The parameters for these questions:
Six decks.
Double down on anything.
Surrenders allowed except where noted.
Draw one card on split aces.
No re-splits.
Doubling down after splitting allowed except where noted.
Except for the surrender option, I'm assuming these rules to be the most common House Rules. I know some of you have spent a lot more time in casinos than me (as is evidenced by the fact that I still have shirts in my closet) so feel free to correct me if this assumption is wrong.
There is one other player at the table besides you and the dealer. His cards are indicated as "Player B". Player B can be on either side of you, so it is possible he plays his hands out before you. If player B plays before you and selects an option that calls for at least one additional card, you will see more than two cards listed for player B. For example, in question #5, player B begins by splitting 9s.
The answers to these questions were determined using Ferrante's Blackjack Program (FBP) and cross-checked with another program that does a similar calculation, so I am confident these answers are correct. Of course, those of you who just surfed onto this page don't know me and should therefore be skeptical about what they're reading here. This is, after all, the Internet, the World's largest storehouse of misinformation. So read, evaluate, be critical. If you think one or more of my answers is wrong, send me an e-mail telling me I'm all wet, and together we can determine which one of us will the one to actually get soaked. It'll be fun.
Okay, that's enough chitchat, let's get to the meat of this material -- for each of the card combinations listed below, what is your best percentage move? Your options are: hit, stay, double down, split (if applicable), or surrender (if allowed). By the way, you will get a poor score on this quiz if you blindly follow "basic strategy", i.e. the recommendations on those cards many casinos pass out freely to their customers, figuring they'll lose anyway.
A note on navigating this document: clicking on the number for a given question will take you directly to the answer for that question. Also in the "Answers" section, preceding the actual answers, are some general comments explaining how all the answers are derived. You may want to read these comments before you read the answers; also, don't worry if some of the comments seem a little obtuse, they'll make sense when you see the answers. (No, that wasn't meant as an insult. I'm just assuming that, like most of us, this kind of material makes more sense when you see examples to illustrate the subject matter.)
You: 9, 7 |
Dealer: 10 |
Player B: 5, 3 |
No surrenders. | |
You: 10, 5 |
Dealer: 10 |
Player B: K, 9 | ||
You: 10, 2 |
Dealer: 4 |
Player B: 10, A | ||
You: 7, 5 |
Dealer: 3 |
Player B: 8, 6 | ||
You: 10, 3 |
Dealer: 2 |
Player B: 9, 9, 10, 10 | ||
You: A, 2 |
Dealer: 5 |
Player B: 10, 8 | ||
You: A, 4 |
Dealer: 4 |
Player B: 9, 9, K, 8 | ||
You: A, 6 |
Dealer: 2 |
Player B: 5, 8 | ||
You: A, 7 |
Dealer: 2 |
Player B: 9, 5 | ||
You: A, 7 |
Dealer: A |
Player B: 3, 3 | ||
You: 2, 2 |
Dealer: 4 |
Player B: 8, 8, 9, A |
No double down after split allowed | |
You: 8, 8 |
Dealer: 10 |
Player B: 3, 2 |
No double down after split allowed | |
You: 3, 3 |
Dealer: 2 |
Player B: 8, 8, Q, J | ||
You: 3, 3 |
Dealer: 8 |
Player B: 2, 4, 3, K | ||
You: 7, 7 |
Dealer: 8 |
Player B: 6, 5, 7 | ||
You: 4, 4 |
Dealer: 5 |
Player B: 7, Q | ||
You: 10, 10 |
Dealer: 6 |
Player B: 3, 2, 4, 2, 5 | ||
You: 7, 2 |
Dealer: 2 |
Player B: 5, 7, 8 | ||
You: 5,3 |
Dealer: 6 |
Player B: 2, 3, 4, 2, 5 | ||
You: A, 8 |
Dealer: 6 |
Player B: 5, 5, 3 |
Just a few definitions before we begin:
In the answers, "base pct" is the base percentage -- this is the advantage the best plan has over the second best plan before considering the cards held by player B. (It doesn't tell you how likely you are to win, just how much more likely you are to win if you follow the best plan versus the second best plan.) The "adjustments by card" that appear next show how specific cards held by player B support or negate the best plan. If there are enough negative adjustments, the result can become negative, which means the plan that was originally the second best plan becomes the best plan. (Have I lost you yet?) Actually, this will seem a lot less complicated when you look at the answers, so don't spend a long time pondering what I just said and just read the answers.
Oh, one word of caution for anyone who did understand the previous paragraph: the adjustments by card are "semi-linear"; in other words, they're accurate when you have six full decks but will gradually change as you get deeper into the deck. Hence, don't try to extrapolate the percentages over a half-played deck. There are a few answers where I mention, for example, that the answer would be different if fewer decks were in use, but this information was derived by asking the program -- with FBP, you can test the percentages by changing the number the decks in use or varying the rules on surrendering, doubling down, splitting after doubling down, splitting aces, even dealer hits on "soft 17s". You can also test different stop counts (both soft and hard) and see how cards that have left the deck affect the percentages. (Note: I am not marketing this program. The resemblance between the previous two sentences and an actual commercial is purely coincidental.)
(1) Stay. FBP calculates a base pct is 0.083 in favor of hit. The adjustments by card calculated by FBP are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
+.092 |
+.047 |
-.001 |
-.054 |
+.143 |
-.215 |
-.149 |
-.069 |
-.026 |
-.039 |
To do the math, start with the base pct, then factor in the adjustments for Player B's cards. In this example, .083 - .215 - .069 is less than zero, so you should stand instead of hit.
To change the problem slightly, if your 16 count had been a 10 + 6 instead of a 9 + 7, the base pct changes to .326. (If you can figure out how to derive the .326 from the above percentages, give or take a rounding difference, you have an excellent grasp of what is going on.) The adjustments by card change to:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
+.093 |
+.047 |
-.001 |
-.053 |
+.144 |
-.213 |
-.148 |
-.068 |
-.026 |
-.038 |
You'll note these adjustments are close to the adjustments for when you hold 9 + 7, but not exactly the same. (For you honors students, this is an example of what I meant when I said the adjustments are "semi-linear".) Now, assuming the same 5 + 3 for Player B, you should hit: .326 - .213 - .068 > 0. However, if Player B has 5 + 4, you should stand: .326 - .213 - .148 < 0.
To summarize, when you have a 16 count and dealer shows 10, 5s and 4s most affect the basic strategy, which is to hit. Note that 6s favor the hit; for example, if you get to 16 by drawing 6, 4, 6, you should hit now. In contrast, you should stay after drawing 7, 5, 4.
(2) Hit. The base pct is .182 in favor of surrender. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
-.111 |
-.093 |
-.076 |
-.058 |
+.250 |
+.183 |
+.110 |
+.075 |
+.037 |
-.005 |
When the dealer shows a 10, hands with a 15 count are borderline hands for surrendering. Cards on the table in the 7 through 10 range are helpful to you, since they improve the odds you won't bust when you hit.
(3) Hit. The base pct is .028 in favor of stay. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
-.209 |
+.115 |
+.098 |
+.133 |
+.121 |
+.108 |
+.098 |
+.104 |
+.022 |
+.034 |
The 10s are clearly the key card when you have a 12 count against a dealer 4; moreover, when your 12 consists of a deuce and a 10, the decision on whether to hit or stay is close to a toss-up. In this example, your 10 plus the 10 held by player B makes it a good hit.
(4) Hit. The base pct is .641 in favor of hit. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
+.206 |
-.118 |
-.156 |
-.142 |
-.131 |
-.116 |
-.103 |
-.024 |
-.011 |
-.035 |
To support changing the basic strategy, there would have to be fewer decks in use or you would need to see more cards in the 4 through 9 range without any offsetting 10s; for example, the answer to this problem would be stay if you were playing with three decks instead of six. When six decks are in use, situations where you stand on a 12 count versus a dealer 3 should be rare.
(5) Hit. The base pct is .573 in favor of stay. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
-.205 |
-.117 |
+.215 |
+.207 |
+.194 |
+.179 |
+.051 |
+.017 |
+.017 |
+.050 |
You might think the only hands where the basic hit/stay decision can vary from basic strategy are the 12 and 16 counts, but it turns out that isn't so -- here is a 13 count where the correct play does not follow basic strategy. True, this is an exceptional case, as it required four 9s and 10s (the cards that can bust you) to justify the hit.
(6) Hit. The base pct is .089 in favor of double down. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
-.114 |
-.086 |
-.226 |
-.141 |
+.094 |
+.164 |
+.200 |
+.195 |
+.156 |
+.119 |
With a 13 count, 7s and 8s are obviously good cards for you, so it makes sense that seeing 7s or 8s in other players' hands would hurt the double down option. Seeing 9s and 10s on the table also hurts the double down option because it means the dealer is less likely to bust -- an important consideration when you're thinking about a double down, and especially important when you double down with a soft hand.
(7) Hit. The base pct is .197 in favor of double down. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
-.096 |
-.065 |
-.031 |
+.153 |
-.004 |
+.050 |
+.067 |
+.062 |
+.042 |
+.125 |
With a few 8s, 9s, or 10s on the table, the odds of a dealer bust are reduced enough to where hitting is a better play. This reinforces a key point in the answer to the previous question: the probability of dealer busting is a major consideration when doubling down with a soft hand.
(8) Double down. The base pct is .229 in favor of hit. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
+.107 |
-.126 |
-.142 |
-.142 |
-.146 |
-.136 |
+.131 |
+.101 |
+.065 |
-.038 |
With a soft 17, a double down is just about automatic when the dealer shows a 3 through 6, and there is a decent chance it is justified when the dealer shows a 2 as well. If you do double down, the cards that are of no use to you are the 5s through 9s, so it is good to see that Player B has two cards in the 5 through 9 range. That is enough to make doubling down the best play.
(9) Double down. The base pct is .174 in favor of stay. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
+.138 |
-.124 |
-.173 |
-.163 |
-.198 |
-.239 |
-.132 |
+.260 |
+.178 |
+.040 |
These soft 18s can be really tricky. In this hand, where you have a soft 18 vs. a dealer deuce, you'd think seeing aces, 2s or 3s on the table would be bad, but in fact it's good -- fewer low cards in the deck increase the dealer's chance of busting. Yes, the same cards would improve your hand as well, but if you double down, you'll get only one chance to draw an A, 2, or 3. On the other hand, the dealer, with only a 2 showing, will draw at least two more cards, maybe more. Hence the low cards are more helpful to the dealer than to you. Once again, we see that the likelihood of dealer busting is a key consideration when doubling down with a soft hand.
(10) Stay. The base pct is .282 in favor of hit. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
+.069 |
+.015 |
-.072 |
+.004 |
+.101 |
-.019 |
+.000 |
-.177 |
-.100 |
-.032 |
It is interesting to compare the above adjustments with the adjustments by card for the previous answer. In this case, the dealer count is 1 or 11, so there is much less chance of a dealer bust. The grim truth is, your 18 count in this situation figures to lose about 55%, and so it is generally better to hit, hoping you get lucky and end up with a count in the 19 to 21 range. With that in mind, it is clear that the 3s and 2s are important to you on this hand, and in fact all it takes are a few 2s, 3s or 8s to change the best play from a hit to a stay. (If you're wondering why 8s make a hit less appealing, well I'm surprised myself, but FBP shows that an extra 8 makes a dealer bust more likely.)
(11) Hit. The base pct is .423 in favor of splitting. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
-.101 |
-.208 |
-.169 |
+.134 |
+.188 |
+.199 |
+.155 |
+.099 |
+.013 |
-.002 |
When the casino does not allow doubling down after splitting, the rule of thumb on when to split 3s and 2s is: split if the dealer shows a 4 through 7, else hit. That's actually a pretty reliable rule. In this example, I managed to create an exception to the rule by loading player B with high cards, but situations when the split is not correct should be rare -- and don't even think about doing anything else if the casino allows doubling down after splitting.
(12) Surrender. The base pct is .332 in favor of splitting. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
+.158 |
+.171 |
+.044 |
-.130 |
-.058 |
-.072 |
-.062 |
-.213 |
-.179 |
-.122 |
Who says you should always split 8s? Of course, if surrenders aren't allowed, it would be best to split the 8s here. Also, if doubling down after splitting is allowed, it is better to split, since the double down possibility if you draw a 3 on either 8 more than offsets the edge you get by surrendering. So I suppose that, all things considered, you can't go too far wrong by always splitting 8s, as the exceptions to the rule will be rare.
(13) Hit. The base pct is .347 in favor of splitting. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
-.115 |
+.092 |
-.095 |
-.062 |
+.053 |
+.173 |
+.116 |
+.096 |
+.070 |
+.030 |
///. ///
(14) Split. The base pct is .500 in favor of hitting. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
-.048 |
+.000 |
+.354 |
+.309 |
+.194 |
-.072 |
-.170 |
-.239 |
-.164 |
-.023 |
Dealer 7s are schizophrenic cards in blackjack. In most situations, they are unfavorable cards for the player, as they don't bust the dealer too often. However, dealer 7s are favorable cards when splitting small pairs, as there is a good chance the dealer will hit 17 and have to stop there. So, the player splits the small pair, hoping to beat that 17 count.
Well, then, if this plan generally works with a dealer 7, are there situations when it also works with a dealer 8? The answer is yes, although rarely. Splitting can be justified when the deck is short in small cards, especially 2s through 4s. On the other hand, seeing 6s through 8s weigh heavily against the split option - these are the cards with the best chance to bust the dealer, while the 7s and 8s would set the player up for a favorable double down.
(15) Hit. The base pct is .631 in favor of hitting. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
+.021 |
+.130 |
+.167 |
-.179 |
-.184 |
-.166 |
+.097 |
+.039 |
+.008 |
-.006 |
Splitting a pair vs a dealer 8 doesn't quite work for this particular hand, although it comes close - one more card in the 5 to 7 range would be enough to change the result. There is a lot going on in this hand, however (certainly more than may be apparent at first glance), so let's look at it more carefully:
First, note that the split create two 7-count hands, which almost matches the dealer's 8-count hand. Since the counts are so close, the favorable cards for both the player and the dealer are also mostly the same. As a result, you see some card adjustments that seem to go against intuition: 3s and 4s, which would set the player up for a double down, also help the dealer, since they reduce his likelihood by busting - and so you see the adjustments favor hitting over splitting when 3s or 4s are out of the deck.
Another key point is that the split breaks up a 14-count hand - not a good hand as a rule, but it would be better than a 7-count hand if the next card is a 5, 6, or 7. That's why seeing 5s, 6s, and 7s out of the deck help the split option, although we see that, in a 6-deck game, it takes a fair number of them to justify making this play.
(16) Split. The base pct is .789 in favor of splitting. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
-.151 |
-.107 |
-.046 |
-.222 |
+.068 |
+.177 |
+.177 |
+.259 |
+.255 |
+.066 |
Since splitting 4s turns a not too terrible 8-count hand into two somewhat questionable 4-count hands, basic strategy recommends the split only when the dealer is showing a 5 or 6. The FBP adjustments show you will almost never go wrong by sticking with basic strategy in this case, as the base percentages are always fairly high. So, split the 4s against a dealer 5 or 6, hit against the other cards, and you will almost always be making the correct play.
(17) Stay. This one is for the members of a radical fringe who suggest it may sometimes be better to split 10s against a dealer 6, even if it means watching everyone leave the table after you do it. Okay, here's the analysis: the base pct is 6.864 in favor of stay. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
+.283 |
+.178 |
+.077 |
-.045 |
-.138 |
-.318 |
-.322 |
-.322 |
-.272 |
+.047 |
The 2 through 5 cards have decent negative coefficients, but it would take a ton of them to offset that base percentage. If you are playing with one or two decks, situations may occasionally arise when splitting is justified, but with 6 decks the possibility is too remote to worry about. (On the other hand, those of you in the radical fringe may be pleased to know that in this example it is correct to split if you are playing with one deck instead of six.)
(18) Double down. The base pct is .320 in favor of hitting. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
+.187 |
-.073 |
-.141 |
-.143 |
-.121 |
-.121 |
-.051 |
-.043 |
-.119 |
+.050 |
Doubling down with a 9 count is usually the best play when dealer shows a 3 through 6. As this hand shows, sometimes it is the best play when dealer shows a 2 as well. A few cards in the 2 through 9 range is enough to change the result (although it should be noted a 10 would weigh heavily against the double down option).
(19) Double down. The base pct is .981 in favor of hitting. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
+.166 |
+.095 |
+.044 |
+.019 |
-.011 |
-.203 |
-.188 |
-.242 |
-.182 |
-.016 |
This hand shows that doubling down with an 8 count is rarely correct but not out of the question, even with 6 decks. If there are enough cards showing in the 2 through 5 range, doubling down is the correct play.
(20) Double down. The base pct is .694 in favor of stay. Adjustments by card are:
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
A |
+.215 |
+.110 |
-.005 |
-.085 |
-.118 |
-.297 |
-.257 |
-.264 |
+.073 |
-.023 |
As with the previous hand, here is a double down opportunity that probably seems surprising. Certainly you don't want to tinker with a 19 count as a rule, but if you have a "soft 19" against a dealer 6 and the deck is light on 3s, 4s, and 5s, the double down can be your best percentage play.
That concludes my survey of some of the more difficult decisions in blackjack. Please note I'm not doing any "card counting" to arrive at my decisions, just factoring in what I see in the other hands. As for how much of an advantage is gained by knowing how to handle some of these situations, well, I don't know -- that's a project in itself. However, I think it is likely that knowing when to hit or stand on 16 against a dealer 10 (question #1) would have the biggest impact in the long run, for two reasons: (1) the scenario occurs fairly often, and (2) one or two key cards can be enough to change the decision. Good luck at the tables, and let me close with the following sound advice (from the FAQs at www.conjelco.com:) If you are card counting, sit where you are the last to play, so you can see more cards before making a decision. If the dealer is flashing, sit where you can best see his hole card. If you are playing at Rio, sit where you have the best view of the waitress.