November in the cavernous Ama-
zon Room of Las Vegas’s Rio
casino, two dozen men dressed
mostly in sweatshirts and baseball
caps sat around three well-worn
poker tables playing Texas Hold
’em. Occasionally a few passers-by
stopped to watch the action, but
otherwise the players pushed
their chips back and forth in dingy
obscurity. Except for the taut, elec-
tric stillness with which they held
themselves during a hand, there
was no outward sign that these
were the greatest poker players
in the world, nor that they were,
as the poker saying goes, ‘‘playing
for houses,’’ or at least hefty down
payments. This was the fi rst day of
a three-day tournament whose offi -
cial name was the World Series of40 1.23.22
Poker Super High Roller, though the participants simply
called it ‘‘the 250K,’’ after the $250,000 each had put up
to enter it.
At one table, a professional player named Seth Davies
covertly peeled up the edges of his cards to consider the
hand he had just been dealt: the six and seven of dia-
monds. Over several hours of play, Davies had managed
to grow his starting stack of 1.5 million in tournament
chips to well over two million, some of which he now
slid forward as a raise. A 33-year-old former college
baseball player with a trimmed light brown beard,
Davies sat upright, intensely following the action as it
moved around the table. Two men called his bet before
Dan Smith, a fellow pro with a round face, mustache
and whimsically worn cowboy hat, put in a hefty reraise.
Only Davies called.
The dealer laid out a king, four and fi ve, all clubs, giv-
ing Davies a straight draw. Smith checked (bet nothing).
Davies bet. Smith called. The turn card was the deuce of
diamonds, missing Davies’s draw. Again Smith checked.
Again Davies bet. Again Smith called. The last card dealt
was the deuce of clubs, one fi nal blow to Davies’s hopes
of improving his hand. By now the pot at the center of
the faded green-felt-covered table had grown to more
than a million in chips. The last deuce had put four clubs
on the table, which meant that if Smith had even one
club in his hand, he would make a fl ush.
Davies, who had been betting the whole way needing
an eight or a three to turn his hand into a straight, had
arrived at the end of the hand with precisely nothing.
After Smith checked a third time, Davies considered his
options for almost a minute before declaring himself
all-in for 1.7 million in chips. If Smith called, Davies
would be out of the tournament, his $250,000 entry fee
incinerated in a single ill-timed bluff.
Smith studied Davies from under the brim of his
cowboy hat, then twisted his face in exasperation at
Davies or, perhaps, at luck itself. Finally, his features
settling in an irritated scowl, Smith folded and the deal-
er pushed the pile of multicolored chips Davies’s way.
According to Davies, what he felt when the hand was
over was not so much triumph as relief.
‘‘You’re playing a pot that’s eff ectively worth half a
million dollars in real money,’’ he said afterward. ‘‘It’s
just so much goddamned stress.’’
Real validation wouldn’t come until around 2:30 that
morning, after the fi rst day of the tournament had come
to an end and Davies had made the 15-minute drive
from the Rio to his home, outside Las Vegas. There, in
an offi ce just in from the garage, he opened a computer
program called PioSOLVER, one of a handful of arti-
fi cial-intelligence-based tools that have, over the last
several years, radically remade the way poker is played,
especially at the highest levels of the game. Davies input
all the details of the hand and then set the program
to run. In moments, the solver generated an optimal
strat egy. Mostly, the program said, Davies had gotten
it right. His bet on the turn, when the deuce of dia-
monds was dealt, should have been 80 percent of the
pot instead of 50 percent, but the 1.7 million chip bluff
on the river was the right play.
‘‘That feels really good,’’ Davies said. ‘‘Even more than
winning a huge pot. The real satisfying part is whenyou nail one like that.’’ Davies went to sleep that night
knowing for certain that he played the hand within a
few degrees of perfection.The pursuit of perfect poker goes back at least as far
as the 1944 publication of ‘‘Theory of Games and Eco-
nomic Behavior,’’ by the mathematician John von Neu-
mann and the economist Oskar Morgenstern. The two
men wanted to correct what they saw as a fundamental
imprecision in the fi eld of economics. ‘‘We wish,’’ they
wrote, ‘‘to fi nd the mathematically complete principles
which defi ne ‘rational behavior’ for the participants in
a social economy, and to derive from them the general
characteristics of that behavior.’’ Economic life, they
suggested, should be thought of as a series of maximi-
zation problems in which individual actors compete to
wring as much utility as possible from their daily toil.
If von Neumann and Morgenstern could quantify the
way good decisions were made, the idea went, they
would then be able to build a science of economics on
fi r m g r o u n d.
It was this desire to model economic decision-making
that led them to game play. Von Neumann rejected most
games as unsuitable to the task, especially those like
checkers or chess in which both players can see all
the pieces on the board and share the same informa-
tion. ‘‘Real life is not like that,’’ he explained to Jacob
Bronowski, a fellow mathematician. ‘‘Real life consists of
bluffi ng, of little tactics of deception, of asking yourself
what is the other man going to think I mean to do. And
that is what games are about in my theory.’’ Real life,
von Neumann thought, was like poker.
Using his own simplifi ed version of the game, in
which two players were randomly ‘‘dealt’’ secret num-
bers and then asked to make bets of a predetermined
size on whose number was higher, von Neumann
derived the basis for an optimal strategy. Players should
bet large both with their very best hands and, as bluff s,
with some defi nable percentage of their very worst
hands. (The percentage changed depending on the size
of the bet relative to the size of the pot.) Von Neumann
was able to demonstrate that by bluffi ng and calling at
mathematically precise frequencies, players would do
no worse than break even in the long run, even if they
provided their opponents with an exact description
of their strategy. And, if their opponents deployed any
strategy against them other than the perfect one von
Neumann had described, those opponents were guar-
anteed to lose, given a large enough sample.
‘‘Theory of Games’’ pointed the way to a future in
which all manner of competitive interactions could be
modeled mathematically: auctions, submarine warfare,
even the way species compete to pass their genes on to
future generations. But in strategic terms, poker itself
barely advanced in response to von Neumann’s proof
until it was taken up by members of the Department of
Computing Science at the University of Alberta more
than fi ve decades later. The early star of the depart-
ment’s games research was a professor named Jonathan
Schaeff er, who, after 18 years of work, discovered the
solution to checkers. Alberta faculty and students also
made signifi cant progress on games as diverse as go,
Othello, StarCraft and the Canadian pastime of curling.