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Home • What's New • Advice & Strategy • Ask the Wizard • Gambling online • Play for Fun |
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This page is for questions about specific hands.
I have studied and used your blackjack appendix 16 (dealer exposes
hole-card strategy) for some time now, and there is still one play that I can not find a mathematical explanation for: A2 vs. 5. Basic strategy would have this as a double, and using your own "effect of card removal" numbers, removing a 2 & 3 from the deck when you have a soft 13 should make the deck favor the player MORE, not less. What am I not seeing? – Rodger from Phelpston ON
The reason is my blackjack basic strategy is based on 8 or fewer decks, and the flashing dealer strategy is based on an infinite number of decks. In an infinite-deck blackjack game you should hit A2 vs. 5 as well. An infinite-deck assumption is the lazy way to analyze blackjack. The reason I went that way is I believe that is not a frequently used page, and the cost in errors is very small, only one unit for every 202,000 units bet. July 25, 2007
Many casinos allow bets behind another player's on the blackjack table. Can you please tell us the proper pair-splitting strategy when the "behind" wager far exceeds the regular wager, assuming the two bettors are working together? – Jim from Brick, NJ
I hope you’re happy, I added a new page to answer this question. Please see my Blackjack Appendix 19. July 17, 2007
I had a situation playing blackjack last weekend, where the dealer had a 6 on top but when he was tucking in the down card he accidentally showed that he had a 3 in the hole. The player on my right had a 15, I had an 11, and the player on my left had a 12. Knowing that the dealer had a total hand of 9, the player on my right hit his hand and busted with a 10. I wound up doubling down and got a 2. The player on the left hit his hand getting a 5, for a total of 17. The dealer opened his hand of 9 and hit a ten for a total of 19. The dealer told us even though you saw the 3 under that you should play your hand as if you did not know the down card. I wanted to ask you what you would have done in the situation for all three players. This is the first time that has ever happened since I have been playing blackjack. Please advise. Thanks! – Larry C. from Daly City
My flashing blackjack dealer strategy shows what to do in any situation where the dealer accidentally exposes his hole card. However, most players don't have that memorized, incluing me. In cases like this where the dealer's two cards total nine or less you may use basic strategy, assuming the dealer's up card is the sum of his two cards. Using that rule of thumb, all three players played correctly. Contrary to what the dealer said, the player has every right to use any information gleaned from dealer errors like this. Not only would I have ignored the dealer’s comment, I would have kept playing, hoping he would do it again. May 2, 2007
I have a friend who starts complaining when his first card is a six, without waiting to see what his second card and the dealer's up card are. I think he should wait because he could get a two, three, four, five, etc. (i.e., a decent second card) OR the dealer could show a two through six (a good card for the table). What do you think? How much worse are his odds of winning with a first card of six without knowing this second card or the dealer's up card? Or is my friend just a whiner? Thank you for your time. – Scott from Long Beach
My blackjack appendix 14 shows that if your first card is a six your expected value is already about –21%. For example, if he bet $100, a fair price to sell the hand and bet would be about $79. Maybe you can take advantage of his complaining by offering to buy his hand for less than the fair 79 cents on the dollar. I’d suggest 75 cents on the dollar, to give you an edge, without taking too much advantage. March 29, 2007
My friend I were playing in LV. We had a big argument on what has statistically better odds, double down with player totaling 10 versus dealer showing 7, or double down with player totaling 11 versus dealer showing 10, in a two deck game. I thought it was the prior. – Brett from Alhambra
My blackjack appendix 9 was created for just these kinds of questions. Assuming 6 decks, my table shows the expected value of doubling 8+2 vs. 7 is 0.396342. The expected value of doubling 8+3 vs. 10 is 0.176919. So you are right, 10 vs. 7 is the much better hand to have.
August 9, 2006
On my recent visit in Vegas I saw two dealers independent from each others (one at The Orleans, one at Circus-Circus) suggest to double on 4-4 vs. 6 instead of split. I was the BJ guy of our group and so my friends started to ask me about that. All I could say was: no, splitting is the right decision. (Of course provided that double after split is allowed.) Can I find out the probabilities of these alternatives or can you tell me? kind regards - Werner I've said this before but as much as I respect dealers as a group they give out a lot of bad advice and misinformation. Splitting fours against a five or six is a frequent play where both players and dealers incorrectly rebuke splitting. Sometimes you hear people say falsely that you should never split "anything that starts with F", in other words fours, fives, and faces. That is true about fives and faces but the player should indeed split fours against a five or six if double after split is allowed. Otherwise the player should hit, except in single deck he should double if allowed. My blackjack appendix 9 shows in a six-deck game where the dealer hits a soft 17 the following expected values of 4,4 against a 6.
Stand: -0.114085
Hi, I just stumbled onto your site, and I think it's a fabulous site for blackjack info. I have a question, though. Can you explain how is there a positive expectation when you follow basic strategy and have a total of ten against a dealer 10 or ace showing (no dealer blackjack). Your table shows a positive expectation for both these scenarios, but I can't understand how. I would think under this scenario the player and dealer follow the same strategy, that is to hit until 17 or better or bust. The soft 17 is eliminated for the player under this scenario so I can't understand where the positive expectation comes from. Thanks in advance, -Srikanth
Thanks for the kind words. Let's assume six decks (it doesn't matter whether the dealer hits or stands on soft 17). My blackjack appendix 9 shows the expected value of 6+4 against an ace to be +0.081336, and 6+4 against a 10 to be +0.026796. The reason the expected values are positive is my expected value tables assume the dealer already has peeked for a blackjack and has confirmed that he doesn't have one. Meanwhile the player can still draw an ace for a 21. In other words the player can make 21 on his next card and the dealer can not by assumption. If I had such a table under the European no peek rule the expected values would indeed be negative.
Jan. 14, 2006
In blackjack where the dealer exposes both cards (appendix 16), a pair of 8's is not split against the dealer's total of 10 or 11; instead, it says hit against the 10 and stand against the 11. Why is this different from regular BS where we split 8's against the dealer's ten or ace? -David from Fort Wayne, IN
In regular blackjack the player should indeed split eight's against a dealer 10 or ace up. However if the dealer accidentally flipped over both his cards, showing a total of 10 or 11, the player should hit against a 10 and stand against an 11. The reason is that when the dealer has a ten or an ace up, by the time it's your turn you know the dealer does not have blackjack, because she peeked at the hole card to make sure. So you can play your hand more aggressively. But when both dealer's cards are exposed to show a total of ten or eleven, then the dealer can certainly draw an ace to the ten, or a ten to the eleven, for a total of 21, so in that case you should proceed more conservatively.
Feb. 11, 2006
The index number of 16 against a 10 in most blackjack counting systems is zero. So if the deck were completely neutral you should stand, because you stand if the count is equal or exceeds the index number. Yet the basic strategy tables tell us to hit. This seems to be a contradiction. In all honesty this is an old question but I got a better answer from Chris F. He correctly says the reason is that when the basic strategy charts are created they assume the player's first two cards and the dealer's up card have already been removed from the deck. A good example of this is that in single deck the correct play is to stand on 7,7 against a 10, because half of the sevens in the deck are already gone, and that is what you need to beat a dealer 20 with 3 cards. In blackjack the strategy for 16 vs. 10 is R,S since once you eliminate the 2-card hands the strategy is stand (not hit) for any number of decks. It is true that in general you should stand on 16 vs. 10 with three of more cards. So if my chart was based on the casino offering the surrender option then you would be right. However that assumption is not made. If I changed the key to Rs (surrender if allowed, otherwise stand) then that would imply that the player should stand on a 2-card 16 against a 10 if surrender was not allowed. Oct. 8, 2004 I heard the other day that if you're playing a 6:5 game (or the even money game at Rio), you should double down when dealt a natural to help offset the lower payout. Is this correct? What would the expected loss be for that play? This would be a terrible play. For example if you doubled on a blackjack against a 5 (six decks dealer stands on soft 17) your expected gain would be 0.622362, according to my blackjack appendix 9I. So even in an even money game this would still be an error costing about 38% of the bet. June 5, 2004 If the dealer does not check for blackjack with a ten showing, instead taking only the original wager at the end of the hand, does that necessitate any strategy changes? No. As long as you stand to lose only the original wager you should play assuming the dealer does not have a blackjack. If the dealer does have blackjack there is nothing you can do about it anyway. Feb. 13, 2004 The basic strategy chart for blackjack states to hit on a 16 if the dealer has an ace showing. I was wondering if the chart takes into account the fact that once it is known insurance is not paying then the dealer does not have a 10 value card down? This obviously decreases the dealer's chance of making a hand, but is it enough that a player should stand on a 16? Yes, the basic strategy assumes the dealer does not have a ten in the hole. Even in Europe where the dealer doesn't check the hit/stand strategy is still the same because if the dealer has a blackjack the player has no hope anyway. When the dealer has an ace, assuming no blackjack, the probability of making 17 or more is 83.3% when the dealer stands on soft 17. So standing is not even a very borderline play, the odds definitely favor hitting. Jan. 31, 2004 On your Blackjack Basic Strategy chart it says to "Double if allowed, otherwise stand" on A,7 against a dealer's 3-6. My question is, why stand? If you're willing to double down but can't, shouldn't you at least hit if you can? You were willing to take another card anyway. Thanks for your time! If the player had the option to double his bet and stand that would be better than a conventional double. So taking the card actually is detrimental to the player's hand in these cases, but it worth it to get twice as much money down. Jan. 20, 2004 The index number of 16 against a 10 in most blackjack counting systems is zero. So if the deck were completely neutral you should stand, because you stand if the count is equal or exceeds the index number. Yet the basic strategy tables tell us to hit. This seems to be a contradiction. Good question. My educated guess is that if the index numbers were not rounded then it would be greater than 0 but less than one half. So it is getting rounded down to zero. Making the index number 1 would result in more of a rounded error, causing players in slightly positive decks to hit when they should stand. Oct. 15, 2003 If you have 15 and the dealer shows an eight...basic strategy say to hit. In this case, whether you hit or stay your chance of losing is over 70%. Why is not the better play to surrender if you are going to lose over 70% of the time no matter if you hit or stay? - Nino Nistri from Glastonbury, USA For the sake of simplicity let's stay with your example and say the probability of winning is 70% and losing is 30% if you hit. The expected value of hitting would be 0.3*1 + 0.7*-1 = -0.4. This is greater than the expected value of -0.5 by surrendering. Aug. 4, 2002 In your blackjack appendix 6, concerning late surrender you advised surrendering a 10+5 and 9+6 against dealer's 10. In the basic strategy of Unified Gaming, you advised hitting 15 against dealer's 10. I don't understand why hit instead of surrender in this case because the 9+6 and 10+5 are much more probable way to have 15 than 8+7. - Moisan from Paris, France This is an interesting situation. Although you should surrender 5/6 of the time with 15 against a 10 in single deck it is still better to always hit than always surrender. Following is the expected return by hitting each way to compose a 15. On a 4-deck blackjack game if you split aces against 5 or 6, and you get another ace. You should double or hit? (no more splits at this point) I am getting different answers on different sites. So far, I have seen one site double on 5 and 6, one site double on 6 only, and other sites list split on all cases and I assume they didn't consider this situation. Another question in 4 deck BJ for 10,2 against 4, one site listed a hit. I would like a confirmation from you. - Larry from Austin, USA Keep in mind most casinos won't let you do either. However if you can you should double on the 6 only. This is true whether or not the dealer hits a soft 17. If the dealer stands on a soft 17 the expected returns against a 5 are .162849 by hitting and .148228 by doubling, so hitting is the better play. Against a 6 the expected returns are .189020 by hitting and .196249 by doubling. So doubling is the better play. You can see these numbers for yourself in my blackjack appendix 9e. About your other question, yes in a 4-deck game the player should hit a 10,2 against a 4, but only if the dealer stands on a soft 17. I don't list 4-deck basic strategy exceptions myself because there are so few and they make such a small difference. Following this exception will help you win more unit every 113396 hands, or lower the house edge by 0.000882%. Not worth the bother of memorizing the exception in my opinion. Aug. 6, 2001 Wiz, This is a spliting 8's against a dealer's 10 question. Splitting is the is the correct play on single hand basis. However, I believe for the typical BJ player it is better to stand when considering you are doubling the amount of the bet. Why double your bet against such poor, way below average, odds? After all, the goal is to maximize your overall return (i.e, the weighted average of all your bets). Your thoughts please? - Miami Al from Baltimore, USA P.S. Your site's great and advertising like banner ads and sidebars is understandable but invasive advertising like pop up windows and question prompts that try to force you to another site gets to be a bit much IMO. Although this is a close play standing is the third worst option. Using blackjack appendix 9G we can find the following expected returns: As a BJ player I regularly play with regularly splits 10s vs. bust cards. This move has a positive expectation, but isn't as profitable as standing pat. Could you please show this friend of mine how much worse splitting 10s is than standing pat, in a neutral deck? Also, lots of BJ players get upset at someone who splits 10s vs. 6, but they often split 2s or 7s vs. 10 themselves. Can you set the record straight on this? - Brett Hall from Richland, USA I took great pains to create my blackjack appendices 9A-9H to answer these kinds of questions. For example in a six-deck game where the dealer stands on soft 17 then you would use blackjack appendix 9G. There you can see the expected return by standing on two 10ís against a dealer 6 is 0.702826. The expected return by splitting in this situation is 0.622165. So the player can expect to win an extra 8.07% by standing as opposed to splitting. Don't pay much stock in what other players say or do at the blackjack table, trust my advice and youíll be in fine shape. March 11, 2001 1) Regarding the basic blackjack strategies you have for different online casino groups. Specifically 2 different ones that both use single deck: Microgaming and Unifed Gaming. I cannot understand why you list 11 VS 10 as a hit for Microgaming, but as a double for Unified. Since they both use single deck, it seems the same strategy should be used here. I lose more often than win when I double this. If you double on 11 at a Microgaming casino and the dealer gets a blackjack you will lose the total amount bet. At Unified Gaming the blackjack would be turned over immediately if the up card were a ten so there is no risk of losing to a blackjack when doubling in this situation. Dec. 24, 2000 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. Q: Mike, On my last trip to Vegas, a dealer I've come to know said he was "toying with the idea" of standing on a 16 against a dealer's 7 because only 5 of the 8 cards give the dealer an automatic win. How does this strategy play out? - Chris from Gaithersburg, Maryland A: This would be a bad play. For example my blackjack appendix 9B shows the return both ways by playing 10 and 6 cards against a dealer 7. Hitting has an expected loss of 39.6% of the bet. However standing has an expected loss of 47.89%. There is no easy explanation I can give why hitting is better. You have to consider everything that can happen, weight it by its probability, and take the sum. Overall hitting is much better. July 30, 2000 Q: Hi there - love your site! If I have blackjack, and the dealer is showing an ace, I am given the option of taking even money or continuing the hand. Should I take the even money or play on? - Ross Heller of New York, New York A: This is another way of looking at the decision to take insurance. The expected return of taking even money is obviously 1.0 units bet. Lets assume an infinite deck of cards for the sake of simplicity. The probability the dealer will have a blackjack is 4/13 and the probability otherwise is 9/13. If the dealer gets a blackjack you push, if not you win 1.5 units. The expected value of not taking insurance is (4/13)*0 + (9/13)*(1.5) = 13.5/13 = 1.0384615, which is greater than 1.0. Thus declining insurance, or even money, and playing the hand is the better bet. In an actual game with a finite number of decks the odds are even better since one 10 is already out of the deck (in your hand) which lowers the dealer's probability of having a blackjack. June 10, 2000 Q: If the dealer checks his hole card, and does not have blackjack,why hit a soft 18 against an ace; also, why not double on an 11? - Randy S. Kurek of Columbus, Ohio A: In blackjack there are seldom simple answers. You have to consider everything that could happen and weight every outcome by their probability. The best play is the one with the greatest expected return. According to my blackjack appendix 9b the expected return in a double deck game of hitting a soft 18 against an ace is -0.1004 and the expected return of standing is -0.1005 . So hitting is just a hair better. 11 against an ace is also a very borderline play. It is actually composition dependent in both single and double decks, in other words depending on which two cards that total 11 determines how to play the hand. However if you don't wish to memorize the composition dependent basic strategy you should double on 11 against an ace in single and double deck and hit with four or more decks. May 6, 2000 Q: In your Blackjack strategy you surrender 16 against A,10,9. You say to split a pair of 8's against those cards. I have been told that a pair of 8's is a 16 and should be surrendered. What do you think? - Jim Weatherly from Naples, Florida A: Whoever told you to surrender two 8's gave you incorrect advice. To illustrate why you should split 8's against a 10 check my blackjack appendix 9b. This shows expected return for any initial situation for any given play. The table shows that splitting 8's against a 10 in double deck has an expected return of -.4706 if allowed to double after a split. In other words you can expect to lose 47.06% of the initial bet on average. This is less than the 50% you would lose by surrendering. If not allowed to double after a split the rate of return is -.4801, again more than -0.5 . Splitting 8's against a 9 or ace has an even greater return. I assure that the numbers for other numbers of decks are still more than -0.5. April 29, 2000 Q: Wiz, You are the man! You have far and away the best gambling site on the 'net. Being an actuary myself (ACAS), I love to see someone putting their math skills to good use. My question: When late surrender is allowed, do you still want to split 8's with a ten showing? I'm guessing yes, but one of the hardest plays in BJ is splitting 8's vs a ten. As a side note, I just spent 3 days in Vegas, if you haven't done so already, you must try the Las Vegas Club and the World's Most Liberal BJ Rules. Doubling is allowed on 3 or 4 cards, 6 cards <= 21 is an automatic winner, and late surrender. At six decks I figured the house advantage to be .14%. Thanks for all of your hard work!! - Jim Hieb of Bloomington, US A: Thanks for the kind words Jim. Yes, you still want to split 8's even if late surrender is offered. Even if you can't double after a split you should still decline to surrender. Based on a 2 deck game where you can not double after splitting the expected value of splitting 8's against a 10 is -0.480673, better than the -0.5 by surrendering.
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