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I have never been to Las Vegas so I was wondering are you allowed to use one of those cards for blackjack that tells you when you should hit or stand, etc. when you are sitting at a table.
Paul from Calgary, Canada
Yes, you can. They even sell them in the casino gift shops. However, it is bad etiquette to slow down the game by checking the card frequently. The least you should try to do is memorize what to do with a hard total, these situations happen most of the time. For non-obvious soft hands and pairs you can be forgiven for checking the card.
First of all, I'd like to say I really like your site. It's hard to find a casino site that actually gives good information. Secondly, I'd like to ask a question. I'm from Europe, so I play blackjack with the European hole card rule. It's a multiple-deck game. The dealer deals out the first card to all of the players and one to himself. After that, he gives all the players their second card and none for himself. The players can make decisions after that. After all the players are done, the dealer gets his second card and after that he can make his "decisions". I was wondering what basic strategy I should use for this game. Should I use the Microgaming strategy? The rules of the Microgaming casinos are a bit different though."
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.
I am a 18 year-old from South Africa and I have recently become very interested in blackjack. In all the casinos I have been to in South Africa (a grand total of 4), early surrender is offered. I was wondering if there are further situations when you should surrender with early surrender apart from the four situations for late surrender. I also wondered how much it cuts down the house advantage, and how effective it could be to exploit this rule while using a card counting system. I would be grateful for any sort of help or direction regarding these matters.
Paul from South Africa
My blackjack appendix 6 has a full strategy for early surrender.
I see that the odds you've published for single-deck blackjack are in favor of the player. Does this mean that if I play over and over again I have better odds than the house?
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.
Using your basic strategy for Cryptologic, what is the probability of winning five units before losing 20. If I played everyday for a year, getting out after winning five units or losing 20 units, what can I expect my net to be?
Bert from Richmond, Virginia
There was a similar question asked in the June 15 column, which I worked out in detail. However, briefly, I estimate the answer to be about 78%. Over a year, you could expect to lose 0.52% (the house edge) of the total initial bets.
I want to play blackjack at Lasseters Casino. They use Access software, whose rules are an infinite number of decks, split any pair and re-split once, double on any two cards, double after split and European hole card rule, and dealer stands on soft 17. Please supply me with the relevant Basic Strategy chart. Thank you.
Peter from Hemel Hempstead, United Kingdom
Here is my Lasseter's basic strategy.
Biloxi, Mississippi casino has single-deck blackjack dealt to the bottom. What is the casino's edge on this game? Does the basic strategy for blackjack still hold still hold for this game? by the way, blackjack in this game pays even money.
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.
Please tell me where I can find a copy that I can print and carry in my purse on the odds for blackjack. I am just learning and I am not sure when to take a hit and when to stay.
Sue from Marquette, USA
One idea is to right click on one of my strategy charts, save the image, and then print it. Some casino gift shops sell basic strategy charts the size of a business card. However, these charts have at least one mistake about half the time.
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.
Dave from 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.
Love your site. I've even taken your blackjack data and made it into a full-color pocket-sized page that I carry in my briefcase for those unexpected trips to Vegas. I've memorized and follow your rules and generally do well (but of course there are times when I lose.) Two questions, you said in a previous answer that you don't cap your winnings. How do you determine when to stop? When have you "won enough" so you avoid regression toward the mean and lose it back?
Second question, does the number of hits one takes effect the outcome? For example, if I have five cards that total 15 against a dealer's 10, am I pressing my luck by taking a sixth card? In other words, are the odds of busting on a 5-card 15 the same as busting on a 2-card 15?
Chris from Gaithersburg, USA
Thank for the compliment and I'm happy to help your bankroll last longer. When I gamble for fun I keep playing until it isn't fun any longer. Usually the fun ends when I have lost too much or have played too long. With the ups and downs of blackjack it takes hundreds of hours before regression toward the mean will cause actual results to look like expected results. Furthermore, the player who puts a conservative cap on their winnings is never going to experience the fun of a long hot winning streak. Keep in mind this is just what works for me. You should do what you are comfortable with. Everything I have to say about money management can be summarized by the following two rules (1) don't gamble with money you can't afford to lose, and (2) don't gamble if it isn't fun.
Regarding your second question, there is something to be said about the composition of a hand. The fewer the decks the more this is true. My blackjack appendix 3A and appendix 3B show the exceptions to single- and double-deck blackjack, based on the composition of the hand. These appendices show that the more cards that are in your hand the more inclined you should be to stand. Regarding your 15 against a 10 example, there are two situations in single deck blackjack where you should stand when the 15 is composed of 5 cards, A+A+A+6+6 and A+A+3+5+5. Note that in both of these situations either two fives or two sixes have left the deck which are the two most helpful cards for the player. The two situations where you should be the most inclined to stand if you have a multiple card hand are 16 against a 10 and a 12 against a 3.
I just got to your site and like it a lot. Is there a table for hits and splits when playing European blackjack? It seems like there should be some remedy for the house taking all the doubles and splits on blackjack.
Jim from Widdleton, Wisconsin
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.
Do you have basic strategy for the following rules? Dealer takes 17-17, 18-18 and 19-19 ties, doubling after split is allowed, 3 resplits, no-peek, player can double 7-11 totals (soft and hard), dealer stands on soft 17, six decks.
Jari from Turku, Finland
Stanford Wong's Blackjack Count Analyzer is perfect for questions like this. Just plug in the rules and it produces an immediately basic strategy and is ready to run a simulation. Following is his basis strategy under these rules. I did a 31-million hand simulation using Blackjack Count Analyzer, which shows a house edge of 4.13%, under these rules. When I was in Finland they had single zero roulette, which has a much lower house edge than this game. Why the blackjack rules are so stingy in Finland I would like to know.
PLR DEALER PLR DEALER 23456789XA 23456789XA 21 ---------- soft 21 ---------- 20 ---------- soft 20 ---------- 19 ---------- soft 19 ---------- 18 ---------- soft 18 +DDDd-++++ 17 ---------+ soft 17 +++DD+++++ 16 -----++--+ soft 16 +++DD+++++ 15 -----+++++ soft 15 +++DD+++++ 14 -----+++++ soft 14 ++++D+++++ 13 -----+++++ soft 13 ++++++++++ 12 +----+++++ 11 DDDDDDDD++ pair A /////////+ 10 DDDDDDDD++ pair 10 ---------- 9 ++DDD+++++ pair 9 /////-/--- 8 ++++++++++ pair 8 ///////--+ 7 ++++++++++ pair 7 -////+++++ 6 ++++++++++ pair 6 /////+++++ 5 ++++++++++ pair 5 DDDDDDDD++ 4 ++++++++++ pair 4 +++//+++++ pair 3 +////+++++ pair 2 +////+++++ Insurance: No + = hit - = stand D = Double if allowed otherwise hit d = Double if allowed otherwise stand, / = split.
I was wondering if you thought continuous shufflers have an effect on basic strategy? I know they speed up the number of hands per hour which is usually bad for the player, but is basic strategy still effective in this instance? Doesn't basic strategy slightly change depending on the number of decks?
Danny from Mission Viejo, California
I first addressed this topic in my December 1, 2000, newsletter. For those who missed it I just added blackjack appendix 10 to my site, which explains the effect on the house edge under both a cut card and continuous shuffler game. To answer your question, no, the basic strategy does not change. Basic strategy is always developed based on a freshly shuffled shoe, which is always the case when playing against a continuous shuffler.
Hey Wizard...I have just got into online gambling and have referred to your site for pretty much everything...I appreciate all the information on the single-deck Unified Gaming information, but what about the six deck game? Can you tell me the player (or dealer) edge in this game as well as a basic strategy? It would seem to me that this would be one of the best bets at which to count cards...what do you think? Thank you in advance!
Chris from Denton, TX
You should follow my multiple-deck strategy but surrender against aces in the same hands as the single-deck strategy. I haven't studied if counting this game is more profitable than the single-deck game, but I would be interested to hear from anyone who is doing as you suggest.
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 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.
First of all, I think your web site is great and want to thank you for all this great, solid information. My question is this: blackjack tables have a maximum bet limit that more than increases when you move up from the five dollar table to the ten etc. I suppose this is to discourage larger stakes gamblers from playing at lower stakes tables but how do they calculate these limits? I notice that they are different at different casinos. Also, on your chart of the house edge, it would be great to see a comparison of house edge for a blackjack player using Basic Strategy vs. one who is counting cards. Thanks again for the great work.
Michael from Santa Cruz, USA
You're welcome! Casinos generally try to keep the maximum bet about 200 to 500 times the minimum bet. Why? If a casino is comfortable with a $10,000 bet on a $100 table, why not take it on a $5 table? The answer seems to be that casinos like to corral their big bettors into certain areas. Such high-limit areas tend to have the best staff and surveillance. Limiting the ratio of maximum to minimum bet is also a defense against cheating and advantage play.
The advantage of card counting depends on how good and aggressive the card counter is. Other than my introduction to card counting, I leave that topic to other gambling writers.
There is an article in the blackjack section that indicates that a CSM, (Continuous Shuffling Machine), actually lowers the house advantage for the basic strategy player. I assume that is in a heads to head game. Would multiple players increase the house advantage?
Gizmo from Los Angeles
That is true. I explain why in my blackjack appendix 10. The number of players doesn't make any difference.
What basic strategy should you use for a CSM (Continuous Shuffler Machine)? Is it the same as a regular shoe for the same number of decks? It seems like the strategy could be a little different (maybe a 4 deck CSM should be played like a 3-deck shoe).
Chuck from New York
Yes, same as a regular shoe with the same number of decks. Most CSMs use five decks, for which you should use my 4-8 deck strategies.
Hi. Do you sell or recommend a basic blackjack strategy card. In the past I purchased some from Winning Publishing NV. Your Site is the very good.
Tom from Lancaster, USA
Your timing with this question is perfect. Marsha Ness, the proprietor of Custom Strategy Charts is now ready to sell laminated blackjack and Spanish 21 strategy cards. The strategies come directly from me and there is a wide variety to choose from depending on the particular rules. As of this writing, electronic payment options are not in place yet so you'll have to send a check by mail.
Update: Since the publication of this question, Custom Strategy Cards has gone the way of the dodo bird.
hi there..love your website....my favorite game to play in ac is triple action blackjack...i wanted to know if u had a strategy chart for that game, and if the strategy changes, which it must.....ex...16 against i face card i usually stand in this game since the dealer usually breaks once....let me know...thanks
Brian from West Hartford, USA
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.
Where can I buy nicely printed and lamenated credit card sized versions of your basic strategy tables for 21? If you don’t offer them--please do!
Steve from Tuscon, U.S.A.
I’m glad you asked. You can get them through Custom Strategy Cards. These are my own blackjack and video poker strategies on nice wallet sized laminated cards.
Nov. 13, 2007 update: The Custom Strategy Cards site is now defunct.
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?
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.
Good job and well done. The question: I notice from your May 5, 2003 Column that you actually CALCULATE your blackjack odds. I am a bit surprised that you were not using your computer to SIMULATE the results. Or is this a stupid question, i.e., the computer will take a million years to do the job?
Yes, I calculate blackjack odds using a combinatorial approach, analyzing every possible ways the player and dealer cards can come out, taking the greatest expected value at every decision point. This is harder to program than a simulation but I feel is more elegant and a nice challenge in recursive programming. However I still respect my peers to do simulations. With today’s computers it doesn’t take long to run off a billion bets, which gets very close to the optimal strategy return.
Your site is amazing. Here’s my question. Does match play change basic strategy at all? My non-math-based instincts tell my that surrender becomes a bad idea, that is if you have to surrender your coupon.
Thanks for the compliment. You are right that you shouldn’t surrender if they take the match play away. There are some other strategy changes but I never worked out a list. Generally the casinos don’t allow doubling the match play chip, in which case you should be less inclined to double. ’Basic Blackjack’ by Stanford Wong indicates when to double if doubling the match play is allowed. My advice is to use the match play on the Player bet in baccarat.
If playing Basic Strategy significantly helps the player not lose as much to the casinos, why do some casinos freely give BS cards out and allow players to consult BS cards while playing? I have seen this in Shreveport, Vicksburg and Black Hawk, CO. Friends have told me that they have done this in Vegas too.
I have played blackjack at casinos all over the United States and have never seen a basic strategy card in blackjack given out for free. However most casino gift shops sell them and they are indeed allowed at the tables. I think the casinos aren’t crazy about the cards the alternative of prohibiting them would be even worse. It would cause a lot of bad player relations to try to enforce a no strategy card rule. Furthermore, where would they draw the line? What if the player wrote the basic strategy on his hand, could the casino prevent a player from looking at his own hand?
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.
What is the basic strategy for "charity blackjack" where the dealer wins on ties?
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%.
I have been using your simplified strategy for jacks-or-better video poker, and I wondered if you also had a super-simplified strategy for blackjack as well for those of us who don’t play often enough to make memorization of the full chart worthwhile.
Yes! Here it is:
- Stand on hard 12-16 against dealer 2-6
- Double on 10,11 against dealer 2-9
- Always split eights, nines, and aces
- Stand on soft 18 or more
- Stand on hard 17 or more
- If rules 1-5 do not apply then hit
- Never take insurance
If played on a game with six decks and the dealer stands on a soft 17 the house edge using this strategy is 0.93%. The correct basic strategy will get you down to 0.41%.
What changes should one make to blackjack basic strategy when playing just a single hand when the objective is to maximize the chance of winning that hand (for example when using a match play coupon)?
It depends if the player is allowed to double and split the match play portion of the bet. Usually the player is not allowed to, which works against the player. The following chart shows how to adjust your double and splitting strategy, assuming the player may not double the match play and if the player splits the match play rides on the first hand played, based on infinite decks and the dealer standing on soft 17. The hit/stand strategy is the same.
In San Juan, Puerto Rico, at blackjack, a number of casinos do not deal the dealers "hole card" until after the players have taken their cards. I am reasonably sure that they don’t take your doubled/split bet if they get a blackjack. What changes, if any should be made to basic strategy.
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.
I have tried, quite unsuccessfully, to locate on your excellent site and elsewhere how to properly calculate a confidence interval based on 1, 2, or 3 standard deviations and number of hands played with Expected Value. For example, I’d like to learn how to calculate the +/- standard deviations for playing $10/hand at blackjack for 300 hands using the .50% house edge for basic strategy. Thanks for your GREAT support and advice.
Peter from Orlando
The expected loss would be 300*$10*0.005 = $15. As I state in my blackjack appendix 4 the standard deviation is 1.17 (based on Atlantic City rules). The standard deviation on 300 hands at $10 each would be 3001/2 * $10 * 1.17 = $202.65. So here are the confidence intervals on the expected win for 1, 2, and 3 standard deviations:
1 standard deviation (68.27% probability): -$15.00 +/- $202.65 = -$217.65 to $187.65
2 standard deviations (95.45% probability): -$15.00 +/- 2*$202.65 = -$420.30 to $390.30
3 standard deviations (99.73% probability): -$15.00 +/- 3*$202.65 = -$622.95 to $592.95
Since most online casinos deal each hand out of a "fresh shoe," is there an opportunity to create a special basic strategy card for the "first hand out of a shoe," or do your various basic strategy cards work as well?
Bill W. from Summit, New Jersey
The traditional way to create a basic strategy chart is based on the odds the first hand after a shuffle. So the existing basic charts, including mine, are already perfectly suited for most online games where the cards are shuffled after every hand.
Great website! Would you please tell me how often the player and the dealer will both bust, on the same hand, when the player is using the basic strategy? I went to the math links that you have listed, but couldn’t figure out how to set up the equation. I would appreciate any help you can provide.
Paul from Portland
The following table shows the probability in a single-player game. Remember, the dealer will not play out his hand if the player busts first. If you add players the dealer’s probability of busting will go up because there will be a greater probability of at least one player not busting.
I have been a dealer for 27 years and have seen a lot. One of my favorites was a guy who never looked at his cards playing blackjack....just tucked them. I thought he was nuts of course but some days he won and some days he lost. Just like most people. I tried this myself on a free gambling website and won 2 out of 3 times gambling 20 minute sessions. My question is this: How much worse off are you doing this than trying to play basic strategy? I really don’t think it matters much at all what you do in blackjack for the ’average’ player.
Mark from Las Vegas
Under typical Vegas rules (6-deck, dealer hits soft 17) the house edge by always standing is 15.7%. In the short-run one could still overcome that, but in the long run you’ll lose badly.
In blackjack appendix 10 you explain how CSM machines actually decrease the houses edge, stating that because the way people play basic there is a tendency for more "10" cards to be drawn. Just playing basic, not counting cards at all, would this not mean that the closer you get to the end of the deck/shoe the worse your odds would be since there there would be a tendency for the 10s to have already been extracted thus leaving more smaller cards to the end?
Hector from Miami, Florida
There is no particular time to expect the small cards. The last hand in a cut card has just about the same odds as the overall shoe. However if the dealer deals out much more than the average number of hands in a cut card game the last hands tend to be very bad for the player. This is because in the early hands the players and dealer didn’t hit much, which in turn is because lots of large cards came out, leaving more small cards for later in the shoe. So if you notice that you have already passed the average number of hands and the cut card is still a ways off then the deck is probably small card rich and it would be a good time to drop your bet or take a walk. However with other players jumping in and out of the game, and inconsistent cut card placement the practicality of this strategy is very small.
In multiple-deck blackjack, I don’t count cards, and I understand that insurance is generally a bad bet. Sometimes, with six or seven hands playing, I check on what cards are exposed for that deal and place an insurance bet if there are two or fewer 10-pointers visible. How foolish is this?
Jim from Atlanta
In a six-deck game you should have to see 24 non-tens, and no tens, for insurance to be a breakeven bet. The probability of that happening is extremely low. So unless you are counting, I would never take insurance in a shoe game. However, in a double deck game if you can see eight non-tens, and the ratio of non-tens to tens in the rest of the visible cards is at least 2 to 1 then insurance would be at least an even bet. For example: 8 non-tens and 0 tens, 10 non-tens and 1 ten, 12 non-tens and 2 tens. In true single deck (blackjack pays 3 to 2) you only need to see four non-tens and then have the same 2 to 1 ratio in the rest of the visible cards.
What does the effect of not burning a card have on a single-deck blackjack game, if any.
If you aren’t counting cards, then it doesn’t matter. If you are, then any burned cards should be added to the number of cards left unplayed in the deck/shoe, when making the true count conversion.
In Las Vegas can I use a hint/cheat sheet chart while sitting at a Blackjack table?
Sharon from Nags Head
Yes, as long as it doesn’t slow down the game too much for other players.
In 2009, the total amount wagered on blackjack tables in Nevada was $8.917 billion. The casinos won $1.008 billion. How much of that is attributable to player mistakes?
From the Nevada Gaming Control Board 2009 revenue report, we see the win for "21" was indeed $1,008,525,000. That probably includes blackjack variants. According to my February 20, 2010 Ask the Wizard column, the cost of mistakes in blackjack is about 0.83%, according to gaming consultant Bill Zender.
The missing piece is what would be the house edge without the errors? I admit this is kind of crude, but the average of the house edge column in the April 2010 Current Blackjack Newsletter is 0.78%. So, the total house edge in blackjack, including errors is 0.78% + 0.83% = 1.61%. The portion of that due to errors is 0.83%/1.61% = 51.55%. So the 2009 profit from blackjack errors in Nevada could be roughly estimated as 1,008,525,000 × 0.5155 = $519 million.
This question was raised and discussed in the forum of my companion site Wizard of Vegas.
Could you please, for your visually impaired gamblers out there, make an accessible blackjack strategy chart? Unfortunately, screen readers (programs that read text allowed as speech) don’t read the chart very well. Instead, could you write a step-by-step guide? An accessible chart will be greatly appreciated!
Never let it be said I’m not a friend of the
blind visually impaired. Here is my Wizard’s Simple Strategy in easy text form. This is not the standard basic strategy, which is more powerful, but would be lengthy to put into words.
- Hit hard 8 or less.
- Stand on hard 17 or more.
- Hit on soft 15 or less.
- Stand on soft 19 or more.
- With 10 or 11, double if you have more than the dealer’s up card (treating a dealer ace as 11 points), otherwise hit.
- Surrender 16 against 10.
- Split eights and aces.
If the player hand does not fit one of the above "always" rules, and the dealer has a 2 to 6 up, then play as follows:
- Double on 9.
- Stand on hard 12 to 16.
- Double soft 16 to 18.
- Split 2’s, 3’s, 6’s, 7’s, and 9’s.
If the player hand does not fit one of the above "always" rules, and the dealer has a 7 to A up, then hit.
For the full basic strategy in text form, please see my 4-deck to 8-deck basic strategy.
In blackjack, is it better to face a dealer two or dealer seven?
A seven. The following table shows the expected value in an infinite-deck game according to the up card and whether the dealer hits or stands on a soft 17. The values for a ten and ace are after the dealer peeks for blackjack, and confirms he doesn't have one.
You can see the player can expect to win 14.40% of his wager against a seven but 9.07% or 9.10% against a two.
Expected Value by Dealer Up Card
|Up Card||Stand Soft 17||Hit Soft 17|
This question was raised and discussed in the forum of my companion site Wizard of Vegas.
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