and all the players who were eliminated before him,
received nothing.
Given the small sample size of several hundred hands
that a player will see over the course of three days, a
single poker tournament is an incredibly inexact way
of identifying the strongest player in the fi eld. Luck will
determine much of the outcome for even the best play-
ers — if the 26 human players in the tournament were
replaced with 26 perfectly programmed poker bots, one
bot would win and one would be the fi rst to be elimi-
nated, despite their sharing the same optimal strategy.
Poker players tend to take the long view, speaking
of tournament buy-ins as investments with a more or
less predictable return when averaged over time. ‘‘In a
relatively tough tournament, the worst players in the
fi eld are losing maybe as much as 30 or 40 percent of
their buy-in,’’ says Ike Haxton, who plays professionally.
Stronger amateurs, he says, should expect to lose an
average of about 15 percent of the money they put in,
while the best pros will earn a return of around 5 to 10
percent over the long run.
To dampen the huge swings of fortune that come
in the short term, many professionals agree to swap
percentages of any potential prize money with one
another before the tournament starts — I agree to give
you 5 percent of what I win, say, if you agree to give
me 5 percent of what you win — or sell stakes in their
future winnings to outside backers, like shares in an old-
time whaling voyage. Seth Davies wouldn’t tell me the
exact details of his own arrangements, but he admitted
that less than half of what he put into this tournament
had come out of his own bankroll. Even so, after being
knocked out on the fi rst day and then paying a second
$250,000 to re-enter, he had ‘‘well into six fi gures’’ of his
own money on the line.
On the third and fi nal day of the Super High Roll-
er, the fi ve remaining players were relocated from
the dilapidated outer tables of the Amazon Room to a
made-for-television set at its center. Stage lights brightly
illuminated the poker table’s gleaming green felt from
above, while a 45-foot camera crane swung from side
to side to get the best angle on the action. All fi ve play-
ers who had made it this far were guaranteed to turn
a profi t, but there was still a lot of maneuvering left
to determine how far up the payout ladder they could
climb. As the game got underway, the chip leader, a
27-year-old Spanish pro named Adrián Mateos, kept up
a steady barrage of giant bets against the other players,
asking them again and again whether this was the hand
with which they wanted to make their fi nal stand, or
whether, perhaps, they would rather fold and wait for
another player or two to bust out so that they could
fi nish fourth or third, instead of fi fth, and take home an
additional $300,000 or $700,000 in prize money.
Situations like these bend the value of players’ stacks
in strange ways, depending on where they are in the
payout hierarchy. Even a single chip can be worth an
incredible amount of real money if another player is
knocked out of the tournament after you’ve folded.
There are solvers that can model these circumstances as
well, but as the chip stacks get shorter relative to the size
of the blind bets and antes players are required to put
in the pot before each hand begins, fl awless play aloneThe New York Times Magazine 43on one screen and then use them to
play optimally on a second screen.
‘‘Any time there are high stakes and
a lot of money to be won, and a
device that might be used for good,’’
Koon says, ‘‘people have a way to
turn it into a cheating tool.’’
Koon isn’t especially worried that
people are cheating in the games he
plays over the internet, but other
players aren’t so sure. ‘‘It’s the main
reason why I don’t really play much
online anymore,’’ a pro named Ryan
Laplante says. In a recent $7,000
buy-in online tournament held as
part of the World Series of Poker,
Laplante says he recognized the
screen names of at least four of the
100 or so competitors as belong-
ing to players who were rumored
to have been banned from other
sites for using what is called ‘‘real-
time assistance.’’ Laplante credits
some of the biggest online sites
with doing a good job of policing
their games, but he worries that as
solvers become more ubiquitous,
the balance of power will continue
to shift toward those who cheat to
gain an edge.
‘‘The only thing I’m confi dent
of,’’ Laplante says, ‘‘is that it’s going
to get a lot worse very quickly.’’
Well after midnight on the Super
High Roller’s second day, a Ger-
man professional named Chris-
toph Vogelsang called a bet for all
his chips with a king and a nine
versus another player’s ace and
jack. According to the solvers,
calling was, in fact, the correct
play — all the same, Vogelsang
lost the hand and was eliminat-
ed from the tournament in sixth
place. Unlike a regular poker game,
where players can leave the table
and cash in their chips whenever
they feel like it, a poker tournament
requires players to continue until
they either lose everything or win
every single chip in play. Prizes,
drawn from the pool created by
all the buy-ins, are paid out based
on how long players manage to
stay in the game. The person who
ends with all the chips is awarded
the fi rst-place prize ($3.2 million in
this tournament), the second-to-
last survivor gets second place ($2
million) and so on down to the fi nal
in-the-money fi nisher, in this case,
fi fth place ($630,000). Vogelsang,
off ers no real insurance against what often becomes
essentially a game of heads or tails. ‘‘When it comes
down to it,’’ Davies says, ‘‘you just end up running these
million-dollar fl ips, and you hope you win.’’
After one competitor was eliminated, Davies found
himself with the shortest chip stack at the table. With
only one more person still to play behind him, he
pushed all-in with the ace and seven of clubs, just as
the solvers said he should, given the size of his stack.
The remaining player, a ponytailed Englishman named
Ben Heath, quickly called and turned over a pair of jacks,
making him a 67 percent favorite to win the hand. None
of the fi ve cards the dealer laid out improved Davies’s
hand, so Heath won the pot, and Davies was eliminated
in fourth place. He stood up from the table, collected his
backpack and N95 mask and left the stage. ‘‘That was
some serious gambling up there,’’ he told me. Davies
at least had the satisfaction of knowing how closely his
play over the last three days had hewed to the optimal
strategy generated on his computer at home. (Another
consolation was the $930,791 in prize money he would
receive for his fourth-place fi nish.)
Stowing his cash-out ticket in his pocket, Davies
walked over to a nearby $50,000 buy-in tournament
already underway. He had planned to get some dinner
and rest a little before buying in, but he changed his
mind after seeing how many of the players here were
the sort most likely to employ decidedly nonoptimal
strategies. ‘‘This 50K looks incredible,’’ Davies told me.
‘‘I just couldn’t not be in there right away.’’
Not every player I spoke to is happy about the way
A.I.-based approaches have changed the poker land-
scape. For one thing, while the tactics employed in most
lower-stakes games today look pretty similar to those in
use before the advent of solvers, higher-stakes compe-
tition has become much tougher. As optimal strategy
has become more widely understood, the advantage
in skill the very best players once held over the merely
quite good players has narrowed considerably. But for
Doug Polk, who largely retired from poker in 2017 after
winning tens of millions of dollars, the change solvers
have wrought is more existential. ‘‘I feel like it kind of
killed the soul of the game,’’ Polk says, changing poker
‘‘from who can be the most creative problem-solver to
who can memorize the most stuff and apply it.’’
Piotrek Lopusiewicz, the programmer behind Pio-
SOLVER, counters by arguing that the new generation
of A.I. tools is merely a continuation of a longer pattern
of technological innovation in poker. Before the advent
of solvers, top online players like Polk used software to
collect data about their opponents’ past play and analyze
it for potential weaknesses. ‘‘So now someone brought
a bigger fi rearm to the arms race,’’ Lopusiewicz says,
‘‘and suddenly those guys who weren’t in a position to
profi t were like: ‘Oh, yeah, but we don’t really mean that
arms race. We just want our tools, not the better tools.’ ’’
Besides, for Lopusiewicz, solvers haven’t so much
changed poker as revealed its essence. Whether poker
players themselves recognized it, or wanted to, at its
core the game was always just the maximization prob-
lem John von Neumann revealed it to be. ‘‘Today, every-
one at a certain level is forced to respect the math side,’’
Lopusiewicz says. ‘‘They can’t ignore it anymore.’’