
The Man Who Broke Atlantic City (2012) - Falcon9
http://www.theatlantic.com/magazine/archive/2012/04/the-man-who-broke-atlantic-city/308900/?single_page=true
======
ryandrake
TLDR: No card counting. He negotiated a 20% discount if his losses were to
reach $500K, and negotiated small tweaks to the rules (eligible splitting,
doubling hands) that brought the house edge down to 0.25%. At that point he
was basically playing a 50/50 game with some downside risk protection, and got
lucky with the cards. EDIT: He could do this because Atlantic City is a dump
and is desperate for customers now that Pennsylvania has casinos all over the
place.

~~~
bhahn

        He won’t say what all the adjustments were in the final e-mailed agreement with the Trop, but they included playing with a hand-shuffled six-deck shoe; the right to split and double down on up to four hands at once; and a “soft 17” (the player can draw another card on a hand totaling six plus an ace, counting the ace as either a one or an 11, while the dealer must stand, counting the ace as an 11)
    

The blackjack rules (excluding the discount agreement) mentioned don't seem
out-of-the-ordinary. Most Las Vegas casinos have these exact rules for their
higher minimum tables [http://wizardofvegas.com/guides/blackjack-
survey/](http://wizardofvegas.com/guides/blackjack-survey/).

The house edge of this game (using
[http://wizardofodds.com/games/blackjack/calculator/](http://wizardofodds.com/games/blackjack/calculator/))
is 0.33457. There's no additional player-favorable rule that I can imagine to
which all 3 casinos agreed (like late surrender, a rule I've never seen in a
Las Vegas strip casino) that would account for the ~0.08 difference in house
edge. Like another comment suggested, I think there's a good chance he
intended to count cards when calculating his odds. A simplistic card-counting
strategy ([http://wizardofodds.com/games/blackjack/card-
counting/high-l...](http://wizardofodds.com/games/blackjack/card-
counting/high-low/)) could account for the difference.

~~~
fsk
If you have 20% downside protection in a nearly even odds game, you can figure
out the optimal strategy. Also, he was betting $100k a hand, so he didn't have
to play too many hands before deciding to stop as a winner or take his 20%
loss rebate. (If you have the 20% loss protection, the optimal strategy is to
bet big.)

For example, his downside protection was 20% of a loss of at least $500k. If
he was at -400k, he had no reason to quit; he should keep playing until he was
ahead or at -500k.

Also, casinos previously negotiated 20% loss rebates on a LIFETIME basis. He
negotiated the 20% loss rebate on a PER-TRIP basic, correctly pointing out
that if he was ahead at a casino, he had no reason to return if another casino
also offered the rebate.

The lt;dr summary is: He didn't cheat or count cards. The 20% loss rebate
combined with blackjack being a nearly even game gave him an edge.

You could do the same thing at craps. At craps, there's an obscure rule that
lets you make a bet at true odds after establishing a point, sometimes for 10x
or more of your original bet. If you're playing at a place that offers the 10x
backup bet and the 20% loss rebate, you could do the same thing at craps.

~~~
bhahn
The article implies that the 0.25 house edge was calculated before the rebates
were considered, still leaving the ~0.08 house edge as a mystery. The quote
below follows the quote from my original comment. The author of the article
may have made a mistake, though.

    
    
      When Johnson and the Trop finally agreed, he had whittled the house edge down to one-fourth of 1 percent, by his figuring. In effect, he was playing a 50-50 game against the house, and with the discount, he was risking only 80 cents of every dollar he played.

------
GCA10
Charming story -- but there's plenty of controversy that comes with it. Some
Canadian mathematicians ran their own analysis in 2014 and published it in
Chance magazine, arguing that Johnson's winning prospects weren't nearly good
enough under the terms described for him to have been likely to have achieved
such scores. The full article is behind a $48 paywall, but here's a link to
the start of it:
[http://www.tandfonline.com/doi/abs/10.1080/09332480.2014.890...](http://www.tandfonline.com/doi/abs/10.1080/09332480.2014.890867)

Meanwhile, Elliot Jacobson, a guy with his own academic pedigree (U of Arizona
Ph.D. in math; former Ohio University asst/assocmath professor) has published
a defense of Johnson's claims and a counter-rebuttal to the Canadians.
Jacobson now runs a gambling-consulting firm. His rebuttal is here:
[http://apheat.net/2014/03/25/fact-checking-an-article-on-
don...](http://apheat.net/2014/03/25/fact-checking-an-article-on-donald-
johnson-in-chance-magazine/)

.

~~~
Falcon9
Jacobson's rebuttal is perhaps more fascinating than the Atlantic article,
though I think the context of the article is necessary. Details such as:
Johnson would coax two or three dealer errors per day in play, valued at
+$200,000 per day; or that the Canadian mathematicians took some strange
shortcuts in modelling or running simulations.

~~~
ikeboy
How do you coax a dealer error?

~~~
_Eliot_Jacobson
Johnson was very aggressive and belligerent at the table. He made the dealers
and pit nervous and agitated. For example, he would sometimes half-way signal
his intention and if the result was not to his liking, dispute that he had
asked for a hit card. He would pound the table and shout. And the casinos were
willing to give him the benefit of the doubt because he was such a high-
roller.

~~~
GCA10
Fascinating! Echoes of Phil Ivey arranging to play baccarat with a deck and
dealer of his own choosing ... and the casino agreeing to it until learning
that Ivey thus had a bigger edge than expected.

------
jere
Seems fairly simple to me. Tightening up the odds and the trip-to-trip 20%
discount means he would be seeing a nearly 10% return on every visit. Those
odds don't sound like good business.

Re: the card counting thing, is it really that clear cut? He sounds like a
sharp guy. Couldn't he just be pattern matching and getting a small advantage
without actively trying to do card counting? I'm kind of talking out of my ass
here, but it seems like you could get some mileage out of simply tracking
whether you've seen a lot of high cards or not:
[https://en.wikipedia.org/wiki/Card_counting#Basics](https://en.wikipedia.org/wiki/Card_counting#Basics)

A couple other related thoughts: I'm taking a course on Markov chains this
summer, and it's nice to be able to relate it to a real world example (i.e.
"Gambler's ruin"). In short, this guy would be _guaranteed_ to lose his money
if he played indefinitely EVEN if the odds were 50-50
[https://en.wikipedia.org/wiki/Gambler's_ruin](https://en.wikipedia.org/wiki/Gambler's_ruin)

>Another common meaning is that a gambler with finite wealth, playing a fair
game (that is, each bet has expected value zero to both sides) will eventually
go broke against an opponent with infinite wealth. Such a situation can be
modeled by a random walk on the real number line. In that context it is
provable that the agent will return to his point of origin or go broke and is
ruined an infinite number of times if the random walk continues forever.

And if you like these sort of pieces on gambling, maybe you'd like this
article I wrote recently about winning money in an indie gambling game:
[http://www.jere.in/13](http://www.jere.in/13)

~~~
mrjaeger
Re Re card counting: The vast, vast majority of advantage when counting is the
choice to change your bet size depending on the count. When a deck starts you
are at some initial count and then it goes up or down as the deck goes along.
While the count is at or below a certain point (low counts are considered bad
and high counts are considered good), you usually just bet the table minimum
as you do not have an advantage over the house. Once the count reaches a
certain level you start betting more aggresively. There is usually a spread to
counts where for example if the count is 1 you bet 2x table minimum if it is 3
you bet 4x table minimum etc. This is how you take advantage of the fact that
the odds are in your favor - if you just bet the same amount all the time you
are not really doing anything different (assuming you are following Basic
Strategy at all times).

The rub here is that this type of betting can be seen by the house. If you are
of enough interest to the casino (something you can get playing $100 hands let
along _$100K_ hands) they will watch you bet and try and look for this
pattern. Most casinos employ former counters or have people on staff you can,
after a little bit of time, determine if you are counting or not and politely
ask you to leave. In fact most counters will specifically give away some of
their advantage by going against the recommended bet at a given count to try
and make it look less like they are counting. One such practice would be to
never go from a minimum bet to a max bet, as it is most likely not something a
regular counter would do (aka bet $100 one hand then bet $1K the next hand).

You are correct however that some advantage can be gained by just "tracking
whether you've seen a lot of high cards". Players use indexes which will
change their play depending on the count, and use this skill to augment their
changes in betting amounts to better take advantage of their current position.
You can see the effect of using indexes vs. no indexes here:
[https://www.qfit.com/cardcountingindexes.htm](https://www.qfit.com/cardcountingindexes.htm)

------
havko
I am not sure I understand this. He never actually gained an edge on the house
and the discount never actually came into play from what I can tell. I did not
think that there was a way to predict variance, though admittedly I know
little about this.

~~~
ikeboy
You should definitely read [http://apheat.net/2014/03/25/fact-checking-an-
article-on-don...](http://apheat.net/2014/03/25/fact-checking-an-article-on-
donald-johnson-in-chance-magazine/) linked by another comment.

It did come into effect on other days, so even though he lost a bunch on some
days, he made more than that on other days.

~~~
havko
Thanks, couldn't read that one earlier(blocked at work). I think I am starting
to get it, But I still feel like all the facts were never presented.
Basically, it was a 50/50 game except he had a 20 percent cushion on losses.
You would think a cool million would at least get you single deck black jack
opposed to 6 deck.

------
nodesocket
The discount is only downside protection, it does not change the odds. The
changes that mattered were playing with a hand-shuffled six-deck shoe and the
right to split and double down on up to four hands at once; and double a "soft
17". These changes essentially made the game 50/50\. Still, an incredible
amount of luck, though he was playing $100,000 a hand, so when you have an
amazing split, split, double, double hand it adds up. The key factor here was
once he was up, he basically could keep going, because statistically odds were
even.

~~~
eric_h
The fact that he insisted on a 6 deck shoe seems to suggest that he was, in
fact, counting cards. I was under the impression that standard casino
blackjack shoes were 8 decks (machine shuffled).

He may not have played as a standard card counter would (as that would make
him more detectable), but he still could have made riskier plays when the shoe
was "hot" to give him a slight edge over 49.75-50.25

~~~
bhahn

      I was under the impression that standard casino blackjack shoes were 8 decks (machine shuffled).
    

In Las Vegas, shoe games are usually 6-deck
[http://wizardofvegas.com/guides/blackjack-
survey/](http://wizardofvegas.com/guides/blackjack-survey/).

And whether a game is machine-shuffled or hand-shuffled will usually depend on
the min bet. The higher the minimum, the more likely the table is to be hand-
shuffled, and the lower tier the casino, the lower that minimum is likely to
be. For example: the Wynn Las Vegas' $100 min table is machine-shuffled, while
Harrah's Lake Tahoe $100 min table is hand-shuffled.

