Perfect Heads-Up Limit Hold' Em Strategy part 2

COMPARING THE PLAYING STYLE OF PHIL IVEY, ANDY BEAL, POLARIS, AND TEXAS HOLD' EM HEADS UP POKER "THE BRAIN" TO DEVICE YOUR OWN

At the highest level of excellence.  There is two obvious reasons that push you to excel in an particular activity. OBSESSION and/or PROFESSION.  So what is the fuel behind the success and the excellence of our four champions?

PROFESSION - Phil Ivey plays for a living.
OBSESSION - Andy Beal was obsessed with facing the bests to be the best.
OBSESSION - Polaris was created to beat the best pro players.
PROFESSION - Texas Hold' Em Heads Up Poker machine was manufactured to legally take the maximum amounts of money out of patrons's pockets.

As you can see in the four above examples.  Those who are mainly fueled by OBSESSION wants to be THE best in the world.  And those doing it as a PROFESSION are mainly interested in the money. 

Now that we know they main motivation.  Let's analyze their playing style and do a mix of it all to create The Ultimate Heads-Up Hold' Em Winning Strategy.

P.S. (Read the first part of this guide... The HULHE winning strategies of Phil Ivey, Andy Beal, Polaris, and Texas Hold' Em Heads Up Poker machine.)

First of all, as I see it. 
All four are hyper aggressive.
All but Ivey are specialized and exclusively play Heads Up Limit Hold' Em.  Phil Ivey is excellent in any form of poker.


All four take on all comers.
All four want to be the best in the world.
All four want to face the bests of the world.
No table selection and bum hunting here! 
 

Phil Ivey learned the game by playing it.
Andy Beal learned the game by studying it.
And Polaris and "The Brain"...  Well?  Are both robots.


Phil Ivey's style is purely exploitative.
Andy Beal is a machine.  Purely GTO (Game Theory Optimal), probabilities and mathematics.
Polaris, despite using the Nash Equilibrium as his default strategy, is exploitative.  Since his playing style is all about adaptation.
"The Brain" can't be exploitative so it is GTO defensive.  All about preventing itself to be exploited.


What is the main strength of each player / robot?  Just one word to describe each player/bot's main secret to win and be so excellent at HULHE.
Phil Ivey = his reads
Andy Beal = mathematics
Polaris = adaptation
"The Brain" = defense


CHANGING GEARS / UNPREDICTIBILITY

We don't know much about Phil Ivey and Andy Beal unpredictibility and different play modes.  This isn't the case with Polaris and "The Brain"

Polaris changes gear to adapt.
"The Brain" changes gear for defense.

Polaris have 5 strategies
"The Brain" have 3 "tag team fighters"

Polaris 5 different strategies
1- Polaris default strategy is Nash Equilibrium.  
2- Exploitative Counter Strategy
3- A compromise between the first 2???
4- A team of all strategies to learn which one to use during the game???
5- 


"The Brain" 3 tag-team fighters
1- Neutral net with optimal number of bluff.
2- A slightly different style.
3- To finish off a short-stacked opponent.  I like this one!
Aggression level might change randomly.

 

So, if we can do a melting of those four winning strategies.  What it would be like? 

I will call it the P.I.B.B. in hommage of our four HULHE gods.
P.I.B.B. stands for... 

Polaris-Ivey-Beal-Brain
or  if you prefer
Poker-International-Big-Boss



Now let's look at the

HULHE P.I.B.B. Winning Strategy aka P.I.B.B. Strategy

Pre-Flop (LOOSE AGGRESSIVE)

• Play nearly every hands

BUTTON (in position): 

• Raise almost 100% of the time

BIG BLIND (out of position): 

• Raise called button 75% of the time.
• Always raise (3-Betting) with Ax, Kx, Q3s+, Q6+, J8+, T7s+, T9+, 98s+, 22+. 

Or you can use the Polaris's 3-Betting strategy from the BB.

Flop

• Continuation Bet 100% of the time.

Turn

• Continuation Bet 100% of the time.
• 8-bet the turn with two pairs

River

• Check-call all the way down the river with any Ace-high hand.
• Call with K-high unless the board is scary.

Extreme Aggression
Be The Aggressor

Tag team fighters / different strategies (P.I.B.B.)

1- Extreme Aggression (default strategy) 

2- Finish off a short stacked opponent 

    Push or Fold when villain (or you) are 4BB

    (Ax, Kx, Qx, Jx, T8, T7s, 98s, 22+)


Guidelines

• You are the aggressor
• Leave after losing one buy-in
• Keep playing when winning
• Obsession with preventing tells

Now, after studying the playing style of my four heads up limit hold em icons, heros and idols.  I have enough information to devise my own strategy.  The Perfect Heads-Up Fixed Limit Hold' Em Strategy.   This will be the third part of this highly instructive guide.


PYGOD


For an analysis of the respective playing style of Polaris. Ivey. Beal. Brain. you have to see

Perfect Heads-Up Limit Hold' Em Strategy part 1

The bio, profile, in-dept playing style of each of our four marvels read the following.

• Polaris
• Ivey
• Beal
• Brain

Stay tuned for the 3rd and last part of this article. Where I will devise a more usable, realistic, and adaptative strategy. Everything you need to know to be a $ucce$$ful poker player from playing style to money management. 

HEADS-UP LIMIT HOLD' EM POKER

DO NOT COPY AND PASTE MY WORK INTO YOUR WEBSITE WITHOUT GIVING ME THE CREDIT

Optimal Heads-Up (Preflop) Limit Hold' Em

The Game has changed. As said in The Evolution of Poker: from Super System to math PhD reading Doyle Brunson's SUPER SYSTEM is not enough anymore to give you an edge.  The 2003 Chris Moneymaker's Effect changed all that. Now the common man has the opportunity to play thousands of hands and read all kind of poker books about game theory and exploitative plays. Todays fishes are way more skilled than their counterparts of 20 years ago.

Let me give the highlights of the Optimal Game Theory as ellaborated by highly lucrative online poker pros and some math wizards. These below were particularly devised for Heads-Up Fixed Limit Hold' Em Poker (HUHU / HULHE). HULHE is the simplest form of poker from a programming and mathematical standpoint. Just like chess computer Deep Blue defeated undisputed world chess champion Garry Kasparov. The best bots like Polaris and casino slot machine named "Texas Hold'em Heads Up Poker" AKA "The Brain" routinely beat world-class pro poker players. To this point, HULHE is similar to chess. While it is possible for Artificial Intelligence to play near optimal strategy to beat the best players. Both chess and Heads-Up Limit Hold' Em aren't solved games. 



Exploitative Players were information seekers to keep an edge over their opponents. They are the old guard.
Game Theory Optimal (GTO, optimal) players the highest limits of online plays. They don't much care what their opponent does. They seek to play a strategy designed in the long run to beat any other strategy in the long run.

An optimal player seeks to find the optimal strategy. For any game, there exists at least one optimal strategy. Any GTO poker pro dedicates his time and effort to get as close as possible to the Optimal Strategy. 

However you need to prioritize the practical over the theoretical at all times.

http://www.highstakesdb.com/community/topic/29580-sauce-on-gto/




Game Theoretical Optimum strategy

Button (Small Blind)
rarely fold in the SB (10/169)
23o-28o and 34o-38o

SB never fold to a raise
SB never raise his worst hands


Big Blind (Out Of Position)
NEVER fold in the BB

BB has the edge (act second and is live)
BB never fold to a raise
BB never re-raise with worst hands



Button & BB
R3 - Raise, reraise and re-re-raise if raised back only with AA


Playing different hands in the same way. 
However, Optimal Strategy dictates to vary strategy randomly in order to be deceptive.

The Two Rules

If Villain bet or raise, you should CALL (usually)

If you bet one street and Villain calls, you should BET again on the next card. (usually)


http://www.amazon.com/Pokers-1%25-Secret-Keeps-Players/dp/1496159187/ref=as_sl_pc_tf_til?tag=strenfight-20&linkCode=w00&linkId=QLUJOVHU7GARZLX7&creativeASIN=1496159187



Some of the people who applied professional level mathematics to real world poker. 

Nick Christenson
Alex Selby 
Ben "Sauce123" Sulsky
Matthew Janda
Dr. Darse Billings
Bill Chen
Jerrod Ankenman
Chris Fergusson

http://www.lvrevealed.com/articles/research/selby.html
http://www.archduke.org/simplex/index.html
http://www.archduke.org/simplex/art
http://www.highstakesdb.com/community/topic/29580-sauce-on-gto/

http://forumserver.twoplustwo.com/109/heads-up-limit/optimal-preflop-play-737220/
https://www.google.ca/webhp?sourceid=chrome-instant&rlz=1C1NCHB_enCA593CA593&ion=1&espv=2&ie=UTF-8#safe=off&q=optimal%20heads%20up%20preflop%20holdem

http://www.pokerlistings.com/poker-bots-overrated-says-dr-darse-billings-29734
http://www.pokerlistings.com/strategy/psychology/poker-bots-the-beginning-of-the-end-um-no
http://www.pokerlistings.com/strategy/psychology/bot-this-too-robots-dont-have-girlfriends

http://billchenpoker.com/

HU FL SNG Blinds structure

Heads Up Fixed Limit Sit & Go (HU FL SNG)

Blinds structure for Regular and Turbo on PokerStars.com

1500 Chips to start

Regular (blinds augmentation every) 10 minutes

Turbo   (blinds augmentation every)  5 minutes

Below is the sheet I use to comparate the Blinds Structure of a Fixed Limit vs. No Limit HUSNG on PokerStars.com

Why you should play HU FL SNG

• Maybe long, but I think this duel, this game of chess, is worth playing. 

• In HU SNG you won't get eaten by the rake like in HU Cash.

• Contrary to No Limit Hold' Em, in Fixed Limit (FL) you don't have that much variance because when your opponent is bad your edge is HUGE. 

;-)

PokerStars Heads-Up FL Sit N Go

Buy-in, winning prize, and rake

hu fl sng on google

NASH EQUILIBRIUM Game Theory for Fixed Limit Heads-Up Hold' Em

Transition from No-Limit to Fixed-Limit
Adapting the Nash Equilibrium for Heads-Up LIMIT Hold' Em


Since our concern here isn't Heads-Up No-Limit Texas Hold' Em but Heads-Up Fixed Limit Hold' Em the number of effective BB (Big Blinds) will be different.

On PokerStar the minimum required stack to play

HU NL HE  40 BB

HU FL HE     5 BB

According to this, we need 8 TIMES less money to play Limit Holdem than we need to play No Limit.

So the 20+ BB mentioned above would be reduced to 2.5 + BB in a Fixed Limit game.  Well... ???? I'm not so sure about the correlation between the two.

A more realistic and representative stack is 100 BB in no limit vs. 20 BB in fixed limit as suggested on Pokerstars.

With that being said: 
HU NL HE  20 BB = HU FL HE  4 BB

I have to admit that I feel pretty naked at 4-5 BB.

The following is copy-and-paste general information about the HeadsUp Push/Fold charts and their usage for Heads-Up No-Limit Hold' Em. For the original source, I encourage you to click the links of the source at the end of the explanations. 

Keep in mind that the explanations below were deviced for HU NL HE. So divide the numbers by 5 to give you an idea of what it could be in Heads-Up LIMIT Hold' Em.



General Information

The charts show the Nash Equilibrium solution of the heads-up push-or-fold game. This is a simplified game where the SB is only allowed to go all-in or fold, and the BB can either call or fold when facing a shove.
It is important to keep in mind that this is not the solution for the full game where limps and smaller raises are also available. The push-or-fold solution is generally assumed to be very close to the solution of the full game up to around 8bb. In practice the strategy can likely be used at least until 10bb without being too exploitable.

Usage

The tables show the highest effective stack size in big blinds where a hand can be pushed or called. Values bigger than 20 are only displayed as 20+, which means the hand can be played for any stack size of 20bb or less. (Playing push-or-fold is typically only recommended up to around 10bb, depending on the situation. Using push-or-fold for >20bb is almost certainly a bad idea.)
Some hands have gaps in their pushing strategies, they are marked with * and the details are displayed below the charts. For example 63s is included in the pushing strategy for stack sizes between 7.1 and 5.1bb, and stacks below 2.3bb.

Example

SB (9.0bb): T3s
BB (6.0bb): Q2o
The effective stack size is the smaller of the two, before posting any blinds. So the relevant stack size for both players in this hand is 6.0 big blinds.
To find the strategy for SBs T3s, check the green area (suited hands) of the "Pusher" chart. The value for T3s is 7.7bb, and since that is larger than the current effective stacks the hand is a push in the Nash Equilibrium strategy.
To determine if the BB should call with his Q2o, check the orange area (offsuit hands) of the "Caller" chart and locate Q2o. The value there is 5.6bb. The effective stacks in the current hand are larger than the value for Q2o, so this hand is a fold in the Nash Equilibrium strategy.

http://www.holdemresources.net/h/poker-theory/hune/usage.html
http://www.holdemresources.net/h/poker-theory/hune.html

http://www.thepokerforum.com/joebenik8.htm




I have included the following chart analyzing the game play of Hyperborean and the legendary Polaris.



http://forumserver.twoplustwo.com/29/news-views-gossip/heads-up-holdem-solved-1379043/index5.html

http://en.wikipedia.org/wiki/Polaris_(poker_bot)

http://www.computerpokercompetition.org/index.php/competitions/participants/93-participants-2013?showall=&start=1

http://www.headsupsitandgo.com/

Strategy to finish off an opponent in Heads-Up (1-on-1) Poker

You see, when you have a big chip lead in heads-up
action, the first secret is YOU MUST ATTACK.

To get a perspective on this, think about how you
play when you're the SHORT STACK...

You're prepared to go all-in as soon as possible,
right?

Well, you must use this to your ADVANTAGE when
you're the big stack, and PUT YOUR OPPONENT ALL-IN
right away... rather than the other way around.

When you have a big chip lead, YOU must be the one
to create "coin-toss" situations... and fast.

A coin-toss situation is when both players have
virtually equal odds... and the winning hand is
determined by whatever the flop, turn, and river
cards are.

In heads-up poker, any starting hand with a FACE
CARD is playable. Or any pocket pair. It's that
simple.

If you've got a big chip lead on your opponent and
he CHECKS or LIMPS-IN (calls the blinds), then you
should IMMEDIATELY put him all-in.

He wouldn't be checking or limping-in if he had
ANYTHING DECENT at all...

If he folds, you've stolen the blinds from him,
which is crucial. If he calls, you've created a
"coin-toss" situation.

Odds are you'll win at least one out of every two
coin toss situations. Or at the very least, you'll
win one out of three.



Push or Fold:

Ax  Kx
Qx  Jx
T8  T7s
98s
22+

(103/169 = 60.95%)


Here's a basic summary of the "rules" you should
follow when playing heads-up poker with a huge
chip lead. When I say "huge", I'm talking about
10 to 1 or more...

And that's the exact moment when you MUST PULL THE
TRIGGER AND WIN THE GAME.

If you don't, the chip stacks can quickly even out
again and you may lose your chance forever.

Anyway... here are the RULES you should follow with a huge chip lead (10 to 1 or more):

1. Any starting hand with a face card or any pocket
pair is good.

2. You should either FOLD or go ALL-IN every time.
Nothing else.

3. Force COIN-TOSS situations... In other words,
leverage the 50/50 ODDS as much as possible. Do
this two or three times and you will almost always
win the match.

4. If you're playing against a tight player, it
will be even easier. Keep going all-in on just
about every hand and let the blinds eat him to
death.

Read and re-read those four principles and you'll
be prepared the next time you make it to a
heads-up match.


Push or Fold:

Ax  Kx
Qx  Jx
T8  T7s
98s
22+

(103/169 = 60.95%)


50/50 ODDS means:

Ax  Kx
Q5  Qxs
J7  J5s
T8  T7s
98s
22+

(91/169 = 53.85%)


> 50% odds are:

Ax  Kx
Q6  Q3s
J8   J6s
T9  T7s
98s
33+

(86/169 = 51% of hands)

http://www.cardschat.com/f11/how-beat-short-stack-heads-up-61283/
http://www.thepokerforum.com/joebenik8.htm

http://books.google.ca/books?id=ix4HeDVvgIYC&pg=PA73&lpg=PA73&dq=finish+a+short+stacked+opponent+in+heads+up&source=bl&ots=DMnInk7bxP&sig=WSx8q9SQBDv0GZsSn6FvbVNvtBs&hl=en&sa=X&ei=VnR-U-KRCOqH8AHhjoDABw&redir_esc=y#v=onepage&q=finish%20a%20short%20stacked%20opponent%20in%20heads%20up&f=false

Loose Aggressive Unpredictable

HOW YOU SHOULD PLAY 

HEADS-UP (1-on-1) POKER

LOOSE

AGGRESSIVE

UNPREDICTABLE






The three cornerstones that must be part of your game. You must play:

Loose – Always pre-flop and usually post-flop against the majority of opponents.
Aggressively – You need to play with frequent (but not mindless) aggression.
Unpredictably – Against all but the very worst opponents.

Get these three things right and you have the core of a good heads-up game.

HEADS-UP LIMIT HOLD' EM POKER

http://www.internettexasholdem.com/?Itemid=766

Perfect Heads-Up Limit Hold' Em Strategy part 1

STUDYING THE STRATEGIES OF THE FOUR ALL-TIME BEST HULHE PLAYERS, MAN OR MACHINE, TO CREATE YOUR OWN

The best way to find the Perfect Heads-Up Fixed Limit Hold' Em Strategy is to study the strategies used by the great ones.  For me the greats in HULHE are two humans plus two machines.  My two human players are Phil Ivey and Andy Beal.  My two poker bots are Polaris and Texas Hold ‘Em Heads Up Poker.  I will try to enter the brain of those four world-class experts to find and analyze their winning strategies.

Phil Ivey's HUHU FL HE strategy:

Step 1. Raise pre-flop in position
Raise pre-flop in the big blind with (1:1)
Ax, Kx, Q3s, Q6, J8, T7s, T9, 98s, 33+
Step 2. Continuation bet on the flop and turn 100% of the time
Step 3. Leaving after losing one buy-in
Keep playing when winning

Why is Phil Ivey so good?

a) hyper aggressive
b) incredible focus and concentration
c) uncanny ability to detect and exploit opponents's weaknesses and betting patterns
d) zero tilt factor
e) intimidating and fearsome reputation

f) unlimited bankroll

Andy Beal High Stakes Heads-Up Limit Hold' Em strategy

Step 1. Play nearly every hands
Raise (most of the time) every pot he enters
Step 2. Check-call all the way down to the river with any A-high hand
8-bets the turn with two pair
Step 3. Obsession with preventing tells

Why is Andy Beal so good?

a) Obsession

b) Specialization
c) Mathematical approach

d) High stakes

e) Ultra-aggressive
f) Impossible to read

Polaris's Strategies: 

Polaris have a total of 5 different strategies.

The Nash Equilibrium plus 4 other to use against different types of opponents. Polaris identifies which common poker strategy a human is using and switches its own strategy to counter.

1- The first approach is to approximate a Nash equilibrium strategy which is robust against any opponent.

2- The second approach is to find an exploitive counter-strategy to an opponent. We will show that these counter-strategies are brittle: they can lose to arbitrary other opponents.

3- The third approach is a compromise of the first two, to find robust counter-strategies.

4- The four approach is to combine several of these agents into a team, and learn during a game which to use.

Why is Polaris so good?

a) Adaptation. Polaris doesn't have a "best way" to play; it has a "best way" to adapt.
b) Specialization
c) No emotion
d) Aggression

Texas Hold ‘Em Heads Up Poker "The Brain" strategy

Pre-flop
Hyper-LAG / maniac
+ Raise almost every time from the Button
+ Raise called button from over 75% of the time from the BB.
... Sometime 3-bet weak hands like T5off (negligible)
... Occasionally fold on the Button or when raised in the BB (negligible)
- Fold more hands from the SB on most streets than from the BB

Flop
Very LAG
+ Routinely raise with middle pair and a weak kicker
+ Call most of the time a check-raise+ Rarely 3-bet the flop with weak overcard, no straight, flush or backdoor possibilities
+ Often fold to a bet if a high card comes on the flop
+ But he will bet the high card on the flop
+ Most likely to fold on the flop

Turn
Tightens up
+ Check-call with middle pair and weak kicker
+ Check the turn most of the time 

River
+ Call with a piece of the board
+ Call down with Ace high unless the board is scary
+ Likely to call with King high
+ Sometimes call down with weaker hands (J high) on a bimodal (monster or miss) board.  Like a pair on the board.

Overall
+ Reasonable adjustment to what the opponent might hold based on the board.
+ Seem to play top pair / top kicker more slowly on board with flushes and straights possible
+ Seem to play high card / no pair more aggressively on paired flops.  Check-raise bluff
+ More likely to check-raise if opponent put the last bet on the previous street.
+ Doesn't fold too often.

Why is "The Brain" so good?

a) Defense. The basic idea behind its play technique is to do everything it can "to prevent itself from being exploited".  "The theory behind it is almost paranoid," 

b) Unpredictable. The pokerbot use knowledge gained from billions of staged rounds of poker fed through neural networks, and the result is an unpredictable poker player that can win almost every time.  Three different banks of knowledge are used depending on the gameplay scenario, but the basic idea behind its play technique is, as I said above,  "to prevent itself from being exploited." "The theory behind it is almost paranoid." So "The Brain" unpredictibility and three different game plays are part of his perfectly defensive game. 
   
Here are his 3 tag-team fighters alternating against an opponent.
    * The first is a neural net with optimal number of bluffs and can do anything in anyone hand.
    *The second play a slightly different style.
    *The third come into play when the opponent has a reduced stack.

Aggression level might change at random moment

c) Aggression.  "The Brain" is the aggressor. Almost never check-calls or simply matches an opponent's bet without a raise. But give credit to your hand when you raise and reraise.  Far too aggressive and steals far too many pots to get beat on a regular basis.


Now that we have a complete overview of the strategies and strengths of our four Heads-Up Fixed Limit bosses.  We will compare their respective style to each other in the second part of this guide.

PYGOD

Perfect Heads-Up Limit Hold' Em Strategy part 2

HEADS-UP LIMIT HOLD' EM POKER

DO NOT COPY AND PASTE MY WORK INTO YOUR WEBSITE WITHOUT GIVING ME THE CREDIT

Phil Ivey vs The Brain

In NVGtard fantasy land (12-01-2010) :

"The Brain" heads up poker machine proves to be remarkably resilient, beating the best minds in poker over a large sample. When the limits are raised to 200/400 Hoss tbf flys to vegas and enters the Bellagio and plays it days on end only to break even until he tires and begins to lose. And so the machine sits outside the poker room unplayed and unscathed save a few suckers from time to time. The stakes are raised to any that the tourist wishes to play, from .50/1 to 500000/1000000. A billionaire is reported to have lost 4 million on may 23, 2011 during a break from highstakes craps. One day at the poker table Ivey is asked if he would play heads up nl omaha by a young upcoming susperstar from norway and Ivey responds that he would play anybody. The kid says I bet you wouldn't play the brain smugly. "Who's that?" asks Ivey. The kid points to the machine. Ivey says sure and spends the next 45 minutes inserting a giant wad of hundreds and over the course of the next 28 hours he beats it for 300 million dollars infront of the ever growing massive crowd of spectators. Finally after being down 324 million dollars and 28 hours of poker, The Brain ask Phil Ivey if he would let him play on credit. A fat executive hobbles out of the crowd red faced and screams hell no! and pulls the plug.


That's exactly what could happen if Phil Ivey was met to play Texas Hold' Em Heads Up Poker machine "The Brain".  This funny story was written by spaceman Bryce on the twoplustwo poker forum.
http://forumserver.twoplustwo.com/29/news-views-gossip/heads-up-poker-machines-raise-limits-929205/index2.html



It's nice to see that Phil Ivey's dominance made him a mythological figure just like Chuck Norris. 

Now you can say that Phil Ivey is the Chuck Norris of Poker.


Originally published in: http://www.heads-up-fixed-limit-texas-hold-em-poker.com/2013/10/phil-ivey-vs-brain.html 

Polaris

Polaris is the Deep Blue of poker.

The patience of a monk or the fierce aggression of a tiger, changing gears in a single heartbeat. Polaris can make a pro's head spin. Bluff, trap, check-raise bluff, big lay-down -- name your poison.


Polaris is a Texas hold 'em poker playing program developed by the computer poker research group at the University of Alberta, a project that has been under way for 16 years as of 2007. Polaris is a composite program consisting of a number of bots, including Hyperborean08, the winner of the limit equilibrium series in the 2008 Association for the Advancement of Artificial Intelligence (AAAI) Computer Poker Competition. Polaris also contains a number of other fixed strategies, and chooses between these strategies during a match. Polaris requires little computational power at match time, so it is run on an Apple MacBook Pro laptop during competitions. Polaris plays only heads-up (two player) Limit Texas hold'em.



Limit Hold'em (LH) Heads-up Duplicate poker


On July 23–24, 2007, Polaris played against poker professionals Phil Laak and Ali Eslami at the Hyatt Regency Hotel in Vancouver, B.C.  The competition consisted of four duplicate matches, with 500 hands per match. In each duplicate match, the same cards were dealt to both pairs of players, human and bot, but with the seating reversed.  After roughly 16 hours of play over two days, Polaris tied the first round, won the second and lost the last two.

Final result -- Polaris record: 1-2-1


On July 3–6, 2008, Polaris competed against six human professional poker players in the Second Man-Machine Poker Championship, held in Las Vegas at the 2008 Gaming Life Expo. Polaris defeated the human players with three wins, two losses and one tie. Each of the six sessions was a duplicate match of 500 hands against two different players, resulting in six thousand hands played.

Across all six sessions, Polaris won 195 big blinds. The version of Polaris used in the 2008 match was much stronger than the 2007 version, both in the quality of the component strategies and in its ability to learn which component strategy to use.

Final result -- Polaris record: 3-2-1

Overall Polaris's record vs. humans: 4-4-2


Polaris and Deep Blue

Comparing Polaris results with IBM chess computer Deep Blue versus reigning world chess champion Garry Kasparov in two games under tournament regulations.

Result: Kasparov–Deep Blue (4–2)

Result: Deep Blue–Kasparov (3½–2½)

Overall Deep Blue record versus Kasparov (5½–6½)

Polaris (4-4-2 or 5-5) vs. Deep Blue (5½–6½)

So with that being said. We can see that Polaris had better results versus humans than Deep Blue.

Polaris's Strategies:

Polaris have a total of 5 different strategies. 
The Nash Equilibrium plus 4 other to use against different types of opponents.  Polaris identifies which common poker strategy a human is using and switches its own strategy to counter.

1- The first approach is to approximate a Nash equilibrium strategy which is robust against any opponent.
2- The second approach is to find an exploitive counter-strategy to an opponent. We will show that these counter-strategies are brittle: they can lose to arbitrary other opponents.
3- The third approach is a compromise of the first two, to find robust counter-strategies.
4- The four approach is to combine several of these agents into a team, and learn during a game which to use.

Why is Polaris so good?

a) Adaptation. Polaris doesn't have a "best way" to play; it has a "best way" to adapt.
b) Specialization
c) No emotion
d) Aggression

http://en.wikipedia.org/wiki/Polaris_(poker_bot)

http://webdocs.cs.ualberta.ca/~games/poker/man-machine/

http://webdocs.cs.ualberta.ca/~games/poker/publications/johanson.msc.pdf


Originally published in: http://www.heads-up-fixed-limit-texas-hold-em-poker.com/p/polaris.html