A Blackjack Strategy Guide for Logicians

This page is an attempt at explaining how to win at Blackjack, a popular casino game. I have played Blackjack, and both won and lost. This FAQ explains what I did or didn't do when I won. Read this FAQ if you are decent at logic, i.e., you are a computer programmer, a mathematician, or just someone who can keep an algorithm straight in his/her head.

Always, always, always, ALWAYS double-check anything I say here before you go betting real money. I am not responsible if you lose money because you didn't follow the advice here, or because you followed my advice and I was wrong. I try to be accurate, but this is gambling after all, and luck plays a signal role.

In this FAQ, I explain two components to a winning session of Blackjack. I call these two components "card strategy" and "table strategy". A third component, of course, is luck. If you require explanation about that component, it may be wise to sidestep around the whole Blackjack experience. In this FAQ, I won't go into depth explaining the rules and terminology of Blackjack because there are several excellent websites that already do so, for example:

However, I will explain a few common terms briefly because we will need them for this FAQ, and I want to make sure you and I agree on them. Next, I will explain the optimal card strategy for playing Blackjack. Yes, there is an optimal card strategy. Probabilistically, all it does is reduce the edge the casino has over you. Even with the optimal card strategy, over the long run, the casino will win against you - naturally. More about that later... The optimal card strategy wasn't invented by me - some mathematicians agonised over it. Several websites show this strategy to you as well, for example: My contribution is to make this strategy easier to digest if you're an aforementioned logician. After you've absorbed this strategy, try it out on several online sites, for example: Beware though - several of these sites may play for real money, not fake tryout money. If they ask for any financial information, avoid them. Some of these sites may require you to install software on your machine. Caveat emptor.

Why Blackjack?

If you're in a casino, determined to gamble, then Blackjack and a few other games are your best bet because if you play to strategy, these games have the odds stacked against you the least. Playing slots is gifting money away; on the other hand, you can have a pretty long and decent run with Blackjack. Another allure Blackjack has is that it does force you to think, even if it means regurgitating the optimal card strategy. To me at least, this small amount of thinking is preferable to the mindless mechanics of slots. Finally, unlike poker, Blackjack doesn't require you to compete against other players - all players play against the dealer. Since the dealer works for the casino and plays according to fixed rules, there's little chance of rancour among participants.

Which Blackjack?

Good question. There are actually different versions of Blackjack. Some of them vary because of the rules forced on the dealer. Some of them vary because of the options available to you in certain situations. For this FAQ I will be using Las Vegas Strip rules (I'll explain these rules later). Be very aware that the optimal card strategy is different for different variants of Blackjack. I have chosen to explain the strategy for Las Vegas Strip rules because I know these rules the best, and because I enjoy playing on the Las Vegas Strip.

What is Blackjack?

About time. Blackjack is a card game in which you and the dealer will receive two or more cards. The objective of the game is to obtain cards whose total face value exceeds the dealer without going over 21. As games go, few are simpler than Blackjack - you don't even touch your own cards. All you have to do is decide whether to accept or decline more cards, and occasionally throw in some more money. Below is a smattering of terms you'll find useful.
Term Meaning Comment
2, 3, 4, 5, 6, 7, 8, 9 Cards with those face values. That's it - that's their value.
10, J, Q, K Cards with a face value of ten. In this FAQ, I'll denote them as X (get it? Roman numerals...).
A Ace, face value of one or eleven. In this FAQ, I'll denote it as A. For every ace you are dealt, you get to choose whether its value should be one or eleven.
Hard hand A hand with no As. There's only one way to count the sum of the face values of the cards.
Soft hand A hand with at least one A. There's more than one way to count the sum of the face values of the cards depending on how each A is evaluated.
Dealer The person standing behind the table. Your impersonal opponent. The dealer is a casino employee. He or she is not a particularly excellent player; all he/she has to do is play to the rules, dispense cards and money when appropriate, and not favour anyone including the casino.
Deal The distibution of cards to players and the dealer. Rules vary on how deals are conducted, but in Las Vegas Strip rules, initially, each player gets two open cards, whereas the dealer gets one open card and one closed card.
Hit A request for one more card. You can do so when it's your turn, and you have not exceeded 21 already. The hand signal for a hit is a light thump of your knuckles on the table, or pointing towards your cards.
Stand Declining any more cards. You can do so when it's your turn. The hand signal for a hit is a wave of your hand palm down over the table.
Win Σ ≤ 21 AND Σ > dealer.Σ
The sum of the face values of your cards is less than or equal to 21 but greater than that of the dealer.
Count any aces as you choose. If you win, the dealer returns your bet for that hand and gives you the same amount again as your winning.
Bust Σ > 21
The sum of the face values of your cards is greater than 21.
Count any aces as you choose. If by counting one or more aces as elevens you bust, but by counting them as ones you don't, then you may hit. If you bust, you lose your bet.
Lose Σ < 21 AND Σ < dealer.Σ
The sum of the face values of your cards is less than 21 but is less than that of the dealer.
If you lose, you lose your bet.
Push Σ ≤ 21 AND Σ = dealer.Σ
The sum of the face values of your cards is less than or equal to 21 but equals that of the dealer.
If you push, you retain your bet only.
Blackjack Σ = 21
The sum of the face values of your first two cards is equal to 21.
Essentially, you are dealt an A and X as your first two cards. After this, if you win, you get your bet back, and the dealer gives you another 150% of your bet as your winning. If you push, you get your bet back.
More Actions
Split Increasing the number of hands you're playing when you're dealt a pair. You can do so when it's your turn, and your hand consists of a pair, i.e., (2, 2) or (A, A) or (J, J). Although 10, J, Q, K are each an X, a hand like (K, Q) is not considered as a pair, therefore is ineligible for splitting. The hand signal for a split is spreading your index and middle finger on the table. You must follow up by betting an amount equal to your original bet. Most dealers will understand if you simply put in the additional bet. By putting the additional bet, you're now playing two hands, each with the same amount of money as your original bet. Evaluate each hand afresh, except that neither hand is eligible for a Blackjack. If opportunity arises, split hands may be split again and again, up to a maximum of 4 splits.
Double Doubling your bet and accepting one more hit only. You can do so when it's your turn. The hand signal for a split is simply putting in an amount equal to your original bet. Whether or not you double depends on what your and the dealer's cards are. If a dealer feels like you are playing according to a strategy but you suddenly double when one normally doesn't, he/she may confirm with you.
Surrender Turning in your cards in exchange for half your bet. If you feel you cannot not win against the dealer based on your cards and the dealer's one open card, you may surrender your hand and get half your original bet back. Many casinos may not permit surrenders. Ask your dealer.
Insurance Betting some more money on the dealer's having a Blackjack when he/she has an A showing. If the dealer has an open A, you could bet 50% of your original bet on the dealer having an X as the second card. If the dealer does have an X, then you may lose your original hand, but you get twice your insurance back, thus breaking even. If the dealer does not have an X, you lose your insurance and the rest of the hand plays out however.

That's pretty much all of the terms we need for the rest of this FAQ.

Which Blackjack again?

Las Vegas Strip rules. According to these rules:

Card Strategy

Here, I will present the optimal strategy in a manner that will be digestible easily for a logician, or someone trying to evaluate his/her next move by solving a Boolean equation. A lot of the strategies are motivated by the fact that Xs are the most common card - 16 cards in a deck of 52 have a face value of 10.
Action Hand Condition Comment
Split (A, A), (8, 8) Always A pair of aces sets you in a good position to win two hands, so split. A pair of eights totals a very vulnerable 16, so improve your chances by splitting.
(4, 4), (5, 5), (X, X) Never A pair of Xs is a pretty good hand - don't ruin it. A pair of fours/fives won't improve much on a split because chances are the split hands will end up with vulnerable totals of 14 or 15. On the other hand, if you keep them together, you may end up with a good total of 18 or 20.
(9, 9) dealer.(9|6..2, ?) Split only if the dealer's open card is a 9 or less, but not a 7. Why? That's how the probabilities are, and even though I don't understand it fully intuitively, I acquiesce.
(7, 7) dealer.(7..2, ?) Split only if the dealer's open card is a 7 or less.
(6, 6) dealer.(6..3, ?) Split only if the dealer's open card is less than or equal to 6, but greater than or equal to 3.
(3, 3), (2, 2) dealer.(7..4, ?) Split only if the dealer's open card is less than or equal to 7, but greater than or equal to 4.
Insurance dealer.(A, ?) Never The odds are poor unless you're counting cards, which is not just illegal, but also impossible with the way cards are shuffled these days.
Surrender dealer.(?, ?) Never "Scared money never wins", apparently. If you're an expert, there are situations where it makes sense to surrender, but then you wouldn't be reading this FAQ, would you?
Double dealer.(A, ?) Never You're in bad shape already - don't compound it by betting more.
Σ = 11..10 dealer.Σ < Σ Your hand looks better than the dealer's.
Σ = 9 dealer.(6..3, ?)
(A, 7..6) dealer.(6..3, ?)
(A, 5..4) dealer.(6..4, ?)
(A, 3..2) dealer.(6..5, ?)
Hit Σ ≤ 11 Always You've nothing to lose.
(A, 6..2) Always Remember, if you get a really high card, you can always treat your ace as a one.
Σ = 12 NOT dealer.(6..4, ?) With a 12, you're entering your zone of vulnerability. Hit only if the dealer is in a worse position than you.
Σ = 16..13 NOT dealer.(6..2, ?) You're deep into your zone of vulnerability. Hit only if the dealer is in a worse position than you. There's a good chance you'll lose if you stand, and that you'll bust if you hit.
(A, 7) dealer.(9|X|A, ?) Your cards are decent, but the dealer looks very good. Hit hoping you'll get a high card and can turn the ace into a one or hoping you'll get a really low card and can keep the ace an eleven.

I like to think that my contribution to the knowledge base of Blackjack is that this table represents an algorithm that you can walk through when you get your cards. I've presented the same algorithm, but more compactly in this link. For other versions of Blackjack, modify this table accordingly.

If you're going to play the strategy, play it always. Don't play it sometimes and not play it at others. First, you may upset some more seasoned players (see Table Strategy below). Second and more important, you will mess up the probabilities, almost always against you. For example, you may say, "I can remember the Hit rules and the Split rules, but I won't risk the Doubles." Well, all you'll have done is reduced your income when you do get paid off, while retaining all the risk. In the long run, your money will be drained off faster than that of another player who gets the same cards as you but doubles when called for.

Another common novice-level strategy is "do as the dealer does". You figure that if the dealer plays according to strict rules and the casino always wins in the long run, aping that strategy implies long-term wins for you, right? Wrong. Your situation vis-a-vis the dealer is asymmetric. You have to make all of your plays before the dealer opens any more cards. Therefore, you may have gone and busted before the dealer busted, in which case you lose your bet - because you busted.

Table Strategy

Here, I will present the strategy you should use to persist or desist playing. I will guide you on which tables to pick, how much to bet, etc. There are several components to table strategy - all of them subjective. You could violate each one of these strategic components and still win, but then you'd rely a lot more on luck, which is fickle.

Pick the right table. The first thing you should check before sitting at a table is whether the dealer stands on hard 17s. Anything else reduces your winning probabilities. Many casinos may shut down such tables during "prime time" or retain them for high betters only. Keep searching. Once you have found such a table, find out what the minimum bet is. Usually, this figure is displayed on the table itself. If I am carrying a total of $100 with me, I like to sit at a table where the initial bet is $5 or at most $10 - anything more risks wiping my entire fortune too quickly. Even if you're carrying more money, it may be wise to start small and work your way up depending on how lucky you're feeling.

Pick the right table. The preceding paragraph dealt with objective matters in picking a table. This paragraph deals with subjective matters. I like picking tables that are not in obscure corners, but also not in crowded locales. Obscure tables rob the fun, whereas crowded tables can result in a goading audience. Next, I like to pick a table that has 2-3 vacant spots, not just one. Even more importantly, I like a table that has an open spot as far to the right of the dealer as possible? Why? The more you sit to the right of the dealer, the later you get your cards, but the longer you have to decide your move (even if it means regurgitating the optimal strategy). I like to have time.

Pick the right dealer. All dealers are equally competent, but I like to pick a friendly dealer. Often, I pick a female dealer, not because I get any tangible advantage, but because I like the empathy from a female dealer. Once I sit at a table however, I try to play to discipline - if I ever lose three hands in a row, I cash out. Sometimes you're just on a bad run, and the friendliest smile won't change it. If the dealer changes midway, then I give the new dealer a small number of deals to do me well, or else I cash out. Should you tip the dealer? Entirely up to you. I have never seen it affect any outcome. The best you can hope for when you tip the dealer is a sympathetic tsk-tsk when you lose big-time. At that point, I'd rather have a reserve of money.

Pick the right drink. "Non-alcoholic" usually works best. In most casinos, the drinks are gratis, save for a small tip. Needless to say, the more you drink, the worse your judgement becomes, the better the casinos get at extracting your money. I like to order my alcoholic drink when I have had a strong, solid run. The moment the drink comes, I cash out. There're few things that match the feeling of a drink in your hand and cash jangling in your pocket.

Pick the right players. Avoid tables that are frequented by loud teenagers, inebriated amateurs or reckless betters. These denizens can only hurt your chances by playing the probabilities incorrectly or hustling you. Instead, choose a table frequented by middle-aged guys who look like they're on business. Typically, these guys are all playing to the optimal strategy, which results in least losses to all of you. Once you're at that table, play to strategy always! If you don't, then in their eyes, you're a reckless better or an inebriated amateur. They may get annoyed with you (though they can't do a thing), but the truth is you're hurting yourself.

Pick the right bets. I usually play just the minimums, although if I have had a good run, I might occasionally double the bet. I'd rather do that than move to a higher-bet table because I retain the option to come down.

Pick the right time. Cash out when you've had enough - enough losing as well as enough winning. If you lose three in a row, walk out, catch your breath and try later. Keep an amount in your head for what you consider threshold values. For example, you may carry $100 in cash, and set yourself these limits: "If my cash goes down to $50 or goes up to $175, I'm done." Keep these limits reasonable and stick with them - that's the only way to consolidate your winnings or fight another day. If you win big, pull out your principal and coast on the winnings alone - that way, even if you lose it all, you won't be out of pocket. These rules are simple, but easily forgotten in the heat of play. That's why it's good to set thresholds before you play and strenuously stick to them during play.

Pick the right attitude. It's gambling, for cryin' out loud! Expect to lose, be thankful if you win anything. Don't be greedy, and learn how to spread your time at the tables so as to enjoy yourself the most. My philosophy is: "Even if I lose my entire principal, I'll have played enough to have made the experience worth it. Winning is just gravy."

Anand Natrajan, nuts@anandnatrajan•com