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Help!  In my game theory class one of the students wants to know a good book or website that explains how to win at blackjack!  What's your favorite? 
Thomas Egense's profile photoH Vandagriff's profile photoGershom B's profile photoNicolas Esteves's profile photo
The only winning move is not to play.
Edward O. Thorpe is a good reference as one of the early systematic card counters. Card counting should be googled and wikipediaed as well.

I know of no full analysis of blackjack. For fun, there are at least two documentaries of how people beat the house. One of them MIT-like, in,d.bGE
, and,d.bGE

The Caltech one is less well documented, at least as far as I know.
I don't know of any books, but I am pretty sure the best way to win at Black Jack is to own the casino.
Put up a casino, that is best way to win at blackjack or any other gamble games. 
It's possible to win in blackjack in theory, but in practice it requires betting significant different amounts, like minimum when you have no edge, and $200 when you do. So it's very obvious to the dealer and pit manager that you are counting.

In Vegas they just throw you out, in Atlantic city they will start reshuffling every time you bet anything other then minimum bet, while explaining to the angry table that " it's because there is someone at the table doing something that messes up the game, but we can't tell who it is for legal reason", while delivering this speech pit boss will look directly at the counter.

Source: a friend of a friend once tried doing it :-)

But there may be obscure places, like on cruise ships in third world countries and such, where casino's are still naive and you can count in piece.

Commodity trading is much more exciting, legal, and profitable way to make money with your mind then blackjack.
Typical card counting strategies track some proxy of the total extra value in the deck/shoe, in a form easily countable by the human mind. You can win handsomely by those means alone, as the MIT/Caltech teams did.

But they never played an optimum game. As I said, I've never seen an optimum strategy being laid out. I'm reasonably sure +John Baez and his student would most appreciate a mathematically well founded strategy which is as close to the perfect one as possible.
I can make about 50 dollars an hour pretty easily playing blackjack. Problem is, my regular job, less stressful than cards because it is guaranteed money, pays more. So I don't bother improving my blackjack skills. 
Beginners should concentrate first on knowing (ie, having memorized) how to play the "basic strategy" (without card counting) for the particular blackjack rules at a table.   I like the (free) iPhone app "BJ101 Free" for that (I have no connection to whomever makes it).   It doesn't bother with "playing out" the entire hand; it just plays them out far enough so that you can be notified when you made a mistake in the basic strategy.    

I've observed that BJ players in casinos rarely even play the basic strategy correctly.  And of the people who talk about card counting, almost none of them can actually do it. On the other hand, if a person can play the correct basic strategy, say 99.5% of the time correctly at a table with reasonably favorable house rules, BJ is a game that is very favorable when compared to other casino games (although somewhat boring to play).
+Sampo Syreeni They should simply Google for basic strategy and blackjack card counting. Strategy differs slightly depending on house rules. There used took be a web site I think that had everything you needed to know, the list of USA casinos and the games they offer, trip reports, strategy calculators, and software to drill basic strategy and counting.
Don't know or care… but, if you get a chance, read the book: "the eudiomonic pie". It documents the actual adventures of a group of UCSC fringe CS and math researchers in their quest to build wearable (shoes, bras, etc.) analogue computers to beat roulette in Vegas.
Same group I think is mentioned in gleik's chaos.
(Santa Cruz was my alma mater, so have a tendency to remember when it is mentioned)
+Max Mikhanosha That will do if you want to do well in the game. But what if you want to make the single best move every time you make any choice at all?

That's the mathematician's question, and it's far from being as simple as counting "advantages" (of any kind) from the shoe. It's bound to be simpler than chess, but I haven't even seen a fully proficient card counting codebase to date. (Those do have to exist by now, even as open source. I just haven't seen them.)
KL Tah
I don't think Thorp works anymore. Nowadays, you need to think Raspberry Pi mod, in your anti-detector underwear, sending signals through your crotch.
Good point +KL Tah I've long wondered what would happen to casinos if when some sci-fi human enchancements became possible.

So like cyborgs would be banned from craps tables cause of dice control, people with neuro-visual implants would be banned/allowed one use in roulette for their ability to identify imperfections, they would also be banned from blackjack for their perfect memory and calculating abilities. They would be allowed limited time by bandit machines so they did not calculate statistics and later share them with subscribing members of an international union of multi-armed bandit explorers and exploiters.

Casinos may just devolve into chess, poker and sports betting halls of a complexity we could not imagine today.
Thanks so far, everyone!  This student actually plays blackjack regularly and was wondering if my course would help him.  I told him that the principles of game theory and probability theory I'll teach will be useful, but that this game requires a complicated analysis far beyond what we'll get to in this course.

I know the house has an edge on every game, but that it's smaller for blackjack than most other card games, but that if you count cards and start to win they throw you out - or, in the good old days, hurt you. 

"Moreover, Thorp became one of the very few applied mathematicians who risked physical harm in verifying a computer simulation."
For all casino games strategy the two best sites on the net are:
But both are lacking a bit in terms of card counting. Both sites have strategy tables or can generate them for all BJ rules.

This site is created by mathematician Michael Shackleford, he actually won world championship in BJ last year.

Chaos books mention "Eudaemonic Pie" because Ralph Abrams was part of the fiasco.
+John Baez I believe Blackjack is one of the few games where you can actually beat the house if you play optimally. That is why it's so wanted, and why they so easily throw you out -- salted with a lifetime ban, with your neighbouring, competing establishment following it to the letter -- if you're caught "doing them bad math gimmicks".
What is it about geeks and games? Its hard to find a scientist so bitten by gambling. What gene is missing in the CS geek that keeps them from knowing the math they know? Keeps them from seeing the forest for the shiny tree with unicorns underneath?
Geeks and music too! :)

Met Ralph a few times. Lovely, lovely man!!

Randall: one word: math. Two words: ordered universe. Many words: in such an ordered universe you can get hard results, which in this case has to do with hard probability and combinatorics. You pretty much can't be a nerd without liking something to the effect.
Oh wait maybe I misunderstood your point. You think many geeks dont get games?

What about minsky? :)
Causality describes a much larger space than is part of the geek game attraction. I don't see this as a mathematician thing. Just a geek thing. Game theory isn't gambling or dungeons and dragons. There is something separate here. Something uniquely geeky. Autism?

You can have theoretically have an edge in blackjack but not really. Casinos put in multiple decks and do stuff like reshuffling before reaching the bottom and even using machine learning to detect betting patterns of optimal play so they can kick those with a long term edge before they can claim the benefits. Not worth the effort anymore. There are much more better ways to spend your time these days in terms risk+return vs effort per hour .

The only game you can play in a casino still with an edge is the one where the house is basically a market maker: Poker.
I've never entered a casino without playing Bj and I have never exited a casino without more money than when I entered. I have a strategy though: a. Determine to only lose a certain amount after which you must leave b. decide not to spend all day there no matter what happens c. Don't start immediately playing upon entering. Instead check out all the tables and players. Choose your table wisely. d. Don't bother counting cards. Unless you have a big bank, and a lot of time, it's not worth the effort. e. bet smart f. change tables frequently, no matter what

If you know the basic strategy and follow the above rules, it's almost certain you will leave with 50 dollars per hour more than what you came in with. Card counting is very very interesting but nothing more than a hobby / interesting diversion unless u have a boat load of extra cash, time, and desire to play with discipline.
+Deen Abiola is correct. You need a special promotion from the casino on top of a good BJ paytable to have a small egde. First of all, learn to to find RTP% for a given BJ game as this is very important. For instance the new 6:5 BJ that the turists play in LV,  they have no idea what they are up against.
+Matthew Phillips Then you've been lucky. Basic strategy is only a little bit less expensive than European roulette, in the long run you would end up doing just a little worse than break even.
I allow that luck is certainly a factor. But so are the rules I mentioned above.

There is a psychological component to the game as well. Don't let on that you are there for any other reason than to pass some time. You will be targeted otherwise, as other posters have alluded above.

If you aren't ready to admit the psychological component, not sure I can have a rational conversation on this topic.
There's much arrogance in announcing that the only way to win is to not play. There are examples to the contrary. Blackjack being one where the player has a slight advantage but only if play is nearly perfect; the house counts on a large majority of players playing imperfectly. Another example, more rare, is the card game war, which I have seen in Vegas with fair rules; the house counts on "Gambler's Ruin" (a simple random walk is transient), wherein the deepness of their pockets makes the game profitable for them. A third example is poker, where the house charges you a fixed amount per hour to sit at the table, and the game is beneficial to some players but not others depending on skill.

The real reason people play, of course, is exposure to the variance. Risk has value, and the asymmetry of the risk (greater risk for the player than for the casino due to the different bankroles) make it possible for casino games to be win-win. They wouldn't be filled with people if the people weren't getting something out of it!

Here's a nice game to consider. 20 people enter a contest with the following rules: you flip a coin repeatedly (once per minute) and your score is H-T, the difference of the number of heads and tails; if your score is ever -10, you must stop, and you must stop before 1000 minutes passes, and otherwise you can stop when you choose. The person with the highest total wins $500, everyone else loses $10. What's your strategy? It isn't "stop immediately", is it? This is a model of the "slot machine competition" that is unjustly derided by serious gamblers.
+Matthew Phillips 

I found the juxtaposition of rational vs psychological amusing. =) Yes one way to look at it is paying Casinos for the service of hijacking your dopamine reward circuitry. Of course if you talk about it in terms of cost instead of win potential people would be outraged at the expense. Definitely casinos are some of the top appliers of both statistical and psychological research. 

Anyways my point is Basic strategy reduces house edge to about 1%, Long term Sum(winnings) + Sum(costs) ~= 0. Any psychological component does not change this unlike in say Poker. I don't believe anyone can time best time to exit/enter tables without some kind of way to track cards and even then I posted why this is not worth it above.
I started with Thorpes book in the late 90's, but the rules of the game vary from casino to casino, and even within the casino they will vary over time. Back in the days, they used to have a shoe with I forget about 8 decks in it. In order to get better I applied for a job at the casino as a dealer. But they chose to train me for roullette and I wasn't interested and left.

I still played blackjack, but limited my money as circumstances didn't allow me to risk a larger amount. Also I realised I don't have the emotional coolness, the temperament to count.

Finally a few years later they came up with machine shufflers, and up to 75 cards (1.5 decks) towards the end of the shoe is not dealt, as they switch to another shoe.

There are so many factors working against the player, including other idiots sitting down on a table and effing up the game with stupid play, or annoying remarks. I had one old geyser sit down next to me and just start abusing me because I wasn't playing like he wanted me to. As if keeping your cool isn't hard enough!

Making money out of blackjack is hard work. Bacarrat is a bit easier, but I prefer to crack the big one with lotto now :)

Game theory is very interesting. Introduce him/her to all the cognitive biases , including the gamblers ones :)
+Kevin O'Bryant As an interesting aside, in games where the return percentages are extremely close to 1.0 and the variance is relatively low, I've even seen an interesting analysis of why the game can serve as a sort of a savings device for time-incongruent people +John Baez You might like this one as well if you didn't already see it elsewhere.

The analysis starts with "the numbers game", where everybody in a neighbourhood picks a number between 1 and 999, then weekly a number is drawn, and everything but the lottery-maker's minor commission goes to the winning number.

In this case the total pool of lottery numbers is limited enough to make it probable that everybody wins multiple times over their lifetimes if they just keep on playing the game. At something like the typical 96-99% return from a round, people's tendency to discount the future hyperbolically easily undertakes the so called "rational", exponential decay in expected profit from the game.

That means that suddenly the numbers game can be analyzed as a probabilistic savings device, which helps otherwise time-inconsistent individuals save for larger investments: if you keep on playing the game, you can be rather sure that eventually you will win, and not just one time. You will eventually get most of your money back, almost certainly, but since you don't know when, the immediate incentive is to keep investing in the game. Provided that you rationally discount over the irrational, hyperbolic, future value curve that behavioral economics ascribes to you.

When that is done, a person without access to the numbers game would always consume away any free income, even if se in the future e.g. wanted to have a television. Se couldn't save for it -- and empirically does not save for it. But with access to this precise kind of small equal odds lottery, every single hyperbolically discounting participant eventually does get the television, and is incentivized from moment to moment to save towards it, in the form of the weekly outlay towards the game.

That is the kind of counter-intuitive analysis I live for. It's the kind of stuff that totally turns around your preconception of something you already knew. In this case, the idea of the numbers game being a means of ripping of the poor and stupid -- suddenly it surfaces that a certain, precise form of gambling can actually help the poor and stupid accumulate capital where they previously might have been unable to do so. ;)
Playing basic strategy in a casino should get you to 99% return over the long run (where 100% is break-even); the same is true for online blackjack, except: 
1. They use infinite decks, which makes counting useless. 
2. I suspect that they push the odds in your favour (over 100%) for the first x hands as a loss-leader, like a free drug sample. 
So one strategy might be to play x games in a given online casino, then move on... 
Many of the above statements about potential returns provided perfect play to a statistically modeled strategy need to be modified with (at minimum) these two disclaimers:

1. Provided the casino is actually offering the ruleset upon which the statistical model was based (which no modern casino intentionally does, having the dealer win pushes over 17, or disallowing doubles, or severely limiting the bet range, etc. etc. etc.)

2. Provided the casino deals deep enough into the deck or decks (or even has decks --- Google "continuous shuffle machines") that statistical variation will eventually guarantee favorable betting conditions AND that pit critters will not be trained to spot players varying their bets in an effort to catch those conditions

Once you've added in these disclaimers, "BlackJack can be beaten!" claims become next to meaningless. But casinos have every incentive to have people believing the larger claims. Indeed, a stack of money is made by casinos because people still believe they can sit down in Vegas, play basic strategy, and walk away a winner. It is in every casino operator's interest to ensure that these ideas never die. Hence the veritable library of "Beat The Dealer" titles that show you how to "beat" games that no casino, anywhere, has ever actually offered.
I believe that casinos introduced continuous shuffle machines to kill off counting, but found that many people stopped playing and profits went down. Now they're back to 4-8 decks and favourable rules in a bid to give the impression that it's possible to beat the house. 
+Nic Johns You suspicion is wrong. Only a few very small (and out of business) online casinos cheat in anyway. Doing a stupid trick like having customer win in the start is suicide for them if caught due to non-random behaviour. Besides they have no reason to cheat, the casino will win eventually! I have 100% confidence is all the big casino providers: Microgaming, Cryptologic, RTG, Rival, Playtech, IGT NetEnt, 3Dice, Galewind Software ... I have played 50+ days (playtime) at these casinos years ago, when you got free bonuses for playing BJ with optimal strategy. The result, you played up almost even(+/-) in BJ and then you kept the bonus which was from 100$ to 500$ typical. Good days.
"How to Cheat at Everything" by Simon Lovell is my favorite con encyclopedia, however, for a quick and thorough treatment of cheating period, the Modern Con Artist series by Todd Robbins .  Book and DVD series.  There are older books that give more in-depth treatment of the long con (one form of which was the plot for the movie "The Sting") and carnival scams.  +Brian Brushwood who stars in the video series called "ScamSchool" (on youtube, and rev3 for ipod/iTunes) is an awesome resource for bar tricks, and now and then some serious scamming, but always good for free beer.  The British version of "The Real Hustle" which can sometimes be acquired on Buccaneer Harbor gives a gloss version of utterly illegal scams, but features card artist Paul Wilson, a world-class card manipulator - if I remember right the Las Vegas season did do blackjack.  And then, there is the ultimate curmudgeon card God:  Ricky Jay...a man who has a deadly combination of esoteric mental capacity, and an iron-willed almost neurotic fastidiousness for exacting perfection from his art(s), which are many.  
As I'm sure other posters have pointed out, security at casinos is state of the art - cheating in Nevada at a casino is a felony offense with a steep sentence.  Using only your mind is legal but quite frowned upon.  Expect to be invited to leave and not return, from the whole chain, not just the one casino location.  And expect to be recognized for the rest of your life in all casinos once 'caught'.  While none of these resources are exactly what he asked for, he will find plenty more there to appease his urge to get one over.  However Dear Student should remember two things:  first, character is what you won't do, and second, if you can't spot the mark, it's you.  
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