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Home • What's New • Advice & Strategy • Ask the Wizard • Gambling online • Play for Fun |
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I absolutely love your site. I enjoy the strategies and probability discussions as much as, or more than, the actual gambling! I was playing six-deck Blackjack in a St. Louis casino recently. After playing a shoe, the cards were returned to the auto shuffler, which indicated a card was missing. The dealer proceeded to deal the next shoe while the floor person inspected the returned set of cards. Upon completion of this shoe, the missing card from the previous shoe (a king) was found in the un-dealt portion of the second shoe. Assuming this King was the bottom card and was left in the shuffler, it would have been in play in this first shoe (the cut was in rear portion of the deck). How much of an additional advantage did the house gain on me with this mistake? — Justin from St. Louis, MO
Thank you for the kind words. I'm going to assume the dealer hits a soft 17, and double after a split is allowed. According to table D17 in Blackjack Attack by Don Schlesinger, removing one ten per deck increases the house edge by 0.5512%. Dividing that by six, for the six-deck game, the effect is an increase in house edge of 0.09%. May 13, 2008
Thank you for your detailed site. In blackjack appendix #9 you state the expected value for the game and the expected value for each play. I would expect the expected value for the game would be the sum of Ei × Pi where Ei is the maximum expected value for the ith play (stand/hit/double/split) and Pi is the probability for the ith play. When I try this calculation I get a different result. For example, six decks, dealer hits on soft 17, and player may not double after split I get 0.04518876.
— Frank from San Diego Those tables assume the dealer does not have a blackjack. This is because by the time it is the player's turn to act, the dealer has already peeked for blackjack. Making correct double and split decisions should be based on the conditional expected value, given the dealer does not have a blackjack. Otherwise, the player would be overly timid about doubling or splitting against a ten or ace. Adding up the dot product of probabilities and expected values will give an incorrect result, because there is no loss represented for a dealer blackjack. To get the house edge of the overall game you should subtract the expected loss when the dealer has a blackjack. With six decks, the probability of a dealer blackjack is the number of tens, times number of aces, divided by the number of two-card combinations, which is (6×16)×(6×4)/combin(312,2) = 0.047489. However, the player will only lose when he does not have a blackjack. The probability of a player blackjack, given that the dealer already has one, is (6×16-1)×(6×4-1)/combin(310,2) = 0.045621. So, the probability of the player losing to a dealer blackjack is 0.047489 × (1-0.045621) = 0.045323. You should subtract this number from your dot product above: 0.04518876 - 0.045323 = -0.00615144. Thus, the house edge under the rules stated in the appendix is 0.62%. April 21, 2008
I was reading the Blackjack entry on Wikipedia, and it said that when blackjack was not that popular, casinos added a bonus payout of 10 to 1 for the ace of spades and any black jack, hence the name. It goes on to say that the bonus was quickly removed, but the name stuck. I was wondering what the house edge was with a 10-1 payout for that hand. — Scott F. from Philadelphia, PA
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%. June 19, 2007
Playing blackjack on a continuous shuffling 5-deck system, are the odds of winning different than playing the dealer with 1 deck or 2 decks? – Tom from Aurora, CO
For the beneit of other readers, my blackjack appendix 10 explains, the house edge in a five-deck game is 0.028% less if a continuous shuffler is used, as opposed to a hand shuffle. The difference between five decks and two decks, all other rules being equal, is 0.18%. So the two-deck game without a shuffler would be much better. Let's compare a 5-deck continuous shuffler game to a 4-deck hand shuffled game. As my blackjack calculator show difference in house edge between four decks and five decks is 0.0329%. So the benefit of a continuous shuffler is worth less than removing a single deck.February 7, 2007
On your web page, you state that continuous shuffling machines reduce the house edge in Blackjack. Although I have no doubt that you have proven this mathematically, this result appears to be in conflict with the "Floating Advantage" concept described in Chapter 6 of Don Schlesinger's
Blackjack Attack. Basically, the "Floating Advantage" concept appears to indicate that the house edge decreases as more decks are removed from play (regardless of the true count). For me, it is difficult to reconcile the fact that the house edge can decrease when cards are immediately replenished (when CSMs are used) and also when cards are utilized and not replenished (when shoes are used). Can you comment on this observation? – Mark from Mississauga I hope you're happy; I spent two days running simulations to answer this one. For the benefit of others, let me briefly summarize both arguments. The Cut-Card Effect states the house edge is less in a continuously shuffled game, as opposed to a cut-card game, all other things being equal. The "Floating Advantage" concept states that for the card counter the odds get better the deeper into the deck or shoe the dealer gets. According to Stanford Wong, "...after we have counted the deck down to where n decks are left, the edge with a count of zero is about the same as if we had started with n decks." - Blackjack Attack, third edition, page 71. So, for example, the house edge in a six-deck with one deck left, at a count of zero, has about the same house edge as a single-deck game with the same rules.
Unfortunately the Floating Advantage does not benefit non-counters. While they will benefit, unknowingly, at close to neutral true counts, they will do worse at extremely high and low counts. According to Schlesinger, "Seems that, at the one-deck level, extremely high counts produce less edge than expected for the basic strategist (many pushes) and the extreme negative counts were found to be even more unfavorable than previously thought (doubles, splits, and stands tend to be disastrous)." - Blackjack Attack, third edition, page 70. As I understand it, the reason the counter benefits from the Floating Advantage, even if he may not know about it, is that he bets more when the Floating Advantage works to his advantage, and less when it doesn't. For the non-counter, who doesn't know when the Floating Advantage is strongest, the pros and cons exactly cancel each other out. In conclusion, both the Cut-Card Effect and Floating Advantage are distinct topics and do not contradict each other. To compare them is to compare apples and oranges. For more information please read chapter 6 in Blackjack Attack by Don Schlesinger. February 7, 2007
What is the house edge in video blackjack? - Mickey C. from Reno
It depends on the particular rules, but it is usually high because of a common rule that blackjack pays only even money. I checked at the Suncoast and they have the following rules: one deck, dealer stands on soft 17, blackjack pays even money, late surrender allowed, player may only double on 10 or 11, double after split not allowed, split aces get one card each, only one split allowed, six card Charlie, dealer must stop with six cards. The house edge of this game is 2.39%.
November 10, 2006
How much would it increase the house edge if the player took insurance every time in blackjack? – RJM
The dealer will have an ace up 1/13 of the time. The house edge on insurance is 7.395% in a six-deck game, on average. However, this is applied to half a bet size. So the expected loss of always taking insurance is (1/13) × 7.395% × 0.5 = -0.00284. So the house edge would go up by 0.284%.
September 22, 2006
What effect does the 'rule of 45' have on the house edge, if any. I understand the rule of 45 to be that you stand on 16 vs. 10 if your cards include either a four or a five. Obviously this would be pointless if counting, as the count would be a better indicator of when to stand on 16. - Erik B. from Toronto, Ontario
It is correct that in general if your 16 has at least one 4 or 5 in it then the odds genrerally favor standing. This is obviously because a 4 or 5 will give you a 20 or 21, and there is at least one less of them in the remaining deck. 16 against a 10 is so borderline that this effect can make the difference in the play. In a two-deck game, I show following the rule of 45 lowers the house edge by 0.015%. In a six-deck game it only lower the house edge by 0.003%.
August 24, 2006
Love your site! I just ran across your detailed list of Las Vegas Blackjack tables and their edges, so I was wondering: Suppose that there two BJ tables, one with an edge of 0.2% with a table minimum of $10 and 0.4% with a table minimum of $5. Both tables have the same $0.02 loss per hand. Is there any advantage to choose one table over the other? – Milton from Santa Fe
Thanks. To answer this question you first have to ask yourself why you are gambling in the first place. If you are trying to lose as little as possible then you shouldn’t play at all. However, if you are playing for the fun of gambling then I would choose the $10 game with the 0.2% edge. The expected loss will be the same but you’ll get more of a fix with the larger wagers.
August 9, 2006
I deal blackjack at my church festival and I'd love to run a basic strategy scenario for our rules...
4 decks The last rule is what I call's "God's House Advantage" and is the one rule that obviously is not in any of the strategy generators I've found online. I'm convinced that the push loses rule might make hitting a 17 a basic strategy play in some cases. Best regards and keep up the great work. - Joe from Floral Park, NY 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. May 18, 2006
Congratulations on a great site. I totally understand your anger over the spread of 6 to 5 Blackjack payouts but am very curious as to why Americans seem to accept 00 Roulette without any argument. This Roulette is almost criminal and should be ranked along side Keno & Slots. - Andrew from Sydney
Thanks. You make a valid point. The house edge in 6 to 5 blackjack is 1.44% under the usual rules, while double zero roulette is 5.26%. That is 3.7 times as bad. However I have learned through the years that it is almost hopeless getting players to leave a game they like, regardless of how bad the house edge is. So the best I can do is advise them how to play their game of choice. For blackjack players there is still no shortage of 3 to 2 games out there. Playing 6 to 5 is giving the casino an extra 0.8% advantage for no reason at all. I also stress the importance of looking for single-zero roulette if you are a roulette player. So I see no inconsistency.
March 20, 2006
In a recent Ask the Wizard column, a reader wrote asking about a $2 video BJ game in North Carolina that pays $13 for a BJ and $1 for any other win (OW). What the reader did not understand is that the payouts are NOT 13:2 for BJ and 1:2 for OW... instead the payouts are 13 for 2 on BJ and 1 for 2 on OW. Like a slot or video poker machine, this machine takes your bet as soon as you hit the "Deal" button. Then, if you "win", it pays $13 for BJ or $1 for OW. In other words, the player actually loses money on any non-BJ win. Given these payouts, what is the EV for a single deck game? -- Dog
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%!
March 13, 2006
Love the site!!! Amazing! Now, according to your BJ House Edge Calculator with 6-deck, dealer stands on soft 17, double on any first two cards, late surrender, and resplit to four hands the house edge is 0.334%. Can you tell me why a similar calculator at a reputable source (QFit) gives a house edge under the same rules of 0.325%, or 0.009% lower? - Daryn from Santa Monica
Thanks for the compliments. There are several assumptions going into the calculation that may cause the small difference. For example are the cards shuffled after every hand or is a cut card used? Does the player use total dependent basic strategy or composition dependent basic strategy? Is rule interaction factored in, or is the calculator simply adding up the effect of each rule? My figures are based on a random simulation using total dependent basic strategy, both of which work against the player, which may be the reason I come in a little higher. It also may be due to an insufficient sample size in the random simulation. Despite all these factors I think the difference is still negligible: just one bet per 11,000 hands played.
Jan. 14, 2006
I deal a blackjack game for friends every now and then using only 2 decks. I was wondering what the best house edge is in regards to how many hands to deal to and splitting and doubling down rules. Thanks in advance. Hope you have the time to answer my question. If not I understand. -Nick from bronx ny
In my opinion the dealer should set the rules on the liberal side in home games. Screwing your friends with stingy rules is just not cool. If you use double decks I would recommend double on any first two cards, double after a split, and dealer stands on soft 17. Otherwise standard rules. That will result in a house edge of 0.19%. However player mistakes should give you much more than that.
Feb. 21, 2006
I play video blackjack using basic strategy at Harrah's Cherokee Casino in NC. They only have $2 machines that previously had paid the usual $3 on a blackjack (3:2) and $2 on a win. Now they have replaced these machines with ones that pay $13 on a blackjack but only $1 on a win. Have you ever heard of machines with these pay schedules? If so do you know how they compare to the normal 3:2 machines? If it helps the dealer stands on a soft 17 and doubling is not allowed after a split. Thanks - have a happy new year and thanks for providing much very helpful information! - Sam from Atlanta You're welcome. This is an interesting game. Assuming all wins except blackjack pay 1 to 2, and blackjacks pay 13 to 2 I get a player advantage of 0.7%, assuming six decks. Here is a basic strategy for that game. Feb. 1, 2006
My local casino has a rule where if the initial 2 cards, for example a pair of 4s, are split to form 2 hands and then the next card is another 4, if the player opts not to split again he will not be given the option to split should a 4 come out as the next card on the second hand of his initial split. My question is: does this rule give the house an advantage and if so, how? - Ken from Tinian Island
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.
Dec. 6, 2005
What is the added house edge in blackjack if players are never allowed to double nor split? No splitting costs the player 0.58%. I have a Blackjack question that I did not see already answered on your site. How would the house edge change if the player always got a glimpse of the dealer's hole card and changed his strategy accordingly? According to my calculations this would give the player about an 8.8% advantage under optimal strategy. The optimal strategy is the same as that of double exposure in most cases. However if you think the dealer will expose his hole card again I would recommend not making it obvious that you know and not make plays that normally look ridiculous (like hitting a 19 against a 20). Jan. 23, 2005 In Boss Media single-deck blackjack the player has the edge? What's the catch? So I could go to one of the online casinos and play it using optimal strategy AND win over the long run? What am I missing? I'm sure they still make money on the game due to player mistakes. There are also forms of video poker here in Vegas that return over 100% with optimal strategy. Again, the casino counts on player mistakes to bring them under 100%. With most games that do pay over 100% the edge is so small it isn't worth ones time to play the game as a living. However if you are going to play anyway you may as well get the best odds possible. Nov. 19, 2004 Why is it better odds for the casino to hit on a soft 17? It seems they would be more likely to bust and hence have worse odds. It is true the casino busts more often if the dealer hits a soft 17. However the dealer also gets fewer seventeens, which is not a very good hand. It is to the dealer's advantage to hit a soft 17 for the same reason the player should always hit or double on a soft 17. A 17 is a lousy hand, and whether the player or the dealer hitting a soft 17 offers two chances to improve upon it. Sept. 30, 2004 Hello Wizard, great site with a wealth of information! My question is this: How much does the house advantage increase when they change the rule from double after split allowed on anything, into Double after split allowed except on aces? I wanted to make sure this wasn't a huge house advantage increase like the 6-5 blackjack payout change. Thanks for the kind words. I think I answered this before somewhere but being allowed to double on split aces gives the player an extra 0.08% in expected value. Nowhere near the 1.39% that the player loses by the 6 to 5 on a blackjack. July 4, 2004 While in northern Michigan I came across a new blackjack rule on splitting aces. Instead of resplitting you still only receive one card but you may double on it if you like. Can you tell me the effect of this rule? 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: You have the greatest gambling site in the world!! If I follow the basic strategy chart intended for "shoe" games in a double deck game what percentage am I sacrificing? Or if I use the double deck strategy in a shoe game what am I losing? Thank you for the compliment. Assuming the dealer hits a soft 17 you are adding 0.012% to the house edge by playing 4-8 deck strategy in a two deck game. Playing double deck strategy in a 6 deck game costs 0.008%. To take this question further I wondered about a more extreme case of playing 4-8 deck strategy for the dealer standing on soft 17 in a single deck game where the dealer hits a soft 17. In this situation the incorrect basic strategy adds 0.038% to the house edge. May 22, 2004 I have reviewed your blackjack site and FAQ, and I have a question about your Blackjack House Edge Calculator. From your description of methodology: "The program played each hand according to the correct basic strategy for those rules without regard to composition dependent exceptions." Can you explain how you determined total-dependent strategy (e.g., that which maximizes expected value)? First, to those who don't know, composition dependent strategy considers each and ever card in the player's hand. Total dependent strategy only cares about the total, whether the hand is soft or hard, and whether it is a pair. So the basic strategy is total dependent. However the analysis of blackjack is generally composition dependent. The way get derive the basic strategy charts is to take every composition of an initial two card hand and weight the expected value of each play by the probability of the composition. Let's look at the case where the dealer stands on a soft 17 and the player has a 13 against a 2. The following table shows the composition dependent expected return of standing and hitting of all ways to compose a 2-card 13. The final column is the conditional probability of each compostion. Hello Wizard, When I use your calculator for BJ it shows a huge differential in house advantage between a single deck and Double deck. Would there be a difference in the double deck house advantage if the deck is cut in half? What would be the difference in the house advantage for any number of decks if you cut off a larger portion of the deck? The house edge for a double-deck game is the same regardless of how many decks they cut off. Many dealers incorrectly claim that a double deck game cut in half has the same odds as a single deck game. It does not. Unless you are counting the placement of the cut card makes no difference. Jan. 20, 2004 If the house edge in a shoe game of blackjack is "x" percent for the first hand after a shuffle, does the house edge also work out to be exactly "x" percent on average if you play through the entire shoe (assuming flat betting and basic strategy)? In a cut card game the answer is no. However in a game where the dealer dealt exactly x hands every shoe the answer would be yes. The reason is hard to explain. For more information please see my blackjack appendix 10. Sept. 26, 2003 How is the house advantage affected by "free Ace" coupons (promotional tools) used with a continuous shuffler? I have been asked this enough time to add a section about it. The short answer is that the coupon is worth just over half of its face value. Visit my blackjack appendix 14 for all the details. Nov. 19, 2003 I play at a local casino that offers a 6 deck, h17, DAS, DOA game. However, they pay 2-1 on a suited blackjack. How much does that reduce the house edge? How would you figure this out mathematically? The probability of a suited blackjack in a 6-deck game is number of suits * number of aces of given suit * number of tens of given suit / number of 2-card combinations out of 312 = 4*6*24/combin(312,2) = 576/48516 = 1.19%. I assume a blackjack tie is a push, so the probability of a suited blackjack, when the dealer does not have a blackjack is 1.13%. Getting an extra half unit 1.13% of the time cuts the house edge by 0.57%. In this case the house edge goes from 0.62% to 0.05%! Aug. 2003 Dear Wizard, Just a quick question, why does the house edge change for an insurance bet in blackjack depending on the number of decks used? Thanks, Rick. Because we already know an ace has been removed for the shoe. That leaves the rest of the shoe slightly ten heavy. A greater the ratio of tens in the shoe the more likely the insurance bet is to win. The fewer the decks the greater this effect is. Insuring a 20 (except A/9) increases the house edge on the insurance bet because there are two less tens in the shoe. April 17, 2003 Can you tell me the expected return in Black Jack if a player wagers all his money in one hand and not having money for split's or double's. Thank You. - Sincerely, Ruben Schachtenhaufen from Copenhagen, Denmark If you can't double or split that adds 1.9% to whatever the house edge is otherwise. This just goes to show that you should always have double or split money available if you need it. March 21, 2003 What would be the house advantage for single deck, hit soft 17, double after split, split to total of four hands, double any first two cards, one card on split A's, Blackjack pays 6 to 5? - Michelle from Las Vegas, USA 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. Nov. 28, 2002 Some casinos are now offering a single-deck BJ game paying only 6:5 odds for a natural. What does this do to the house edge? - Marty from Redlands, CA This increases the house edge by 1.39%! This is by far the worst blackjack game in Vegas. Aug. 11, 2002 The Mohegan Sun casino here in Connecticut recently added a limited number of blackjack tables that don't seem to be addressed in your synopsis. It is a 4 deck shoe dealt from a Shufflemaster that, essentially created an infinite deck, inasmuch as the dealer puts the dead cards back into the machine for reshuffling pretty much as the completion of each round of decisions. The game allows splitting to 4 times, double down on splits, dealer stands on all 17's, early surrender, and double on any first 2 cards except 10's and face. I have had some very good luck at this game and was wondering if it is one I should continue to play or switch back to the conventional 6 or 8 deck shoe. - Ray Zaleski from Shelton, Connecticut 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. June 28, 2002 What advantage does a 6-5 payoff on a blackjack add to the house? - Barabbas from Las Vegas, USA It depends on the number of decks. I have only seen this rule in single decks games, so we'll assume one deck. The probability of a blackjack in a single deck game is 2*(4/52)*(16/51)=0.0483. The probability of the dealer not having a blackjack, give that the player does have one, is 1-2*(3/50)*(15/49) = 0.963265. So the probability the player has a blackjack and the dealer doesn't is 0.046492. The casinos keeps an extra 0.3 units every time this happens to the increase in the house edge is 0.3*0.046492 = 0.013948, or about 1.39%. This is a huge increase, making this game the worst blackjack game in Vegas. April 22, 2002 The Flamingo is offering a single deck blackjack game with regular downtown rules (hs17). The only difference is that they altered the natural payoff to 6 to 5 instead on the normal 3 to 2. My questions are; How does that affect the starting advantage on this game? What would it be? How would it affect the insurance wager? Specifically what would Insurance have to pay in order for the player to get "even money" and be square to the 6 to 5 payoff? - DW from Las Vegas, USA Using my good ol' blackjack house edge calculator normal downtown rules result in a house edge of 0.1896%. In single deck the probability of a player blackjack and no dealer blackjack is 2*(16/52)*(4/51)*(1-2*(15/50)*(3/49))= 0.046492. Reducing the BJ win from 1.5 to 1.2 results in increasing the house edge by 0.046492*(1.5-1.2)= 1.3948%. So the house edge of this game would be 1.3948%+0.1896%=1.5844% (ouch!). For insurance to result in even money it would have to pay 5-1 but the player could only bet 20% of the original bet on it. Aug. 6, 2001 I was at the Soaring Eagle Casino in Mt. Pleasant, MI this past weekend and while I was there I noticed a game called "Pitch" blackjack. The game uses 6 decks, which are put into a shuffle machine, and then the machine delivers one "deck" to the dealer. Dealer cuts and deals (usually only two hands for a full table). Then he takes the deck, puts it back in the shuffle machine, and retrieves another 52 card "deck" from the machine. The rules are the same as for a standard shoe game except that the player is allowed to double down with 3 cards if they total 9, 10, or 11. I'm always suspicious of "special" games, so I wondered how the house advantage on this game would differ from a standard shoe game. Does the house have a greater or lesser advantage? - Bruce Keaton from Champaign, Illinois 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. July 18, 2001 There are a great number of Casinos in the Vancouver area, all except one offer no surprises, however, one of them allows a funky variation on Blackjack....the player may double down or surrender after ANY number of cards until that player stands or busts. Could you please inform me as to how exactly this affects the odds....I would think it would be of great benefit to the player? - Ryan from Vancouver, Canada According to 'Basic Blackjack' by Stanford Wong this add 0.2% to the player's expected return. Wong also indicates some strategy deviations under this rule on pages 60-61. May 13, 2001 I just came back from Vegas and played at the Las Vegas Club. They have a game called 'Most liberal 21'. You can split aces and pairs as many times as you choose or doubling down on any 2, 3, or 4 cards. Plus any 6 cards, totaling 21 or less, automatically wins. The only thing is there are 8 decks, and they take out about 2-3 decks, shuffle, deal, then place at the back of the shuffling machine. Also, dealer hits on soft 17. What kind of advantage does the house have with these kind of rules? -Dennis Vasquez I have never analyzed the effect of the double one 3-4 cards rule but skister.com says the house edge is 0.48%. This is higher than the conventional Vegas shoe game, where the dealer stands on soft 17, at 0.43%. They used to stand on a soft 17 in that game, in which case their claim was almost true. However it is now not competitive at all. May 1, 2001 Your web site is awesome! I enjoy your advice and am amazed at the simple way you explain things about gaming in a way I can understand. My question is this; While playing a benefit blackjack game where they have from what I could tell, all the "Vegas" rules, I found out they were paying two to one for a blackjack. This seems like a big benefit to the player; just how big is it? (this is no joke or prank, I actually played at the table where they were doing this!) -Bob Brown from Canton, Ohio Thanks for the compliment. If I had been at this game I would have played it hard and turned it into a benefit for myself. Assuming six-decks and otherwise Vegas rules the player edge would have been 1.94%. The 2 to 1 on blackjack adds 2.37% to the player's expected return in a six-deck game. May 1, 2001 I know that you have the casino advantage for blackjack listed on your web site in the case that a person plays the basic strategy, but I was wondering what the casino advantage was on average against a typical beginner. Also, can you formulate what the best advantage a casino could have over the worst of players, assuming that they would never hit anything higher than a hard sixteen? Thank You Kindly, John Desmarais from Storrs, Connecticut According to 'Extra Stuff' by Peter Griffin the cost due to mistakes of the average player is 1.41%. This is above whatever the house edge is assuming proper basic strategy. It also varies by place, Atlantic City player are better than Las Vegas player, for example. Your other question about bad strategies was such a good one I added information to my blackjack section about it. See my remarks on bad strategies. April 15, 2001 Top notch site you are running! My question to you is: by how much does the house edge in blackjack increase if the player cannot afford to split or double? - Martin Olsen from Odense, Denmark Thanks for the compliment. That is a good question. Not having enough money to double or split, but otherwise playing correctly, adds 1.9% to whatever the house edge is. April 15, 2001 I was visiting an Indian casino the other day where the blackjack minimum bet was $2, but for each bet, they asked for an additional 25 cents (they did this by giving you 4 special 25 cent chips for each dollar chip you had) so essentially, you bet $2.25 to win back $2. While I was still able to walk away with a bit of a profit, I was wondering if there was a quick and easy way to calculate just how much of a house edge this "commission" gave them? I know that compared to dealer hitting on soft 17, it's gotta be a killer. - SM You should divide the fee by the wager and add this to house edge under the house rules. For example if the house edge is normally 0.4% without the commission then the overall house edge would be 0.004+.25/2=12.9%! Feb. 10, 2001 I don't have a blackjack simulator personally, but wondered what the house edge would be on the video blackjack here in RI. It is single deck (reshuffled every round of course), split pairs only once (no splitting unlike tens), double on hard 10&11 only, pull 6 cards automatic winner regardless of dealers hand (i.e. If you have a soft 19 or 20 after 5 cards, you automatically hit because it is 100% impossible to bust on 6th card) double on splits on hard 10&11 only) split aces receive only one card each. BUT, here's the clincher, split Blackjacks pay 3 to 2 whereas traditionally they pay 1 to one) I know this can make a difference of maybe .5 % in the overall house edge. Also late surrender on any hand, and dealer hits soft 17. So, playing optimum basic strategy for these situations, what is the overall house edge. My guess is that it's in the 1.5% range because of the single deck and 3-2 pay out on split blackjacks. JF from Providence, USA We can determine the rules for 1 deck, dealer hits soft 17, double on 10-11 only, split one time, six-card Charlie, and late surrender from Stanford Wongís ëBlackjack Edgeí which says the house edge is 0.30%. This assumes you can double after a split, if you canít the edge is 0.40% (you didnít specify this rule). That just leaves the rule about a blackjack after a split paying 3:2. Even with this rule you still should never split tens. So the expected number of these blackjacks per hand is (4/52)*(3/51)*2*(16/50)=.0028959. Iím going to ignore dealer blackjacks to keep this simple. So multiply this by a half unit and this rule adds .14% to the playerís advantage. The house edge is thus 0.26% or 0.36% depending on whether you can double after a split. Feb. 10, 2001 Michael, thanks for your advice. I have two questions regarding the Odyssey machines that are very popular at Vegas casinos. I like to play their Top Hat blackjack and my first question is how much of a dealer edge do I lose from only getting paid dollar for dollar in winning a blackjack versus receiving the standard 1 1/2 times my bet? Also this machine has a double or nothing feature that seems to give the person a 50/50 chance of winning. Is it worthwhile to use this feature? ñ Dave from Los Angeles, California If you only win even money on a blackjack that increases the house edge from 2.32% (one-deck) to 2.26% (eight decks). The double or nothing feature is up to you. If it is fun then play it, if not don't. Dec. 31, 2000 Can blackjack be beaten under the following casino conditions:
- Alex from Auckland, New Zealand I haven't done any simulations but my educated option is a definite yes, this game can be beaten. The strategy to use in this game would be to bet the minimum when the odds are against you and the maximum when they are in your favor. Normally a sudden 50 times increase in bet size would set off a huge red flag but it seems the counter could do this with impunity in your game. When Atlantic City first opened the casinos could not ask card counters to leave and entire tables were filled with people jumping suddenly from a $5 bet to $300, or whatever the minimums and maximums were. After taking a huge beating the Atlantic City casinos begged the gaming authorities for a change in the rules, which they got. Not only could this be beaten, but I think it would be a card counters dream. Dec. 10, 2000 I just came back from Costa Rica. They pay even money on a blackjack. What is this worth to the house and should I double down on 21 versus say a dealer 3-6, since I am only going to get paid 1to1? - Rick Ronveaux of Jacksonville, USA If a blackjack only pays even money that increases the house edge by about 2.26%! If you do get a blackjack you should still stand regardless of what the dealer is showing. Nov. 4, 2000 Just one more question today. In your introduction to your site, you make a big deal of losing in the long run at all games of chance. However, what is your opinion of playing tons of hands at Unified Gaming sites with the -0.57 house advantage? How realistic would it be to make $5.70 per hundred hands with $10 bets for a few hours a day? It would sure beat getting another part-time job:), even if I could only do it for a few months (while I'm finishing school at the U.of U.). The math seems correct even to me (a history major), yet I have this nagging feeling that I've left something unaccounted for, and this wishful thinking is just too good to be true. I'd appreciate your opinion. ñ Dave Palmer of Provo, USA Your math is correct. For every 100 bets at $10 you make you could expect to make $5.70 assuming you follow my basic strategy. Keep in mind this is a long-term return and in the short run you could easily lose. There is also a problem with broken connections with Unified Gaming casinos, which slows down the number of hands playable per hour. Somebody told me that turning off the sound card can take care of this problem. Whatever your gambling bankroll is I would recommend dividing that by 100 and bet in those units. So to bet $10 a hand you should have $1000 to risk. Nov. 4, 2000 How did you derive the house edge in blackjack? John C., London, Canada I wrote my own combinatorial program which cycles through every possible event and keeping a running tally of all the possible outcomes weighted by their probability. Except in cases where resplitting pairs is involved my calculations are exactly right. Oct. 15, 2000 Biloxi, Mississippi casino has singledeck black dealt to the buttom. What is the casino's edge on this game? Does the basic strategy for blackjack still hold still hold for this game? but the way, blackjack in this game pays even money. ñ Roger from Baton Rouge, U.S. 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. Sept. 26, 2000 Here in Finland we have blackjack tables in some nightclubs and restaurants but these tables follow the following rules: six decks, stand off only on 21 and blackjack, stand offs on 17,18,19 and 20 the house wins!! No surrender, European no hole card rule, double 9-11, unlimited splits! I understand this is a bad deal for players but how bad is it? What is the house edge in this game? - Kim Johansson from Helsinki, Finland I have actually seen these rules when I went to Helsinki in 1986. Without a doubt the worst blackjack rules I have ever seen. Again I turn to Stanford Wong with questions like this. His Blackjack Edge software indicates that the house edge under these rules, aside from the losing to ties, to be 0.75%. This assumes the dealer stands on soft 17 and doubling after splitting is not allowed. You didn't indicate these rules in your e-mail. When I need to know about an unusual rule variation I turn to Wong's Basic Blackjack which says on page 93 that losing all on a tie, except 21-21, adds 7.0% to the house edge. Thus the overall house edge is 7.75%! Are these very fair rules:
These are the rules at 4aces casino where I always seem to bust if I hit a 12,13 and the dealer wiped me out with a mind numbing over 40 21's including twice 21's four times in a row. They do allow late surrender even though it states otherwise in their rules. What is an infinite deck? If these are good rules could you point out a good strategy. Thanks. - Douglas C Hilleary from Cumberland, Maryland According to Stanford Wong's Blackjack Edge software the house edge under these rules with eight decks is 0.36%. This is assuming you can resplit to four hands. My own analysis has shown that the house edge in an infinite deck game is 0.08% higher than eight decks. Thus the house edge under these rules would be 0.44%. An infinite deck is essentially a game dealt from an infinite number of decks of cards. In other words when a card leaves the deck it has zero impact on the remaining distribution. You seem to also imply that this casino is not dealing a fair game. Unless you provide some hard data I can't comment. Sept. 10, 2000 Q: First off-- great web site! I love it! In Reno I saw a game with the following rules: six decks, dealer hits soft 17, double after a split, resplit anything except aces, and the player could double on any number of cards. For example the player could draw to a 4 card total of 11 and then double? What is the house edge on this game? - Andrew Solovay from ? A: According to Stanford Wong's Casino Edge software the house edge under these rules is 0.39%. The rule allowing doubling on any number of cards lowers the house edge by 0.24%. However note that they slipped in the rule that the dealer hits a soft 17, this increases the house edge by 0.22%. So you are only 0.02% better off than a regular six deck game where the dealer stands on soft 17. Aug. 27, 2000 Q: I think your website is one of the best gambling sites on the net, and I have a question that I am hoping you would be able to answer. There is an Indian casino a few hours from my house that has some odd rules and regulations. I was wondering if you would be able to determine the house edge from these rules: -There is a 50 cent charge on each hand if your wager is between $5 and $25 Any help you can give is appreciated. - Bryan Mitchell 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. Unfortunatley this advantage is not available at greater bet sizes as the comparitive 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. Aug. 13, 2000 5Q: Dear Wizard! I¥m about to play Blackjack on finnish site with the following rules:
Are these rules a good deal for me? What is the house edge? Thankful for an answer. - Kim from Helsinki, Finland A: The house edge in this game is 0.51%. July 9, 2000 Q: On your blackjack page in the House Edge section you indicate that the player has the edge in single deck blackjack. Numerous Vegas Casino's offer single deck blackjack, but I doubt they are dealing a losing game. What gives here? Is your page incorrect or are the casinos just gambling on their clients not being able to play basic backjack. A friend of mine and I have a bet riding on this. Also. Is it true that with even a simple card counting system a competant blackjack player can consistently walk away a winner in the long run? Thanks for your help. ñ Alex Paradi of Toronto, Canada A: You have a legitimate point. At the time you wrote this I indicated the house edge according to a fixed set of rules that varied only by the number of decks. However in real life when single deck is offered the other rules invariably become more stingy. I have already enhanced the house edge table in the blackjack section to include a wider variation in rules. The typical Las Vegas single deck game does not allow doubling after a split and the dealer hits a soft 17. With these rules the house edge is 0.18%. The best single deck game is at the Slots-a-Fun (next to Circus Circus) where the dealer stands on soft 17 for a player edge of 0.01%. Next door at the Westward Ho double after a split is allowed but the dealer hits a soft 17 for a house edge of 0.04%. About card counting, absolutely not, even the best of card counters will lose often. An entire month can be at a loss. Only over the very long haul does a net profit become likely. July 9, 2000 Q: I see that the odds you've published for single deck blackjack are in favour of the player. Does this mean that if I play over and over again I have better odds than the house? - Peter A: It is hard to find a blackjack game where the basic strategy player has an edge over the house. The player edge in single deck blackjack on my site is based on otherwise multiple deck rules, which rarely exist in single deck. I organized the table this way to illustrate the effect of the number of decks. Unified Gaming offers the best blackjack game for the basic strategy player I have ever seen is offered anywhere. For a list visit my online casino index. If you do play a game with a negative house edge then, yes, that does mean you will have better odds than the house, assuming you play the basic strategy. July 2, 2000 Q: When calculating the house edge in blackjack, do you include pushes as you do in baccarat? - Erica Shumener from Los Angeles, California A: Yes. I always include pushes in the house edge. The only exception is some parts of my page indicate the edge both ways on other games. July 2, 2000 Q: In a live casino, if you could find a bj table that uses Perplexa rules, including a single deck, but deals reasonably deep into the deck before shuffling, would the house edge be different than -0.14%? - Ron from ? A: 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 better to play with the same rules at an online casino as opposed to a physical casino. March 11, 2000 Q: How does the house have the advantage in Blackjack? - Rob Woods from ? A: The dealer has the advantage because the player has to go first. If both of you bust it isn't a tie, you lose. Q: Are there any casinos in Vegas besides Mandalay Bay where the dealer stands on a soft 17? I ran a shoe of spanish 21 at MGM. Don't see any advantage with the tens missing. Especially on double downs. -Jim Dietz of North Olmsted, Ohio A: As far as I know the vast majority of shoe games in Vegas stand on soft 17. Usually the dealer will hit a soft 17 in single deck and double deck can go either way. It is complicated to explain why a ten rich deck is beneficial to the player but I do mention that in my blackjack section. However a ten rich deck is very beneficial when doubling on most hands, like 9 to 11, because you want a big card. Any good card counter can tell you that if 1/4 of the tens were removed from the deck the odds are strongly in the dealer's favor. circa Jan. 2000
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