns banking. If you can afford the risk of paying off all other wagers at the table, then by all means, do so. When it isn’t your turn to bank, don’t bet.

If we assume 70 hands per hour, a house edge of 0.64%, and a $5 bet, the cost of playing before the fee would be $5 × 70 × 0.0064 = $2.24. That $20 fee is pretty high in comparison. Considering you would bet $350 per hour, the total expected loss would be $22.24, for a house edge of $22.24/$350 = 6.35% (ouch!).

My blackjack appendix 9 is useful to answer questions like this. For example, assuming six decks and the dealer hits a soft 17, the expected value of doubling on a blackjack against a dealer 5 is 0.622136 and against a 6 is 0.667063. Both are much less than 1.2, costing over half a bet. Even if a blackjack only pays even money, as is unfortunately sometimes the case now, you should stand on the blackjack. The only game where you should not stand on a blackjack is in Triple Up 21, where the player should triple on a blackjack against a dealer 6.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

A reader of my Wizard of Vegas site says the following changes should be made, relative to the standard multi-deck strategy where the dealer hits a soft 17:

• Hit soft 13 vs. 5 or 6
• Hit 2-card soft 15 vs. 4
• Hit 3,3 vs. 2

The reason for hitting the soft hands is you might get a better soft double after the hit. The value of hitting the threes is higher under this rule, because getting an ace would be a good 3-card double.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

According to the September 2010 Current Blackjack Newsletter, there were 2099 blackjack tables in Las Vegas. The following table shows how many were the biggest four variations.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

I’m going to assume six decks, dealer hits a soft 17, double after split, surrender, and re-splitting aces. If double for less is not allowed then I get a player edge of 4.9%. Here is that correct strategy. Obviously, this strategy may set off some red flags.

If double for less is allowed, then I get a maximum player edge of 9.4% with the following strategy. When doubling for less, bet as little extra as possible, preferably just one penny. My 9.4% figure assumes a tiny double down wager. In reality, most casinos require doubling with at least the table minimum.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.