Useful and obscure poker theorems. Where is the Sklansky-Chubukov chart used?

When playing poker, there are situations when it is better to go all-in than to call your opponent's previous bet. This move becomes especially relevant when the ratio of stack size to BB size is too small. After all, here it is simply unprofitable to call a bet in order to see the flop. After all, most often the player does not hit it. That’s why, with this kind of playing tactics, the short stack is consumed much faster than the poker player gets the cards he needs to fold, so it’s better to go all-in or fold.

But not every player is clear when it is best to pass or go all-in. Sklansky-Chubukov table designed specifically for such situations. Thanks to it, you will be able to understand what is the best move to make using push-fold tactics. Note that this strategy is also used in cases where a player wants to take over the opponents' blinds. If you have a good card and go all-in, you will have an excellent chance of winning the mandatory bets. But if someone calls your bet, you will still have the opportunity to take the pot due to having a stronger hand.

Push-fold tactics give good results over a long distance. That's why all successful players resort to it.

Sklansky-Chubukov numbers

First of all, let us voice the idea on the basis of which such a table was compiled. It is best understood with a concrete example. The player's position is the small blind, and he has a good hand. All your opponents have folded before you, so the move is yours. If the poker player on the BB guesses the strength of your hand, he will call a small raise in order to see the flop, since he has already invested money in the pot.

But here it is important to avoid a retaliatory bet. This is why, when you have a good hand, you go all-in. The opponent will respond to such a move by calling only if he has a strong enough hand, otherwise he will simply fold his cards.

The decision to make an all-in from the small blind position should be based on the stack size. The smaller its size, the wider the range of pocket cards that can be played. If the stack is relatively large, then it is not profitable to go to the flop with all hands. In some cases you should fold. After all, when all-in, the losses will be significant. Whereas if a small stack loses, it will be possible to cover losses by stealing the blinds more often.

The Sklansky-Chubukov table gives an idea of ​​which stack is best to go all-in with in the presence of a particular hand. If its size is less than the number that corresponds to your pocket cards, then the push will be relevant. Conversely, if the stack size exceeds the specified value, then it is better to resort to folding, otherwise you may face serious losses. It is unlikely that you will be able to win them back by stealing the blinds.

notice, that The Sklansky-Chubukov table includes calculations that are relevant for the small blind position. But you can also rely on them when making moves from other positions. The Sklansky-Chubukov table looks like this:

To get an idea of ​​the appropriate move, you need to look at the line that indicates the stack size above yours. So, if you have 13 BB in chips, then look at the next line - 15 BB.

But note that the Sklansky-Chubukov table does not take into account two key parameters that play a role in deciding whether to push. Firstly, if the poker players before you have folded all their hands, then the likelihood of your opponents having cards after you is very high. Secondly, when playing in poker rooms, part of the pot will be retained in the form of rake, which will reduce your profit from successful hands.

The hands in the table below have good strength. That's why it's worth playing them anyway. But remember that pushing is not always the most optimal solution. After all, if you have a monster hand, going all-in will only scare away your opponents. As a result, they will all be folded and the pot will amount to a meager amount. In this case, a small raise of 3-4 BB is relevant, then you will increase the pot and be able to win a significant amount.

When a medium or small pair comes preflop, then pushing is the most relevant option here. Indeed, in most cases, at least one overcard comes postflop; it gives a potential advantage over your opponents. With higher pairs and suited connectors, it is better to call with a raise.

Also, do not forget to pay attention to the playing style of your opponents. So, if there is a tight opponent behind you, then limit yourself to only raising. After all, if he has a bad hand, he will fold. If you push in this situation, then the player, if he has a good hand, will simply call your bet, and in the end you will seriously lose. If a loose opponent makes a move after you, then you can go all-in, but only with cards of a narrower range than indicated in the table:

The Sklansky-Chubukov table has another drawback - a possible increase in the dispersion of results. You can steal the blinds for a long time thanks to pushing, but losing a couple of stacks can cause you to go on tilt. But over a long distance, such tactics will give good results.

Let's imagine a situation: you are playing in a tournament, but after a number of unsuccessful hands, the game is clearly not going in your favor, and your stack is rapidly melting, while the blinds continue to grow! And now you are sitting in the small blind position, you have a marginal card that you can throw away, or you can try to play, but all the players before you folded their cards. What to do? Should I go all-in or fold? And if you put out all the chips, then on what cards can you do this? To answer these questions there is a Sklansky-Chubukov table...

It was developed by two professionals in their field - one of the best poker analysts, David Sklansky, and a leading mathematician at the University of Wisconsin, Andrei Chubukov. Together they developed a set of numbers that show which cards can be shoved all-in from the small blind, and this decision will be profitable for us even if our opponent plays optimally.

Moreover, the Sklansky-Chubukov numbers work even if our opponent in the big blind knows our cards for sure! Even in this case, this strategy will be profitable, since our blind gain if our opponent folds will be higher than our loss if he calls us with a stronger hand.

Additionally, pushing all-in from the small blind is good for two additional reasons:

1. First of all, there will only be one player behind us, who has already posted the big blind without even seeing his cards. Accordingly, there is a high probability that he will have “garbage hands” in his hands, which he will not want to play, preferring to fold them.
2. Secondly, even if he has marginal hands, if he has a sufficient stack in the later stages of the tournament, the player is unlikely to want to risk it, and therefore may also fold. This way, even if we don't get called on our all-in, we'll still be in the black because we'll win back his big blind.

Below is the Sklansky-Chubukov table, which indicates with which stacks (in the big blinds) and with which cards you can go all-in. However, you should not blindly follow this table, placing each time on the stack that we will have. Let's take pocket aces as an example - A-A. According to the table, we can move all-in on them with almost any stack. However, if we push all-in with a large enough stack, we will most likely just take the big blind, while a raise or 3-bet will allow us to get much more chips from our opponent.

Therefore, you should try to play each card in poker as profitably as possible, taking into account the size of your stack, the level of play of your opponents, your position at the table, and the stage of the tournament as a whole.

You must make any decision in poker based not only on the strength of your cards, but also on the playing style of your opponents sitting behind you. Although, of course, on some cards it is much preferable to immediately push all-in rather than try to play them in the hand, especially with a small stack. So, for example, if you come to the flop with a medium or small pair, then most likely you will see an overcard on the table, after which it will be quite difficult to understand whether one of your opponents hit the board or not. The same goes for weak aces, which are quite difficult to play.

However, keep in mind that the Sklansky-Chubukov table is designed exclusively for the small blind position, and only for those cases when all opponents before you have folded their cards. If at least one limper enters the hand, then you can no longer use it. In this case, you can use it, for example, to determine your further actions in the distribution.

You are the small blind in a game with blinds of $l-$2. Everyone gives in to you. You

But you accidentally flip your cards over and your opponent notices them (assuming your hand doesn't become dead in this case). Unfortunately, your opponent is a good counter who will thoroughly and accurately determine the best playing strategy for himself now that he knows your hand. After your small blind is revealed, you have $X in your stack. You decide that you will either go all-in or fold. For what profitability of $X is it better to go all-in and when to fold? Clearly, with a small profit of $X, you're better off just going all-in and hoping your counter opponent doesn't have a pocket pair. In most cases, he really won't have it and you'll win $3. Otherwise, you will be a loser, but this will only happen in a small percentage of cases. Typically, the odds are 16 to 1 that your opponent has a pocket pair. So, with a stack of 16 x $3 = $48, going all-in would be an immediate win. Since you will win 16 out of 17 times, you can lose 100% if you get called and still make a small profit. And you will not lose less than 100% of the time (in the end, only the lot will determine queens or deuces). But with a very high return of $X, you won't win $3 enough to be able to fend off your opponent when he gets lucky with a pair (aces or kings). For example, if you have $10,000, going all-in is a stupid move. Any time your opponent has pocket aces and kings, he has a huge advantage. You won't win enough blinds to compensate. The question then becomes, where is the breakeven level for $X? If your stack is below this value, you should go all-in. If higher, you must fold. Once you play A K♦, there are still 50 cards left in the deck. This gives your opponent 1,225 possible hand combinations:

Since the counter knows your assets, it will never answer you without an advantage. 40

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40 As a matter of fact, he will not answer if this gives him a negative expectation. Although, if the bank gives odds of the blind's money, he will call, even if it makes him a slight loser. After you go all-in for $X, the pot will give odds ($X+$3) to ($X-l). For a real return of $X for A K♦ (we'll calculate that soon), the counter would only win 49.7% of the time, it would still call. As it turns out, there are no range hands that give odds of 49.7 and 50% against Ace-King. The closest hand is the one that gives 49.6%.

Every unpaired hand, except the others Ace and King, is an outsider, so the counter will pass all hands. Additionally, of the nine remaining ace-king combinations, two of them are outsiders to your hands: A♠K and A♣K. Your hand can beat these hands with a heart or diamond flush, but these hands can beat you with a spade or club flush. A K under your A is a serious handicap. Seven ace-king combinations will answer your all-in raise, and that's for unpaired hands. Each pocket pair will also call. Your opponent can play pocket aces or kings in three different ways, and six different variations for queens and deuces. Thus, there will be 72 pocket pairs in total.

72 = (3)(2) + (6)(11)

79 hands out of a possible 1,225 will call you if you go all-in with Ace-King. If you get the answer, you will win 43.3% of the time. This value is close to 50%, since in most cases when they answer you, it will be a “heads-tails” situation. The only time you will be a loser is when you are facing pocket aces or kings.

To find the value of $X, we'll write the EV formula for the all-in, then set it to zero and untie it for X. You'll get the call 6.45% of the time (79/1, 225), meaning the counter will pass the other 93.55%. . When the counter passes, you win $3. When he answers, you win $X + 3 43.3% of the time, and lose $X the other 56.7%. So the formula for EV is:

0 = (0.935)($3) + (0.0645)[(0.433)($X + 3) + (0.567)((-$X)]

0 = 2.81 + 0.079X + 0.0838 - 0.0366X

2.89 = 0.0087X

X = $332

Break-even level is $332. We call this the Sklansky-Chubukov (S-C) number for A K♦ (or any off-suit Ace-King). 41 If your stack is less than $332 in a $l-$2 game, it's better to go all-in, even if your hand was open. If you have $300 and ace-king, you should bet $300 to grab $3 of the blind's money rather than fold. 42

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41 The numbers are named after David Sklansky, who was the first to state that calculating these values ​​will help avoid many problems preflop, and Viktor Chubukov is a game theorist from Berkeley who calculated the expectation for each hand. The returns calculated by Chubukov appear in this book.

42 This provision assumes that you cannot extract any useful information from other players' passes. In practice, if seven or eight players fold, it is very unlikely that any of them have an ace. This means your opponent in the big blind has a 3/1.225 chance of holding pocket aces.

Let's hope this is a perfect solution for you. Very few people's instincts will tell them to go all-in more than 150 times when the big blind plays knowing their hands with anything less than a pair of aces or kings. These conclusions are hard to accept because most people are uncomfortable with the idea of ​​losing chances. Ask someone to bet $100 to win $1, and you will be rejected almost 100% of the time, no matter what you bet. “It makes no sense to risk $100 to win one single dollar,” is a typical line of thinking. But it’s worth it, if only for the sake of expectation.

Moreover, in real poker, you try not to show your opponent your hand. When your opponent doesn't know you have Ace-King, it's even better for you and you can make a profitable all-in with a stack that's even a little larger than $332. After all, pocket deuces are the favorite against you, but who would call $300 with a hand like that? In reality, the player could only call you with pocket aces, kings or queens, and would fold in all other cases. Since they save so many winning hands, you can go all-in with stacks even larger than $332.

Now, before you get all excited, realize that we've only shown that going all-in is better than folding if you have less than $332. We're not saying that all-in is the best possible play; Raising a smaller amount or even calling may be better than all-in. But, in any case, it is better not to pass. You might say, "Great, now I know not to fold face-up Ace-King in a heads-up game. Thanks, I actually read the book and looked into the formulas to find out." But you'll really soon be glad you learned this, since this calculation method can be used for any hand, not just Ace-King. And the conclusions for some hands may be a surprise to you.

A precise definition of the Sklansky-Chubukov number: If you have an open hand with a $1 blind, and your only opponent has a $2 blind, what should your stack be (in dollars, not counting your $1 blind) to make it more profitable to fold rather than go all-in? , assuming your opponent will either make a perfect call or fold.

We provide a list of several representative hands and their corresponding Sklansky-Chubukov numbers. You can see a complete list of hands in the book "Sklansky-Chubukov Rankings," beginning on page 299.

Table 1: Sklansky-Chubukov numbers for selected hands

With some limitations and adjustments, you can use the Sklansky-Chubukov numbers for a hand to determine how good a hand you have for an all-in. You have to make some adjustments. Remember, S-C numbers are calculated with the assumption that your opponent knows your hand and will be able to play against it perfectly. This assumption slightly distorts the assessment of the situation that the S-C numbers offer. You almost can't make a wrong S-C (unlike folding), but you can also avoid making a mistake if you go all-in with a significantly larger stack.

How much larger it can be, in any case, depends on how the S-C values ​​are calculated. There are two main types of hands, hard and weak. With solid hands, you can call profitably with a lot of hands, but they won't be truly bad against those hands in general. Vulnerable hands may not cause frequent calls, but when they do, they are significant underdogs. For example, pocket deuces are a prototype of a strong hand. More than 50% of the time, the big blind will have a hand that can make a profitable call against him: 709 out of 1,225 hands (57.9%). But when it is answered, twos will win in almost 46.8%, almost 50%.

Offsuit ace - three is a vulnerable hand. Only 220 out of 1,005 hands can call it profitably (18.0 percent), but if that happens, it will only win 35.1% of the time. Both pocket deuces and ace-three offsuit are worth S-C $48. A solid hand, deuces, in some cases, a hand that is better for an all-in. This is why your opponent will be inclined to do more errors, when you have deuces rather than ace-three. Let's say you go all-in with $40. Most players will make a relatively tight call to this raise. Even if they know you're all-in with a weak hand, they still won't call without a pocket pair or an ace. For example, most players will almost certainly fold T 7 before a $39 raise.

This pass is correct if you have ace-three, but wrong if you have deuces: ten-seven is actually a favorite against pocket deuces. Thus, your opponents' tendency to fold too many hands before a big all-in raise will hurt them more when you have a strong hand rather than a weak one.

Suited connectors are also solid hands, and therefore the strength of their shoves is greater than the S-C values ​​would suggest. For example, 8 7 has a relatively small S-C value of $11. But it is a very tough hand: it can be called in 945 of 1,225 hands (77%), but it will win 42.2% of the time it is called. Because many hands that could have been profitably called will fold instead (J 3 ♣ ), you can make a profitable all-in with seven-eight suited and get significantly more than $11.

The script we used to find out the S-C values ​​is getting everyone to fold to you in the small blind. But you can also use these values ​​when you are on the button. If there are more likely to be two callers left than one, your chances of getting called doubles. Very roughly, you can halve the S-C value of a hand and determine whether it would be profitable for you to go all-in from the button.

As you might have guessed, these S-C values ​​are most useful if you are playing in a no-limit tournament. Despite their low profitability, they can help you decide whether to go all-in or fold when you have an average hand.

For example, let's say the blinds are $100-$200 and you have $1,300 on the button. Your stack is significantly shorter than average. Everyone gives in to you. You see K 8♦. Should you go all-in or fold?

The S-C value for king-eight offsuit is $30. You're on the button, not the small blind, so divide by two - $15. Your $1,300 stack with $100-$200 blinds is equal to a $13 stack with $l-$2 blinds. Since your $13 is less than $15, you should go all-in.

S-C values ​​tend to underestimate the all-in strength of a hand, so the solution is not as simple as it seems. Add a $25 ante and it's just an automatic all-in.

Final words

The decision to go all-in should be automatic if you have king-eight offsuit on the button with a stack of 6.5 times the blind. All-in is automatic and with J♦9♦ (S-C value - $26). Does this surprise you? If so, study the S-C values ​​starting at 164 and test yourself.

Any ace is a potentially strong hand for an all-in. Ace-eight gives an S-C value of $71, and even ace-three gives a value of $48. They are vulnerable, not steady hands, which is worse. But remember that S-C is underestimated and vulnerable hands. When everyone folds to you, on or near the button in a tournament, and you have an ace, you can often easily move all-in, even if your stack is more than ten times the big blind.

The tournament process assumes that these "loose" all-ins are the right decision; in fact, this value is the main reason why most of them win money in all tournaments. This is the secret that makes the difference between professionals and amateurs in a tournament. Use tables. Starting on page 164, this will help you decide when to go all-in, and you'll see your tournament results improve very quickly.

When to use (and when not to)
Sklansky-Chubukov classification

In the last section, we explained what S-C values ​​are and we gave you a basic idea of ​​how you can use them to make decisions. But we've only given you the basics, and we'd be remiss if we stopped there, because there are right and wrong ways to interpret S-C meanings. We offer you additional guidance in this section to help you get the most out of this toolkit.

Adjustment for ante

Although certain S-C values ​​are designed for a certain situation - you have a $1 small blind, and your only opponent has a $2 big blind - it is only slightly incorrect to consider this situation in terms of your odds. In other words, if a hand has an S-C value of 30, that means you will have positive EV if your odds are 10 to 1 or less (30 to 3). Thinking this way is very useful, especially if there is an ante. When there is one, you divide the S-C value by three to see the odds you can lay down. For example, the blinds are $300 and $600 with a $50 ante. The game is for ten players, so the initial pot is $1,400. You

In the small blind, your stack is $9,000. If everyone in front of you folds and you go all-in, you're setting odds of 6.5 to l. The S-C value for Ace-Four offsuit is 22.8, divided by three, and your chances of profit are already 7.5 to l. Thus, all-in will be profitable, but only because of the ante. Without it, you would be laying odds of 10 to l.

Best hands for all-in

While guidelines for S-C values ​​are useful, especially in one-on-one play, they should not be followed blindly. Sometimes you should go all-in even when the S-C values ​​do not suggest it, and sometimes vice versa, even if it could make a profit. As a basic principle, all-in is most attractive if the S-C values ​​prove that it will not create negative EV for the play, and you have no particular reason to play the hand differently. This situation most often occurs when you are out of position against a good and aggressive player, and your hand is weak except for its showdown value. The king-four offsuit that was mentioned earlier is a good example of such a hand. With a $200 stack in a $10-$20 game, it's natural to want to fold K 4♠ in the small blind if everyone else has done so. This desire is especially strong if your opponent in the big blind is a good player.

Limping will most likely trigger a raise (which you don't want to respond to). And a small raise will most likely trigger a call. Neither of these alternatives are attractive.

Folding won't be a good choice anyway, since the S-C value for king and four offsuit (22.8) is larger than your stack size (we'll briefly discuss one exception). All-in and showdown will be profitable, so all-in without showdown may simply be less profitable. In fact, not showing up can make your hand more profitable if it's possible for your opponent to fold hands like K♠6 ♣ and A 2♦, which he would have called if he had seen your hand.

In general, speaking, the best hands for all-in are not those that play well, but those that have showdown profitability. These are hands like A ♣ 4♦ and Q♠7♦ until you have more chips than the S-C value.

All-in exception

If the S-C value suggests that you should go all-in with hands that you would otherwise fold, you should listen and go all-in. But there is one exception: if you are in a tournament with a very weak hand and a minimal short stack, sometimes you should fold if you can see a few more hands for free.

For example, let's say you have $500 in the small blind on a ten-player table with blinds of $100-$200, no antes. You

everyone gives in to you. The S-C value for offsuit tens - threes is 5.5, which implies all-in.

For an all-in, the expectation is positive, but for a pass, the expectation is even more positive, since it guarantees that you will see 8 more hands intended for you for free. If you go all-in, you will most likely get called and lose. The guarantee that you will see free hands is worth more than the positive expectation you will get if you go all-in.

All-in with too many chips
Often you should go all-in even if you have more chips than the S-C value. This is because the S-C values ​​were calculated with the assumption that your opponent will play excellently against your hand, and in practice this assumption rarely holds up.

Let's take this hand

The S-C value for suited tens-fives is 10. But this value is only so low because your opponent will presumably call 72% of his hands correctly. This list of hands includes a lot of really nasty ones, like J 3♠ and T♦6 .

In practice, most players will fold these hands to a significant all-in raise without a second thought. Instead of calling 72% of their hands, they might call with only 30%. Since they will fold with so many hands as you want, you can get out of the situation by raising with a stack larger than the S-C value. Because of this effect, the real value for an all-in becomes 20. All-in, for example, with 13 small blinds is also practically correct. This approach applies to many other average hands with an S-C value below 20.

All-in may not be the best option with hands that play well

Remember that we are after all talking about hands that don't play well, especially out of position. These are the hands that make you think about passing.

If you have a better hand or you're in position (like the small blind on the button in a heads-up game), you often shouldn't go all-in, even if the S-C value says otherwise. You should limp in or make a small raise. (But you should never fold, and you should almost never make a large raise to the size of a significant portion of your stack—it's always better to go all-in than to raise 25% of your stack.)

The most basic case in which you should ignore the S-C advice to go all-in is when you have a fairly large stack, but the S-C value is still higher (the S-C value is 30 or more). In this situation, the only hand suitable for an all-in is offsuit aces or kings with weak kickers (A ♣ 3♠ or K 7♦).

Of course, you lose out on a hand like jack-ten suited if you go all-in with 20 or 30 small blinds. Whether you should just call or make a small raise depends on your opponent's playing style. But all-in, while profitable, is almost certainly less profitable than other options since you have a fairly large stack. (Of course, if the stack is relatively short, all-in with jack-ten suited is the same as suited nine-eight, eight-seven, or any other hand with the appropriate S-C value)

Small couples are a little different. Pocket deuces have almost the same S-C value as queen-jack suited (48 vs. 49.5), but the two hands play completely differently.

The main difference is that deuces will often lose if you make small raises with them (suited queen-jack will win more often in this situation).

This justifies the idea that it is better to make small raises with a queen-jack of the same suit, and go all-in with deuces. But against most players, in our opinion, going all-in with deuces is not the best option with 20 small blinds. We believe that limping, which may seem unnatural here, is still better, although not by much.

When in doubt, go back to the S-C strategy and just go all-in.

Before you start playing for money, it is advisable to read several books on different topics (psychology, mathematics and poker strategies), and it would also not hurt to familiarize yourself with the theorems of poker. This article contains the most popular of them.

Clarkmeister's theorem

“If there are two players left in the game and the fourth card of the same suit comes out on the river (to three suited on the board), and your move is the first, then you need to make a bet (more than 3/4 of the pot size).”

Such a move will force the opponent to fold if he does not have a flush or if he has one, but it is weak. The larger the bet, the higher the probability of folding a weak flush.

When there are multiple players in a hand, there is a high chance that someone has a strong flush, so it is less effective in this case.

Sklansky-Chubukov numbers- a table designed to determine the stack size for each hand (in the big blinds) with which it is profitable to go all-in preflop in the small blind position, when all players before you have folded.

David Sklansky is a legend of professional poker, winner of three WSOP gold bracelets, the most authoritative poker theorist, author of thirteen books and two educational videos, as well as a large number of publications devoted to various aspects of poker and gambling theory.

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The essence pushes Sklansky-Chubukov is this: when you have a small stack, and preflop all the players before us folded, it is profitable to go all-in. Then we will most often receive a fold from the big blind, and the number of such folds and the BB we take will pay for the losses that may follow when our opponent calls.

Experience shows that such pushes are profitable at a distance.

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“When you play the way you would play if you saw your opponents' cards, you win. And vice versa".

The logic is clear, but what is the point of knowing this theory? Go ahead.

Aedjohns' theorem:

"Nobody has anything."

It shouldn't be taken literally. The idea of ​​the theorem is simple: opponents will not always have a strong hand (thanks, cap), so a moderately aggressive playing style will increase your win rate.

Baluga's theorem reads:

“After a raise from your opponent on the turn, you need to re-evaluate the strength of your top pair.”

Several important conclusions follow from this theorem: A check-raise on the turn from your opponent always indicates that he has a strong hand.

Big bets on the turn are rarely made with clean draw hands. In the worst case, your opponent will have a pair + draw, in the best case, he will have the nuts.

In the event of a raise/reraise from your opponent on the turn, it would be more profitable to fold.

P.S. Most of the above-mentioned theorems were invented by experienced players and posted by them on the 2+2 website, after which they became recognized theorems. Only relevant for Texas Hold'em.