The challenge
of poker
NDHU CSIE AI Lab
羅仲耘
Outline
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Introduction
Texas Hold’em rules
Poki’s architecture
Betting Strategy
– Pre-flop betting strategy
– Basic betting strategy
• Reference
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Introduction
• Bridge and poker involve imperfect
information
• Traditional methods like deep
search can’t play these game well
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Texas Hold’em rules (1)
1. Opening deal – Each player is dealt
two cards face down, which are known
as hole cards or pocket cards.
2. First round of betting – Starting with
the player to the left of the big blind,
each player can call the big blind, raise,
or fold. The big blind has the option to
raise an otherwise unraised pot.
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Texas Hold’em rules (2)
3. The flop – The dealer burns a
card, and then deals three
community cards face up. The first
three cards are referred to as the
flop, while all of the community
cards are collectively called the
board.
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Texas Hold’em rules (3)
4. Second round of betting –
Starting with the player to the left of
the dealer button, each player can
check or bet. Once a bet has been
made, each player can raise, call,
or fold.
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Texas Hold’em rules (4)
5. The turn – The dealer burns
another card, and then adds a
fourth card face-up to the
community cards. This fourth card
is known as the turn card, or fourth
street.
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Texas Hold’em rules (5)
6. Third round of betting – It follows
the same format as the second
round, but the size of the bets have
usually doubled in limit games.
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Texas Hold’em rules (6)
7. The river – The dealer burns
another card, and then adds a fifth
and final card to the community
cards. This fifth card is known as
the river card, or fifth street.
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Texas Hold’em rules (7)
8. Final round of betting – It follows the
same format as the second and third
rounds.
9. The showdown – Using the best fivecard combination of their hole cards and
the community cards, the remaining
players show their hands, with the bettor
or last raiser showing first. The highest
five-card hand wins the pot. (In case of
a tie, the pot is evenly split among the
winning hands.)
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Poki’s architecture
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Pre-flop betting strategy(1)
• Income rate: base on roll simulation
• Roll simulation: an off-line computation
that consists of playing several million
hands (trials) where all players call the
first bet, and then all the remaining
cards are dealt out without any further
betting
• David Sklansky wrote books on this
game and classify the hand cards.
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Pre-flop betting strategy(2)
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Pre-flop betting strategy(3)
• Prefer roll-out simulation than
David Sklansky’s classification
– Roll-out simulation information is
quantitative rather than qualitative
– Can apply many difference specific
situation
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Basic betting strategy(1)
• Hand strength (HS): is the probability that a
given hand is better than that of an active
opponent
• For example: hand is A♦-Q♣ and the flop is
J♥-4♣-3♥.47 remaining unknown cards and
therefore {47 choose 2} = 1081 possible hands
an opponent might hold. 444 cases are better
than hand, 9 are equal, and 628 are worse
than hand.
• There is a 58.5% chance that hand is better
than a random hand.
5
• If there are 5 opponents, the HS5 is 0.585 =
6.9%
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Basic betting strategy(2)
• Hand potential
– Positive potential (PPot):
Chance that a hand which is not currently
the best improves to win at the showdown
– Negative potential (NPot):
Chance that a currently leading hand ends
up losing
• All possible opponent cards is
{47 choose 2} = 1081, therefore remains
{45 choose 2} = 990 possible turn and
river cards to consider for each
opponent
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Basic betting strategy(3)
• For example: if the hand A♦-Q♣ is
ahead against one opponent after 5
cards, then after 7 cards there is a
449005 / 621720 = 72% chance of still
being ahead
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Basic betting strategy(4)
• Effective hand strength (EHS):
combines hand strength and
potential to give a single measure
of the relative strength of Poki’s
hand against an opponent
P(win) = P(ahead) x P(opponent does not improve)
+ P(behind) x P(we improve)
= HS x (1 - NPot) + (1 - HS) x PPot
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Basic betting strategy(5)
• Weighting the enumerations
– The probability of each hand being
played to a particular point in the
game will very
– For example: the probability that the
opponent holds Ace-King is much
higher than 7-2 after the flop,
because most will fold 7-2 before the
flop
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Basic betting strategy(6)
• To account for this, Poki maintains
a weight table for each opponent
• The weights have a value in the
range zero to one
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Basic betting strategy(7)
• For example:
[ A♠K♣, 0.40 ],…[ Q♦2♦, 0.20 ],…
the PredictOpponentAction procedure
generates probability distributions
{ P( fold), P( check / call), P( bet / raise)}
A♠ - K♣ { 0.0, 0.7, 0.3 }
Q♦ - 2♦ { 0.0, 0.1, 0.9 }
• If the observed player action is a bet,
after reweighting, the new table entry for
A♠ - K♣ will be 0.4 x 0.3 = 0.12
Q♦ - 2♦ will be 0.2 x 0.9 = 0.18
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Basic betting strategy(8)
• Probability triple PT = {f, c, r}, such
that f + c + r = 1.0, representing the
probability distribution that the next
betting action in a given context is
fold, call, or raise, respectively
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Reference
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The challenge of Poker
/ Darse Billings, Aaron Davidson, Jonathan Schaeffer, Duane
Szafron / Artificial Intelligence 134 (2002)
http://www.cardplayer.com/rules-of-poker/texas-holdem.php
http://www.ultimatebet.com/rules-strategy/texas-holdem.html
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Thanks for your
attention!
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