Commissioned Art Credit by Patricia Doria The New York Times Magazine 41
tournament, I visited Koon at his
multimillion-dollar house, located
in a gated community inside a larg-
er gated community next to a Jack
Nicklaus-designed golf course. On
Day 1, Koon paid $250,000 to play
the Super High Roller, then a sec-
ond $250,000 after he was knocked
out four hours in, but again he lost
all his chips. ‘‘Welcome to the world
of nosebleed tourneys,’’ he texted
me afterward. ‘‘Just have to play
your best — it evens out.’’
For Koon, evening out has taken
the form of more than $30 million
in in-person tournament winnings
(and, he says, at least as much from
high-stakes cash games in Las Vegas
and Macau, the Asian gambling
mecca). Koon began playing poker
seriously in 2006 while rehabbinghundreds of thousands of dollars to help poker players
develop software that would identify perfect play and to
consult with programmers building bots that would be
capable of defeating humans in online games. Players
unable to front that kind of money didn’t have to wait
long before gaining more aff ordable access to A.I.-based
strategies. The same year that Science published the
limit hold ’em article, a Polish computer programmer
and former online poker player named Piotrek Lopu-
siewicz began selling the fi rst version of his application
PioSOLVER. For $249, players could download a pro-
gram that approximated the solutions for the far more
complicated no-limit version of the game. As of 2015, a
practical actualization of John von Neumann’s mathe-
matical proof was available to anyone with a powerful
enough personal computer.One of the earliest and most devoted adopters of what
has come to be known as ‘‘game theory optimal’’ poker
is Seth Davies’s friend and poker mentor, Jason Koon.
On the second day of the three-day Super High RollerPoker, though, remained a particularly thorny problem,
for precisely the reason von Neumann was attracted to
it in the fi rst place: the way hidden information in the
game acts as an impediment to good decision making.
Unlike in chess or backgammon, in which both play-
ers’ moves are clearly legible on the board, in poker a
computer has to interpret its opponents’ bets despite
never being certain what cards they hold. Neil Burch, a
computer scientist who spent nearly two decades work-
ing on poker as a graduate student and researcher at
Alberta before joining an artifi cial intelligence com-
pany called DeepMind, characterizes the team’s early
attempts as pretty unsuccessful. ‘‘What we found was
if you put a knowledgeable poker player in front of the
computer and let them poke at it,’’ he says, the program
got ‘‘crushed, absolutely smashed.’’
Partly this was just a function of the diffi culty of mod-
eling all the decisions involved in playing a hand of
poker. Game theorists use a diagram of a branching tree
to represent the diff erent ways a game can play out. In
a straightforward one like rock-paper-scissors, the tree
is small: three branches for the rock, paper and scissors
you can play, each with three subsequent branches for
the rock, paper and scissors your opponent can play.
The more complicated the game, the larger the tree
becomes. For even a simplifi ed version of Texas Hold
’em, played ‘‘heads up’’ (i.e., between just two players)
and with bets fi xed at a predetermined size, a full game
tree contains 316,000,000,000,000,000 branches. The
tree for no-limit hold ’em, in which players can bet any
amount, has even more than that. ‘‘It really does get truly
enormous,’’ Burch says. ‘‘Like, larger than the number
of atoms in the universe.’’
At fi rst, the Alberta group’s approach was to try to
shrink the game to a more manageable scale — crudely
bucketing hands together that were more or less alike,
treating a pair of nines and a pair of tens, say, as if they
were identical. But as the fi eld of artifi cial intelligence
grew more robust, and as the team’s algorithms became
better tuned to the intricacies of poker, its programs
began to improve. Crucial to this development was an
algorithm called counterfactual regret minimization.
Computer scientists tasked their machines with identi-
fying poker’s optimal strategy by having the programs
play against themselves billions of times and take note
of which decisions in the game tree had been least
profi table (the ‘‘regrets,’’ which the A.I. would learn to
minimize in future iterations by making other, better
choices). In 2015, the Alberta team announced its suc-
cess by publishing an article in Science titled ‘‘Heads-Up
Limit Hold’em Poker Is Solved.’’
For some players, especially those who made a living
playing that variant of poker online, the Alberta group’s
triumph represented a serious threat to their livelihood.
‘‘I remember when we read it about it,’’ says the former
professional Terrence Chan. ‘‘We were just like, ‘Oh,
good game, it’s been a fun ride.’ ’’
It quickly became clear that academics were not the
only ones interested in computers’ ability to discover
optimal strategy. One former member of the Alberta
team, who asked me not to name him, citing confi -
dentiality agreements with the software company that
currently employs him, told me that he had been paid