Heads Up

The Art of a Heads Up SNG

By | Heads Up | 2 Comments

Sorry for not blogging in awhile. I've been grinding 10hr days, which is not what I should be doing but since I've been running extremely well I feel like putting in volume while I'm playing my best is the right thing to do. For those of you who don't know, I specialize in HU SNGs, and for the last two years I have been making a living grinding these things, and I feel like I have a good understanding of the game. So today I would like to talk about some of things I've learned about these 1500 chip duels.

First off, to be successful, you must have a an above average understanding of the game and you must have confidence that you can beat anyone. If you're not capable of bluffing the turn just to jam the river then this might not be for you, and I suggest you go nit it up at a cash game. HU is the best way to maximize your individual skill, and there is no other game in poker where your skill prevails more than in a HU match. That being said, you need the keen ability to bluff as well as know when your opponent is bluffing, and only great players have both skills. A lot of that comes with experience, and I do not recommend heads up to anyone new to poker. Heads up is all about the button, because position means everything. If I see a kid that doesn't open from the button and isn't c-betting (continuation betting) then I know right there that he has no idea what he's doing.

Don't be standard, I swear to God, every kid is min raising button and half potting the flop. It's getting ridiculous, and I know its optimal play but like every kid on PokerStars is doing it. Understand situations and if you're bluffing or not. Don't bluff just because you know your hand is not good, but understand what you're trying to represent as well as your opponent's hand range/calling range. Have the balls to jam the river just because you know your opponent is middle pair at best (make sure you bet the turn so you can represent a hand). Heads up is all about the story you tell, and if you want to triple barrel and represent a made hand, then you can. However, it takes a great player to know when they're beat and hold off on firing that last bullet.

Aggressive play is optimal in heads up because most the time, players are playing marginal hands. Picking up as many pots as you can is vital. Understand how to play very short stacks because at 50-100 and up, push/fold poker is very key.

Timing tells: I can't explain them for the life of me and I think it's all intuitive and it just comes with seeing situations over and over again, but I can pick up on tells in my sleep.

You have to put in volume, and I mean sick volume, because you're playing little edges, and those little edges with volume is what gets you paid. For example, the best players at HU don't win above 57% of their games, and the only way to make a great profit is to put in the volume. Love the game and love every moment of the grind, and if you're miserable grinding, then this is not for you. If you have the passion to learn and get better and use strict bankroll management, then take a shot and dream big and don't fall short.

Thanks to TBone for this guest post.

Sage busts Lee Jones’ SAGE

By | Heads Up, Mathematics, Theory | No Comments

"Are you Sage?" Lee Jones asks. Yes, I am. And I'm here to show people why your system is a weaker version of the Better Than Nash Equilibriums here on Risk Oriented.

In 2006, Lee Jones created a system which tired MTT players, heads up at the end of a tournament, could memorize and effectively use to push-bot with very big blinds.

Fortunately for me, any time you simplify a complex system like a game theory optimal solution, cracks begin to form.

Leak: The SAGE system "stops working" above 10BB.

Exploit: Simple, if the player has more than 10BB, assume he's using a different strategy. Exploit that strategy. For example, a SAGE player might be push/folding when under 10BB, but minraising over 10BB. This is a good indication that your opponent is using SAGE. If you can figure out the percent of hands he minraises, then you can create a counter strategy that includes calls, 3-bets, and folds. This kind of deep-stack exploitative play is outside the scope of this article.

Leak: The SAGE system requires perfect play.

Exploit: For example, if your opponent is minraising when he gets KK or AA, but playing push/fold any other time, you know that when he pushes, KK+ is not in his range. Therefore, the hands he pushes will, on average, be weaker. If his strategy was a proper equilibrium, this "weaker range" would dictate a lower "SAGE" number. If he is still shoving with his entire range, we should slightly open our calling range.

So, in short, don't use SAGE, because there are better alternatives available, for instance, the Better Than Nash Shoving Equilibriums I developed.

Better Than Nash Equilibriums for Poker (Game Theory)

By | Heads Up, Mathematics, Pro, Theory | 8 Comments

What if you were to find out the Nash Equilibrium for Poker that you've been using all this time was... wrong? Who actually did the math originally? Do you know? I surely don't. I've done the math and found that the Nash equilibriums for poker chart that so many new players use is actually wrong. It's true, the chart touted by thousands of poker players around the globe is bunk. It tells you to push hands you shouldn't. What is a Nash Equilibrium? It is a chart that brings you to 0EV. Playing according to Nash equilibriums for poker guarantees that you won't lose money, but the goal of poker is to win money, not avoid losing it.

Clearly, against a player who folds 100% of their hands, even at very large stack sizes we could profit by shoving hands that the Nash equilibrium charts would tell us to fold. This proves that there exists maximally exploitative all-in range (called a "best response") that is different from the Nash ranges. To solve for a better solution, I considered the three variables that actually matter: your hand range, your opponents calling range, and your effective stack size.

Register for free and get access to additional resources on our Better Than Nash solution.

1 - Beating the Nash Equilibriums for Poker

In this first chart, I will posit the assumption that our opponent will call with no more than 30% of their hands. If this is the case, then the following chart illustrates the hands you should push with based on your effective stack size.

A 30% Calling range is very loose and means the opponent knows that you are pushing light and is trying to call light in order to exploit you. Why 30%? A few reasons:

  1. Because you cannot know with any accuracy if your opponent's calling range is 25% or 35%. It seems like a good, middling range.
  2. Because it is the optimal calling range for someone shoving 40-50% of their hands. I believe people intuitively settle on something like 30% for somebody who is opening "very loose"
  3. Because many players have a real issue calling a shove with hands like Q5, even though it may be optimal.

Chart #0: Opponent Calls Your All-in 30% Of The Time
nash equilibriums for poker

Teal: Push <20BB
Red: Push <15BB
Purple: Push <10BB
Blue: Push <7.5BB

Unless our opponent is willing to call extremely light, we are pushing 100% of our range under 7.5BB.

For the rest of these charts, the following legend applies.

Blue/Red: Always Push These Hands No Matter What (Unexploitable)
White: Push 100% Of Hands If Opponent's Folding Range Includes a SINGLE Hand Colored in Red
Chart #1: 12BB Effective Stacks
better than nash equilibriums for poker 12bb

11BB chart removed. Log in or register for free to access it.

Chart #3: 10BB Effective Stacks
better than nash equilibriums for poker 10bb

Chart #4: 9BB Effective Stacks
better than nash equilibriums for poker 9bb
8BB chart removed. Log in or register for free to access it.

Chart #6: 7BB Effective Stacks
better than nash equilibriums for poker 7bb

6BB chart removed. Log in or register for free to access it.

To clarify, if we're 7BB deep with our opponent, we shouldn't shove 32o unless our opponent folds a hand like Q8, but if he does, we should be happy to push all in with 32o. If we were to use the Nash equilibrium charts, we would fold 32o at 6BB no matter what our opponents strategy. In fact, we would even fold hands significantly stronger than 32o, like J4o. This accounts for another 30% of our range that we could be profitably shoving, instead of folding.

Against an opponent who will not fold a hand in red, you play hands in white according to the Nash Equilibrium strategy found here.

2 - What is a Nash Equilibrium?

The brilliant economist, John Nash, in the 1950s, developed a system by which zero-sum games can be solved. He put forward the question, "If everybody is trying to maximize the amount of money they win, what is the strategy that each player should rationally adopt?"

3 - Why do we use the Nash Equilibrium?

A sit and go is very similar to a zero-sum game where each player is trying to rationally win more money. Therefore, some enterprising poker minds, originally, the Austrian Helmuth Melcher, have used Nash's equations and assumptions to develop an equilibrium strategy for play. You can find the Nash Equilibrium developed by Mr. Melcher here. Unfortunately, an equilibrium strategy results in an expected value of ZERO, which means you lose money to the rake by playing this strategy.

4 - Why is the Nash Equilibrium insufficient?

Nash supposes several things that are simply not true about poker. Nash's assumptions:

  1. The players will do their utmost to maximize their expected payoffThis should be the case in poker, but emotions, fears, and irrationality still exist and can get in the way. Additionally, when using Nash equilibriums for poker, we have to assume that every game is independent of each other, but this is not the case in poker. An otherwise rational player might be hesitant to take a big risk with a large portion of his bankroll, for instance. We have no way of knowing what other factors are involved in our opponents' decisions.
  2. The players are flawless in execution. -- No human player can be flawless in their execution of any strategy. Even if we assume they were, read on...
  3. The players have sufficient intelligence to deduce the solution. Ultimately, poker is too complex to be solved. We can reach some solutions for specific questions, like, "should we go all-in preflop," but in these cases our opponent has yet to act. Once the opponent acts, the permutations of possibilities are endless. To deduce the solution, we would need to know exactly how he plays every hand.
  4. The players know the planned equilibrium strategy of all the other players. We cannot know this, ever. Best case scenario, we're playing an opponent that we know is using a specific system, exactly. A good example of this is the SAGE system. If we know this, we can define an optimal strategy, but it is not a Nash equilibrium.
  5. The players believe that a deviation in their own strategy will not cause deviations by any other players. If I deviate from my strategy, other players should and will deviate from theirs to exploit me. Why does Nash require this assumption? It's very simple. If I deviate from my strategy, and it causes my opponent to deviate in order to exploit me, he has unbalanced his strategy. If I know that he has unbalanced his strategy, I should find an exploit for his strategy. Then, he should find an exploit for mine. According to Nash, all of these levels must happen between hands, in an instant, essentially bringing us back to a Nash equilibrium. This idea that every player engages in Nth-level metagame on every hand is only possible in theory.
  6. There is common knowledge that all players meet these conditions. So, not only must each player know that the other players meet the conditions, but they must know that they all know that they meet them, and know that they know that they know that they meet them, and so on. This is not the way poker works. Nash is giving us an academic solution to a problem. It simply does not apply as well to poker as many players think it does.


Waiting for a Better Spot

By | Beginner, Heads Up | One Comment

In certain situations, it pays to wait for a better spot. Since the hand you really want to spend your money on may be just around the corner, you shouldn't put money in with hands you feel "lukewarm" about. First, it's hard to tell if you're a 55% leader or a 45% dog in lukewarm hands. Since the hand you feel good about pushing your stack in with may be the next hand you're dealt, you shouldn't risk your chips on marginal spots. Think about it like this -- the chips you're using to chase with borderline hands are money you'll wish you had later to use, when the better hand comes along.

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Hand Values are Relative

By | Heads Up | 2 Comments

A lot of things matter in a poker game. Your opponents matter. The stakes matter. The way you play matters. What really doesn't matter are the cards that you hold. The cards you hold are relative to the cards the other players hold.

You may have KK, but that's only a good hand if you're up against a weaker hand, not if you're against AA. It's your job throughout the entire poker hand to determine how good your hand is relative to the other hands in the pot.

What really matters is the action at the table. How are the other players betting at the table. Are they showing strength or are they bluffing? How can we determine the strengths of our opponents hands compared to how strong ours is, and how can we manipulate them into giving us all their money when our hand is stronger and still losing very little when we're behind?

Over the course of your poker career, you're going to have every poker hand.

You're going to have 72o and you're going to have AA. Over time, you'll have all of them in equal proportions. All we can do is ensure that, when you have a hand, you play it to the best of your ability and you analyze the situation in front of you so you understand how you can go about making sure you play that hand better than they would play that hand if they had it.