Starting hand chart. Nash Equilibrium Static Push Fold Nash Table

Our topic for today's conversation is all-in fold or push fold, depending on who likes which option. It is used more often with a short stack.. If only two options remain for the player (fold the hand to go all-in), the chances of doubling up will increase, therefore, the likelihood of a deep tournament progression will improve.

Everyone who takes an individual training course at the Poker Academy (see ) improves their performance. These are not just words. That being said, the savvy might allow us to use the stack for ante and steal. Also, save your chips and don't splurge on very sensible raises or limps. And quickly double. Push fold can mean exactly what is put in the name of such a player forgets what a call is, works exclusively on the preflop - either fold or all-in. In cases where the stack drops to the level of 10 BB, raising or limping is already inappropriate, since it is no longer possible to fold the hand post-flop. Therefore, you need to use the remaining full potential preflop. Push fold applies in and , where it is best to become a short stack due to the increase in constant blinds. Usually, push-fold is the last weapon and resort to this weapon at 10 AP and below.

How to push fold

And then I accidentally got on the page of the site "Academy of Poker". I listened to the lecture “The Beginning of a Career of a PRO-Player” and got very interested. The push-fold strategy is based on make decision making as easy as possible especially for beginners. After mastering some basic concepts, playing with short stacks will no longer be a torment, but an easy walk. The percentage of mistakes will be very sharply reduced, which will naturally increase the survival rate in tournaments. Just in case, "short stack" is a loose term. Many players, of course, will have their own definition, but in most cases, a stack with 10 big blinds or less is assumed. You need to constantly monitor your own stack. And it is especially important not to miss the 10BB mark.

There is also such advice from: in order to better understand stacking and taking into account the blinds with antes, you need to read about, which was introduced by Dan Harrington in the poker zone system. Also, why is a raise worse than an all-in? The main thing for a short stack is just to survive, and what needs to be done to survive? Avoid confrontations. It is necessary to imagine that we have 10 BB and we are on the button. For example, if the player is watching T J in the big blind, we raise 3x. The vast majority of players would have called our raise in this situation, but when they saw a 10BB shove they would likely just fold. And with a short stack, you need to enjoy every little thing. In all situations (of course, except for those when we have aces, kings and other monsters), we want to take the blinds from the antes, and not compare, while risking being eliminated from the tournament. And on the way to a fat stack, instead of trying to double up on all-ins, we should aim to progressively increase the stack., through the use of aggression and position.

The Nash equilibrium is a part of game theory, its author was the American mathematician John Nash. This theory demonstrates the optimal play "in a vacuum": when to bet all-in or call opponents' pushes. It is important to understand that pushing/calling according to Nash in modern poker realities is no longer the only correct one. It is only optimal if your opponents are aware of this strategy and stick to it without deviation.

The Nash push/fold strategy can only be used optimally against strong and understanding players. With a minimum deviation, the effectiveness of this strategy is significantly reduced. The most profitable use of the Nash equilibrium is to adjust for opponents, and correct own game based on opponent's ranges.

Where to use Nash equilibrium?

Nash Equilibrium ranges are suitable for , Sit&Go and Tournament play. This strategy should be used when your stack is down to 15 big blinds or less and your game is down to a single push/fold decision. To hone your playing skills, you should use special software that simulates such situations: and ICMIZER.

Let's say your opponent goes all-in and you have 14 big blinds left. By Nash equilibrium, you can call with a wide range of hands with 20 big blinds, including pocket threes, QJ, QT and even K2s.

But this is a range in a vacuum, which does not take into account the type of tournament, the stage and the difference in payouts. This strategy is correct, but only if the game consists of only two preflop decisions: a push or a fold. In modern realities, strong players are able to play a deep post-flop hand with a stack of 15 big blinds.

Aside from using the Nash balance, you can always just wait for a good hand and call your opponent. But if you don't know exactly what is a good hand relative to your stack size, then look at the Nash tables.

Nash shoving range

Nash calling range

Green color– effective stack from 15 to 20 big blinds.

Yellow and dark yellow color– effective stack from 6 to 14 big blinds.

Red color– effective stack from 1 to 5 big blinds.

Using a Nash balance in your game will suit players as it will give players an initial understanding of shoving or calling ranges for standard tournament situations and will help them get started in poker fairly quickly.

In this article

• Is push/fold Nash play optimal?
  
• Can Nash shoving or calling be -EV?
• When and how should adaptation be carried out?
  
• Does the adaptation depend on the magnitude of the ICM (bubble multiplier) effect?
  

An important success factor in SNGs is good game in heads-up. Since the blinds are usually quite big when heads up, you will usually find yourself in situations where you either fold your hand preflop or shov. This stage of the game is called push/fold.

In this regard, the so-called Nash ranges (NR) play an important role. Because heads-up you will often be up against a fish that has built a big stack with crazy moves, using Nash ranges requires some caution.

This article is a complement and extension of the SAGE articles - Sit and Go Endgame System and Heads-Up Push/Fold.

However, you do not need to read them to understand the concepts presented here. The so-called SAGE is based on the Nash equilibrium principle, however, this principle is used in it in a somewhat simplified form, which makes this system less flexible.

Basics

Abbreviations
BB	big blind	NCR	Nash calling range
BL	Blind level	NPR	Nash shoving range
CR	Call range	NR	Nash ranges
ES	Effective Stack	P/F	Push/fold
EV	Expected value	PP	Pocket Pair
HEV	EV hands	PR	Push Range
HU	heads-up	REV	EV range
ICM	Independent Chip Model	SB	small blind

First of all, let's clarify the basic terminology:

Effective Stack

The effective stack is an important parameter when analyzing heads-up push/fold situations. It refers to the smaller of the two stacks before the blinds were posted and is measured in BB. So ES is always the same for both players.

The blind level (BL) is 500/1000, after paying the SB you have 5500 left, and your opponent who put the BB has another 8000 in the stack. Accordingly, ES = 6.

Ranges

Range in poker implies a certain set of hands. When it comes to heads up, "x% ranges" are of particular interest: they consist of x% of the strongest hands out of 1326 possible starting combinations.

If ES = 9, then the calling range (CR) is 42.7% of hands, which includes 22+, Ax+, K2s+, K4o+, Q4s+, Q8o+, J7s+, J9o+, T8s+, T9o, 98s. The "+" sign means that all hands with the best kicker (or high pockets) are also included in the range. So K4 is also part of the range, while 87s is not.

Compare to a pushing range (PR) of 43.3% with ES = 16. It consists of: 22+, Ax+, K2s+, K7o+, Q5s+, Q9o+, J6s+, J9o+, T6s+, T9o, 96s+, 98o, 85s+, 75s+, 65s, 54s. As you can see, hands K4, K5 and K6 are not included here, and 54s here, on the contrary, is part of the spectrum.

This example illustrates the fact that a 43% calling range at ES = 9 is far from equivalent to a 43% shoving range at ES = 16. That is why we will always list hands in these situations. Percentage values ​​and exact ranges are taken from the ICM calculator, which you can find at the following link: .

It is quite obvious that the following statement is also true:

If you add a random hand to a % range, you will get a new range if that hand is the strongest outside that range. Conversely, if you remove a hand from a % range, you will get a new range if that hand is the weakest within that range.

Independent Chip Model has already met you in previous articles:

A feature of heads-up is that the ICM effect is no longer active here. That is why heads-up in SNGs (like heads-up in MTT) is essentially the same as heads-up in a cash game, where the value of each chip is equal to

[($1st) - ($2nd)] / (Total Chips)

So your decisions to shove or call a heads-up shove mainly depend on the following parameters:

• Your ES
• Your opponent's calling or shoving range

In all stages of MTTs and SNGs, with the exception of heads-up, there is always an ICM effect to a greater or lesser extent. In SNGs, this effect usually peaks on the bubble, so at this stage it is known and measured as a bubble multiplier (see below).

Tournaments need to master strategy. When playing in many tournaments, tactics such as pushing and folding help us take much more high levels, and means to win a large amount of prize money.

It all happens because of wrong decisions or just a combination of circumstances. Currently, there are many strategies for playing poker, as well as all possible poker tricks, and in such positions, they sometimes have to be forgotten. The point is, when with short stacks, there may be a shortage of chips, and therefore we will not be able to successfully use a bluff in poker or other poker tricks. Further, we cannot afford to see the flop for the blind, to make a standard raise, because even such bets in poker will simply completely ruin our stack. And for a player with a good, large stack, any of our bets will not be threatening, because even if he loses, he will not jump out of the tournament, but will retain the advantage. The only, as it were, serious bet that we can make is all-in.

Only in this case there will be hope that our bet will be called by a certain number of opponents or opponents will all fold. For this reason, when playing with a short stack of twelve or less big blinds, we recommend using push-fold tactics. Which implies that the player will have only two solutions: he goes all-in or folds. This strategy can allow you to play as efficiently as possible while still having a short stack. And based on mathematical miscalculations, experts make a chart starting hands, which allows beginners to make decisions with a push-fold strategy.

Ranges when entering the game

There are poker starting hand charts that should be followed if we are the first to enter the auction. That is, when all the opponents who made the decision before us have folded and our stack is twelve big blinds or less. Guided by such tables is quite simple, they indicate hole cards when it is recommended to go all-in, when the amount of blinds in the stack corresponds to the indicated number for the position at the poker table in which we are. Other charts already regulate when you should go all-in if one of the opponents is already trading before us. This table cannot take into account the size of the opponent's poker bet because in most cases, when we put all the chips, the opponent who made the bet will call. The correct and only decision that we need to make is to go all-in in this hand or not to go.

During tournaments, the size of the stacks of participants is constantly changing - for some it becomes larger, and for others it is smaller. At the same time, the monetary equivalent, which demonstrates the stack size, is not important here. Here its value relative to the size of the blinds is important. After all, it is in them that it is customary to measure the stacks of poker players. The larger the stack-to-blind ratio, the more aggressive you can play, and vice versa. Accordingly, the strategy of the game depends on the number of chips remaining in the hands of the poker player. In some cases, the most optimal tactic becomes push-fold.

When is push-fold relevant?

In the case when the stack size becomes catastrophically small, then the player needs to take decisive action to increase it. If you continue to fold weak cards and wait for a monster hand, then your stack will simply be used up due to the need to post blinds. To prevent it, you should start active game. But how to lead it? Perhaps you need to call opponents' bets to see the flop, and if you miss it, fold? However, such solutions are unacceptable.

If you call with a small amount of chips, you will use them up even faster. At the same time, the chance of hitting the flop here is very small. However, even if you get the right cards, there is a risk that you will only win the blinds. This is why calling short stacked preflop is a bad move.

With a small number of chips, it is important to resort to push-fold tactics. It involves two moves to choose from - push or fold. In some cases, you will shove, that is, go all-in, and in others, you will fold. But not every player understands how to choose one of these actions, being in a given situation? Exist poker nash table, it is she who helps to make the right decisions with such tactics. It provides information that will help you understand when to call opponents' bets depending on the size of the stack, and when to fold.

But let's start with why the push-fold strategy is optimal when you have a short stack. The thing is that if you go into the hand with a call, then other opponents who still have enough chips for return bets can support him. As a result, a large number of opponents will participate in the draw, which, even with a strong hand, seriously reduces the chances of winning.

When a poker player makes an all-in, not everyone will call such a move, especially if you have invested in the pot more money than the blind value. This means that you will be able to weed out most of the participants with this action and at the same time increase your chances of winning.

Visual tables

Now let's move on to the poker Nash table itself. It includes two diagrams. The top one is for when you decide to go all-in. In it you will find numbers that indicate the number of big blinds. The names of pocket cards go horizontally and vertically:

Using this table is very easy. First, you look for your preflop hand in it, and then compare the indicated number with the number of big blinds. If it is less than or equal to the size of the stack, then push.

Note that the stacks for pocket pairs, green for suited cards, and brown for offsuit cards. Having studied the data presented here, it will become clear that the better hole cards, the more chips you can push.

The following diagram shows the action options for a call. Here everything goes by analogy with the first table, which will not cause difficulties in understanding. At the same time, you can use both of these schemes not only when playing with a short stack, but also within the framework of distributions, when you need to knock opponents out of the game.

Summing up

When you have a small amount of chips left at your disposal, then you should actively join in game process and make informed decisions. At the same time, the best tactic in this situation is push-fold. To properly implement it, use the Nash table in poker. We advise you to download and print it so that you always have it at hand.