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

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