Made famous in books and movies, card counting is considered cheating, at least by casinos. In most states (but not New Jersey), known practitioners are banned. The wagering of card counters assumes a clearly recognizable pattern over time, and Johnson was being watched very carefully. The verdict: card counting was not Don Johnson’s game. He had beaten the casinos fair and square.
Card counting is not cheating, at least if you can do it without an external device. That's like saying that you can play this game but only if you don't think about it really hard. Even with card counting the casinos have a slight edge against you. They swap the shoe out frequently so that you have to reset your count.
The reason it's not illegal in NJ is because someone sued them and won. It should be legal everywhere.
As of January 2012, there are no federal, state or local laws which prohibit card counting in the United States as long as no external card counting device or person assists the player in counting cards.
BUT:
In all parts of the United States, with Atlantic City being the sole exception, casinos may ban any player for any reason including card counting as long as the Federal laws against discrimination based on race, creed, sex, national origin, age, or physical disability are not violated.
--
I think that a casino should be able to kick out anyone that they want for any reason, including card counting, being extremely lucky, being a jerk, etc...
Yeah this article is awfully written. Its portrayal of counting as even possibly unfair ("he had beaten the casinos fair and square [by not counting]") is ridiculous, and it does a horrendous job explaining his method. His method isn't even addressed until half-way through the article, the article is littered with totally unnecessary comments like "He plays perfect cards" (if you're not counting, every hand's decision should be set in stone), and the actual method they describe isn't logically consistent. At first they make it sound like he won by bargaining down special rules to give himself a substantially greater discount than the house's edge, but then they go on to say that he won $2 million later on without the discount (despite the house having a fractional edge), without further explanation. They've already made it clear that this guy plays to win rather than to gamble, so he obviously didn't win it by pure luck. So we're clearly missing something here...
It's not illegal, but how do you define cheating - is it by laws, or by rules set by the game runner?
For example, in football (soccer) it's cheating to punch the ball into the goal... but the associations that decide on the rules could make this perfectly fair play next year, just by deciding that they no longer define it as cheating.
Because of the recession casinos are desperate for high-rollers. To lure them in they offer perks. Some of those perks include slight modifications to the rules and a "loss discount" -- for example: losing $500k only costs you $400k.
This guy negotiated rules that changed his odds to 50/50. Then he negotiated an 80% loss discount, which meant for each $1 of upside, his downside was $0.80.
So to pull this off, you need $1m to put down, great negotiation skills, even better blackjack skills, good luck, and a very sophisticated understanding of stats.
No, that still doesn't make sense. The loss discount was on a per-trip basis, not per hand, so basically if at the end of the week you were down $100k, you only owed $80k.
The rules were generous but NOT totally even. The house still had around 0.25%, which is low, but not unheard of. Even on the Vegas strip you can find Blackjack games open to the general public under 0.50% house edge. Of course, that's
with optimum general strategy, not "playing your hunches", which could easily open the house edge to 10% or more depending on how dumb you're playing.
My guess is that he was card counting, but not with a traditional system, and he wasn't using it to size his bets, just to make strategy decisions, which would be harder to detect.
The odds of beating 3 separate casinos, over a reasonable number of hands, even against a very low house edge, are quite small.
“They began offering deals that nobody’s ever seen in New Jersey history,” he told me. “I’d never heard of anything like it in the world, not even for a player like [the late Australian media tycoon] Kerry Packer, who came in with a $20 million bank and was worth billions and billions.”
Kerry Packer's gambling is pretty legendary.
There's a story about how he was in a high-roller room in Los Vegas and there was a Texan (oil?) millionaire boasting about how big his ranch was.
Packer was annoyed at how noisy he was, so he walked over.
Packer: "So how much is this property worth then?"
Texan: "'bout $20 million"
Packer (pulls out a coin): "toss you for it"
Apparently the Texan didn't like that idea much...
Packer successfully invested a lot in building casinos in Australia and Macau. His son has taken over his empire and invested even more, though not as successfully.
There's a lot in this article that doesn't add up. For example this quote:
"So my philosophy at that point was that I can afford to take an additional risk here, because I’m battling with their money, using their discount against them."
If he's already up significantly (battling with their money) the discount isn't likely to come into play. And he's still playing a negative expectation game so every hand he plays he should expect to give back a little of his gain.
“You’d never lose the million. If you got to [$500,000 in losses], you would stop and take your 20 percent discount. You’d owe them only $400,000.” ... So when Johnson got far enough ahead in his winning sprees, he reasoned that he might as well keep playing.
I don't quite see how this makes any sense - if you get far ahead in a winning spree, the value of your discounted loss diminishes significantly... doesn't it? For instance, if you won $2 million, the discount is now $100k on a $2.5 million loss, which is only 4% (much smaller than the initial 20% discount of $100k on a $500k loss)
The article is a bit confusing. If I take it correctly, a few casinos offered him nearly 50:50 odds, and a discount on his losses if he lost more than ~500k. In other words, a great deal, worth ~$50k. And then he proceeded to have amazing games, winning millions by sheer luck. The article doesn't talk much about the luck this requires, and one wonders if he does have something else going on.
As far as the "luck" goes nothing is recounted of the nights when he didn't win big. This all took place over 4 months and while he didn't gamble every night he didn't just gamble once at each place.
Probably his nights while he had the discount followed a normal distribution with most of them break evenish but as explained losses were cut off around 400K and winning streaks were allowed to spiral.
I don't really see luck being a major factor. In the long run he's going to have a blockbuster night and then get kicked out of each place just like he did.
The article makes it clear that he's very good at the odds of Blackjack. It was a bit confusing when it described the difference between the odds-sheets given by the casino and his method. But, basically, he follows optimal betting technique for every card played.
The negotiation on the rules of the game is key. For example the difference between a 'soft 17' and a 'hard 17' is worth a few percentage points, and those points are valuable.
hey guys, i actually think he might have positive expectation:
he negotiated a .25% houe edge (roughly half of normal perfect play) and if he loses 500k he gets 20% back, each session independent.
check this analysis. he is +EV by martingaling his wins - 7/8 times he loses 400k with a 20% discount (400k x 7 x .80 = 2 240 000), 1/8 times he wins 400k x 8 with no reverse-discount = 3 200 000, so that's a mil in EV. if he pushes his martingale as far as he can his expectation grows superlinearly, which is why he martingales his wins until they cut him off.
is this math right? if he was -EV, the house would let him keep playing, hence telling him he can continue to play under normal rules. note he refused.
update: an easy way to see this (gross oversimplification) is if he plays only one hand/session he stands to win 100% of the money 49% of the time and loses 80% of the money 51% of the time.
This explanation seems most consistent with the limited information in the article.
We don't know whether he had several -$400K sessions before his big run. Gamblers and non-gamblers talk more about upswings than downswings.
There could be some other unmentioned factors that aided him a little, but the capped downside, a lucky run, and selective reporting are probably a sufficient explanation.
It depends on how he expects to be taxed. If this is his only session during the year, he actually wins 60-70% of the money vs losing 80%. So he needs to either be way ahead or way behind from other gambling activity for this to work out the way you described (assuming he's a US citizen).
It seems that every once in a while an enticing story comes out about a person (or team) who beats the house and wins big.
I spent a short time in the 'gaming' industry building electronic slots and other types of games. The word on the street was that the industry encouraged these types of stories. And, while maybe they didn't directly sponsor them, they looked favorably on them. These types of stories perpetuate ideas of the little guy beating the house.
The profit of the gaming industry comes from the average person thinking that they can beat the house, when, the fact they can't. When the average person begins to believe that they can't win, casino profits go down. As such, casinos put billions of dollars into R&D and marketing to give the average person the illusion that they can win.
I wasn't involved long enough in the gaming industry to be an expert, and I'm sure there are some exceptions. But, generally, to average people, of which I would classify 99.9% of the population, even those of us terribly smart people, the house advantage always wins.
The description of his odds system did not make a lot of sense to me; especially in light of the statement that he does not count cards. Can anyone elaborate?
"Many casinos sell laminated charts in their guest shops that reveal the optimal strategy for any situation the game presents. But these odds are calculated by simulating millions of hands, and as Johnson says, “I will never see 400 million hands.”
More useful, for his purposes, is running a smaller number of hands and paying attention to variation. The way averages work, the larger the sample, the narrower the range of variation. A session of, say, 600 hands will display wider swings, with steeper winning and losing streaks, than the standard casino charts."
Here's the simplest example I can think of. Basic strategy says to split 8s, even if the dealer is showing a face card or an ace. Statistically, you are most likely to lose this hand whether you stand, hit or split it.
By splitting them (following strategy) you give yourself the best odds of your choices, and according to probability, this makes it a better option in the long run. However, by splitting them, you are doubling the money you have risked on them, and therefor if you are only playing a single hand and then never touching blackjack again, you are basically risking twice as much money on a hand that, more often than not, you will lose.
The charts are maximizing EV without taking into account the discount he negotiated. With the loss discount, it becomes more profitable to increase short term variance beyond what the chart strategies would lead to.
The article is clear on only one point, but it's not an explanation for his winning. That point is that if he loses $500K, he only has to pay $400K of it. I'm pretty sure that if you bet $100K a hand, and stop whenever you hit the first of +$500K or -$500K, and get a $100K rebate if you hit the lower number ... well, the whole plan would seem to have a positive expected value. And perhaps the same would be true even with a bet increment of $10K or less,
Second, it is strongly implied (without details being given) that he has negotiated rules giving him an unusually favorable expected value per hand -- either a very slightly negative one (which would explain why Tropicana is willing to keep playing with him), or perhaps even a positive one that they keep overlooking. The only rule I saw in there that sounds odd to me is "calling the hand" -- is that a recent twist to blackjack or something?
> It was the dealer’s turn. He drew a 10, so the two cards he was showing totaled 15. Johnson called the game—in essence, betting that the dealer’s down card was a seven or higher, which would push his hand over 21. This was a good bet: since all face cards are worth 10, the deck holds more high cards than low. When the dealer turned over the house’s down card, it was a 10, busting him. Johnson won all four hands.
Pretty sure that by "betting that the dealer’s down card" it means that this was the logic behind his betting on the four hands, not that there was a seperate bet on it.
"Calling the hand" most likely refers to the kind-of-tradition of cheering on what you want ("come on facecard... COME ON FACECARD!!")
The line that annoyed me most in this was about card counting, saying
> "The tactic requires both great memory and superior math skills."
Not honestly true, at least about the maths skills. Memory... isn't how I'd describe it, though I suppose it's sort of right.
In my opinion, the most difficult thing is concentrating on multiple things at the same time (1. Keeping the running count 2. Counting how many cards have been played 3. Following the game itself and deciding what to do 4. Chatting with dealer / other players) - so this can perhaps be called "memory" as you have to remember these things all at the same time.
But for each thing you need to remember, it's a very simple thing on its own. Counting isn't about remembering the order of every card that's come out, it's not even about remembering what card has come out.
If you were to watch a video of a Blackjack game, i.e. you were left in peace and not doing anything yourself, few people would be incapable of counting the cards.
There's also remembering your strategy index tables. True, that's not a lot of numbers - some might use as few as 18 indices - but still: You're keeping in mind at the same time (a) the count, (b) a set of basic strategy rules appropriate for your specific game (c) a table of strategy variance index numbers appropriate for your specific game, (d) a deck depth estimate. And probably a few other relevant numbers.
I skimmed over the comments, and I'm surprised to see no mention of it here. Maybe I missed it.
The house always wins, and they still won. This is, for each of them at just a few million, very cheap advertising. Consider how poker/holdem was hyped during the last decade, this is just the same in a different setting.
They will easily win those few millions each back and more. For every smart person such as this guy, there are thousands of idiots out there. The article itself mentions they're trying to lure in high-rollers. This looks rather obvious.
Thus, the title, how Atlantic City supposedly "got broke" by a man, seems very misleading in this context.
Even taking into account his negotiated edge, which is impressive, it isn't enough mathematically to account for such substantial winnings over such a short period of time. I agree with what others have said and think he must either have had a counting system or had a terrific run of luck.
Great runs are rare of course, but not unheard of. The reason people don't hear about them often is that very few players play at such a sophisticated level to minimize the house advantage to a paper-thin margin, and even fewer do so at a high-stakes table where this would make big news.
Classic ringer's game: they underestimated his ability, including the meta-ability to calculate odds and stay unemotional. Most players, even high rollers, get into the game and start to make hunch bets as play goes on. He was disciplined enough to trust the math and not waver his strategy.
I thought casinos were mostly fronts for money laundering, but since this has a story to it, there is credibility that a growth industry like gambling has real credibility in the startup scene. Therefore, there should be more gaming startups in YCombinator.
Calling card counters cheaters is like calling people who get good grades on tests cheaters because they discovered the solution to the problem during the test with their mind by eliminating the wrong answers using statistics and probabilities.
Card counting is a code phrase that translates to "if you don't let the house win, we won't let you play".
What is surprising is how easy it is to compute the odds..its just permutations and combinations..not that hard its a 100 level math course in most colleges.
What makes it different is that we needed two things to leverage the $1 million he put up per Casino and the Casino management being fool-hardy enough to believe that they computed the odds on the change in rules and discounts correctly.
It would be like say oh stacking the deck in that the founders get one class of stock and everyone else another class which allows the founders to retain ownership control of a start-up.
You do not need to card count as he changed the rules to only have hand shuffled six decks in the shoe..I can with a certain memory system compute the odds on cards dealt from that shoe and so can you..its not hard..its simple math..
[+] [-] po|14 years ago|reply
Made famous in books and movies, card counting is considered cheating, at least by casinos. In most states (but not New Jersey), known practitioners are banned. The wagering of card counters assumes a clearly recognizable pattern over time, and Johnson was being watched very carefully. The verdict: card counting was not Don Johnson’s game. He had beaten the casinos fair and square.
Card counting is not cheating, at least if you can do it without an external device. That's like saying that you can play this game but only if you don't think about it really hard. Even with card counting the casinos have a slight edge against you. They swap the shoe out frequently so that you have to reset your count.
The reason it's not illegal in NJ is because someone sued them and won. It should be legal everywhere.
[+] [-] dantheman|14 years ago|reply
As of January 2012, there are no federal, state or local laws which prohibit card counting in the United States as long as no external card counting device or person assists the player in counting cards.
BUT:
In all parts of the United States, with Atlantic City being the sole exception, casinos may ban any player for any reason including card counting as long as the Federal laws against discrimination based on race, creed, sex, national origin, age, or physical disability are not violated.
--
I think that a casino should be able to kick out anyone that they want for any reason, including card counting, being extremely lucky, being a jerk, etc...
[+] [-] dsrguru|14 years ago|reply
[+] [-] corin_|14 years ago|reply
For example, in football (soccer) it's cheating to punch the ball into the goal... but the associations that decide on the rules could make this perfectly fair play next year, just by deciding that they no longer define it as cheating.
[+] [-] kiba|14 years ago|reply
[+] [-] nostromo|14 years ago|reply
Because of the recession casinos are desperate for high-rollers. To lure them in they offer perks. Some of those perks include slight modifications to the rules and a "loss discount" -- for example: losing $500k only costs you $400k.
This guy negotiated rules that changed his odds to 50/50. Then he negotiated an 80% loss discount, which meant for each $1 of upside, his downside was $0.80.
So to pull this off, you need $1m to put down, great negotiation skills, even better blackjack skills, good luck, and a very sophisticated understanding of stats.
[+] [-] TylerE|14 years ago|reply
The rules were generous but NOT totally even. The house still had around 0.25%, which is low, but not unheard of. Even on the Vegas strip you can find Blackjack games open to the general public under 0.50% house edge. Of course, that's with optimum general strategy, not "playing your hunches", which could easily open the house edge to 10% or more depending on how dumb you're playing.
My guess is that he was card counting, but not with a traditional system, and he wasn't using it to size his bets, just to make strategy decisions, which would be harder to detect.
The odds of beating 3 separate casinos, over a reasonable number of hands, even against a very low house edge, are quite small.
[+] [-] gcheong|14 years ago|reply
He plays blackjack.
[+] [-] raldi|14 years ago|reply
[+] [-] nl|14 years ago|reply
Kerry Packer's gambling is pretty legendary.
There's a story about how he was in a high-roller room in Los Vegas and there was a Texan (oil?) millionaire boasting about how big his ranch was.
Packer was annoyed at how noisy he was, so he walked over.
Packer: "So how much is this property worth then?"
Texan: "'bout $20 million"
Packer (pulls out a coin): "toss you for it"
Apparently the Texan didn't like that idea much...
Packer successfully invested a lot in building casinos in Australia and Macau. His son has taken over his empire and invested even more, though not as successfully.
[+] [-] jacques_chester|14 years ago|reply
He later said "You only get one Alan Bond in a lifetime ... and I've had mine".
[+] [-] harryh|14 years ago|reply
"So my philosophy at that point was that I can afford to take an additional risk here, because I’m battling with their money, using their discount against them."
If he's already up significantly (battling with their money) the discount isn't likely to come into play. And he's still playing a negative expectation game so every hand he plays he should expect to give back a little of his gain.
I don't think we're getting the real story here.
[+] [-] fragsworth|14 years ago|reply
“You’d never lose the million. If you got to [$500,000 in losses], you would stop and take your 20 percent discount. You’d owe them only $400,000.” ... So when Johnson got far enough ahead in his winning sprees, he reasoned that he might as well keep playing.
I don't quite see how this makes any sense - if you get far ahead in a winning spree, the value of your discounted loss diminishes significantly... doesn't it? For instance, if you won $2 million, the discount is now $100k on a $2.5 million loss, which is only 4% (much smaller than the initial 20% discount of $100k on a $500k loss)
[+] [-] alpad|14 years ago|reply
[+] [-] Steko|14 years ago|reply
Probably his nights while he had the discount followed a normal distribution with most of them break evenish but as explained losses were cut off around 400K and winning streaks were allowed to spiral.
I don't really see luck being a major factor. In the long run he's going to have a blockbuster night and then get kicked out of each place just like he did.
[+] [-] DanBC|14 years ago|reply
[+] [-] krschultz|14 years ago|reply
[+] [-] dustingetz|14 years ago|reply
he negotiated a .25% houe edge (roughly half of normal perfect play) and if he loses 500k he gets 20% back, each session independent.
check this analysis. he is +EV by martingaling his wins - 7/8 times he loses 400k with a 20% discount (400k x 7 x .80 = 2 240 000), 1/8 times he wins 400k x 8 with no reverse-discount = 3 200 000, so that's a mil in EV. if he pushes his martingale as far as he can his expectation grows superlinearly, which is why he martingales his wins until they cut him off.
is this math right? if he was -EV, the house would let him keep playing, hence telling him he can continue to play under normal rules. note he refused.
update: an easy way to see this (gross oversimplification) is if he plays only one hand/session he stands to win 100% of the money 49% of the time and loses 80% of the money 51% of the time.
[+] [-] gojomo|14 years ago|reply
We don't know whether he had several -$400K sessions before his big run. Gamblers and non-gamblers talk more about upswings than downswings.
There could be some other unmentioned factors that aided him a little, but the capped downside, a lucky run, and selective reporting are probably a sufficient explanation.
[+] [-] cityhall|14 years ago|reply
[+] [-] ap22213|14 years ago|reply
I spent a short time in the 'gaming' industry building electronic slots and other types of games. The word on the street was that the industry encouraged these types of stories. And, while maybe they didn't directly sponsor them, they looked favorably on them. These types of stories perpetuate ideas of the little guy beating the house.
The profit of the gaming industry comes from the average person thinking that they can beat the house, when, the fact they can't. When the average person begins to believe that they can't win, casino profits go down. As such, casinos put billions of dollars into R&D and marketing to give the average person the illusion that they can win.
I wasn't involved long enough in the gaming industry to be an expert, and I'm sure there are some exceptions. But, generally, to average people, of which I would classify 99.9% of the population, even those of us terribly smart people, the house advantage always wins.
[+] [-] dfc|14 years ago|reply
"Many casinos sell laminated charts in their guest shops that reveal the optimal strategy for any situation the game presents. But these odds are calculated by simulating millions of hands, and as Johnson says, “I will never see 400 million hands.”
More useful, for his purposes, is running a smaller number of hands and paying attention to variation. The way averages work, the larger the sample, the narrower the range of variation. A session of, say, 600 hands will display wider swings, with steeper winning and losing streaks, than the standard casino charts."
[+] [-] corin_|14 years ago|reply
By splitting them (following strategy) you give yourself the best odds of your choices, and according to probability, this makes it a better option in the long run. However, by splitting them, you are doubling the money you have risked on them, and therefor if you are only playing a single hand and then never touching blackjack again, you are basically risking twice as much money on a hand that, more often than not, you will lose.
[+] [-] gibybo|14 years ago|reply
[+] [-] CurtMonash|14 years ago|reply
Second, it is strongly implied (without details being given) that he has negotiated rules giving him an unusually favorable expected value per hand -- either a very slightly negative one (which would explain why Tropicana is willing to keep playing with him), or perhaps even a positive one that they keep overlooking. The only rule I saw in there that sounds odd to me is "calling the hand" -- is that a recent twist to blackjack or something?
[+] [-] corin_|14 years ago|reply
> It was the dealer’s turn. He drew a 10, so the two cards he was showing totaled 15. Johnson called the game—in essence, betting that the dealer’s down card was a seven or higher, which would push his hand over 21. This was a good bet: since all face cards are worth 10, the deck holds more high cards than low. When the dealer turned over the house’s down card, it was a 10, busting him. Johnson won all four hands.
Pretty sure that by "betting that the dealer’s down card" it means that this was the logic behind his betting on the four hands, not that there was a seperate bet on it.
"Calling the hand" most likely refers to the kind-of-tradition of cheering on what you want ("come on facecard... COME ON FACECARD!!")
[+] [-] corin_|14 years ago|reply
> "The tactic requires both great memory and superior math skills."
Not honestly true, at least about the maths skills. Memory... isn't how I'd describe it, though I suppose it's sort of right.
In my opinion, the most difficult thing is concentrating on multiple things at the same time (1. Keeping the running count 2. Counting how many cards have been played 3. Following the game itself and deciding what to do 4. Chatting with dealer / other players) - so this can perhaps be called "memory" as you have to remember these things all at the same time.
But for each thing you need to remember, it's a very simple thing on its own. Counting isn't about remembering the order of every card that's come out, it's not even about remembering what card has come out.
If you were to watch a video of a Blackjack game, i.e. you were left in peace and not doing anything yourself, few people would be incapable of counting the cards.
[+] [-] glenra|14 years ago|reply
(here's an example of the "Illustrious 18" set of strategy index numbers for one counting system: http://bjmath.com/bjmath/tcindex/i18index.htm )
[+] [-] nikcub|14 years ago|reply
[+] [-] grepherder|14 years ago|reply
The house always wins, and they still won. This is, for each of them at just a few million, very cheap advertising. Consider how poker/holdem was hyped during the last decade, this is just the same in a different setting.
They will easily win those few millions each back and more. For every smart person such as this guy, there are thousands of idiots out there. The article itself mentions they're trying to lure in high-rollers. This looks rather obvious.
Thus, the title, how Atlantic City supposedly "got broke" by a man, seems very misleading in this context.
Still, maybe I'm missing something here.
[+] [-] unknown|14 years ago|reply
[deleted]
[+] [-] dkrich|14 years ago|reply
Great runs are rare of course, but not unheard of. The reason people don't hear about them often is that very few players play at such a sophisticated level to minimize the house advantage to a paper-thin margin, and even fewer do so at a high-stakes table where this would make big news.
[+] [-] danbmil99|14 years ago|reply
[+] [-] signalsignal|14 years ago|reply
[+] [-] seanp2k2|14 years ago|reply
[+] [-] 3am|14 years ago|reply
edit: I am completely serious
[+] [-] tucson|14 years ago|reply
[+] [-] maeon3|14 years ago|reply
Card counting is a code phrase that translates to "if you don't let the house win, we won't let you play".
[+] [-] shareme|14 years ago|reply
What makes it different is that we needed two things to leverage the $1 million he put up per Casino and the Casino management being fool-hardy enough to believe that they computed the odds on the change in rules and discounts correctly.
It would be like say oh stacking the deck in that the founders get one class of stock and everyone else another class which allows the founders to retain ownership control of a start-up.
You do not need to card count as he changed the rules to only have hand shuffled six decks in the shoe..I can with a certain memory system compute the odds on cards dealt from that shoe and so can you..its not hard..its simple math..
[+] [-] pellias|14 years ago|reply