Sklansky-Chubukov Numbers: The Stack Where a Shove Cannot Be Punished

The number only means something inside one very specific situation, so pin that down first. Two players. You are in the small blind, the seat that posts the smaller forced bet, here 1. Your opponent is in the big blind and posts 2. You act first, and you have exactly two legal choices: shove, meaning push your whole stack in, or fold and give up your 1. There is no smaller raise, no limp, no flop played out with bets on it.

Then comes the assumption that makes the whole idea work. Your opponent is dealt a hand and is also shown yours, face up. They know you hold KQs. They call or fold with that knowledge, and they never get it wrong.

Now vary your stack and ask one question: does shoving beat folding? With a very short stack it plainly does, though not for the reason people usually give. You are risking little to pick up the 2 your opponent has posted, and when they call, which face up they will do with most of the deck at that depth, the stack at stake is too small for their edge to outweigh the 1 you would have handed over by folding. As your stack grows, the shove risks more and more while the prize stays fixed at that same 2, and the calls you do get hurt more, because a player who can see your hand calls only when calling pays. Somewhere between those two extremes the shove and the fold are worth exactly the same. That stack is the Sklansky-Chubukov number for your hand. At or below it, shoving is at least as good as folding. Above it, that guarantee is gone.

The usual first reaction to the face up assumption is that it is absurd, and it is. Nobody plays against an opponent who can read their hand. That is the point. The assumption is there to make the answer a worst case rather than an average one.

Consider what it rules out. Every read your opponent could have, every tendency they could exploit, every timing tell, every note in their database, every leak in the way you construct your range: all of it is already covered, because knowing your exact two cards is strictly more information than any of those could give them. So when the number says the shove holds up at that stack, it holds up against every opponent who could ever sit down, not just a typical one. That is what unexploitable means here. Not that the play is the best one available, but that no counter strategy exists that can make it worse than folding.

The direct consequence is that these numbers are deliberately conservative, and you should read them that way. Your real opponent cannot see your cards. They will fold hands a psychic caller would call with, and call with hands a psychic caller would fold. That uncertainty is worth money to you, which is why shoving above your hand's number is often still the right play in practice. It just stops being guaranteed, and starts depending on who is sitting there.

The published Sklansky-Chubukov table has always been quoted in small blinds, so that is the unit the slider and the grid use here. The same model expressed in big blinds gives exactly half of every figure, and the table lists both columns so you do not have to convert anything in your head.

• The slider runs from 1 to 60 small blinds, with quick pick buttons for the common depths, and the label beside it reports the same depth in big blinds. The grid and the frequency line under it both redraw as you move it, and the last column of the ranked table reruns the same test hand by hand. What does not move is the number itself: a hand's Sklansky-Chubukov figure is a fixed property of the hand, not something computed from the stack you have chosen.
• The grid is the standard 13x13 layout of all 169 starting hands. A hand is shaded when its number is at or above the stack you have selected, which is to say when shoving it at that stack is unexploitable.
• The frequency line reports the share of all 1326 two card combinations that qualify at that stack, not the share of the 169 boxes. Combinations are the honest measure, since there are more ways to be dealt an offsuit hand than a suited one.
• The table ranks hands by their number and shows it in both small blinds and big blinds, the second column being exactly half the first. It opens with the top 25 and expands to all 169 on request, and its final column tells you whether each hand qualifies at the stack you have set.
• Aces appear as an infinity symbol in the grid and as "any stack" in the table. Once stacks are meaningful, no hand in the deck holds enough equity against aces for a call to show a profit, so a face up shove either takes the blind uncontested or gets called by a large underdog. There is no depth at which it turns into a mistake.
• Precision is one decimal, or whole numbers at 100 and above. The solve itself carries the extra tenth, which is why figures over 100 are quoted with a decimal in the text on this page even though the table rounds them. The engine behind the numbers is a simulation, so any further digits would be noise dressed up as accuracy.

Treat a Sklansky-Chubukov number as a permission slip, not as a strategy. It answers one question, and it answers it with certainty: can this shove be punished at this stack? The workflow is short.

• Count your stack in the unit you actually think in, then read the matching column. Most players count big blinds, so read the big blind column of the table. The slider and the grid are set in small blinds, so double your big blind count before you move the slider.
• Compare, then act. If your hand's number is at or above your stack, the shove is safe by construction. You do not need a read, you do not need to know whether the big blind is loose or tight, and you cannot be exploited for it.
• Do not read the reverse as a fold. A stack above the number means the guarantee has lapsed, nothing more. The shove may still be clearly correct against a real opponent, and often is.
• Use it where the model fits. Heads up, small blind against big blind, short enough that shove or fold is genuinely the whole decision. That covers heads up play, the final two of a sit and go, any late stage where you are down to one opponent in the blinds, and any hand at a fuller table that folds around to your small blind.

The practical range is narrower than the table suggests. The premium numbers are enormous, and by the time your stack is deep enough for them to bind you are not in a shove or fold game any more. The part of the chart you will genuinely use sits in the region where the marginal hands live, and that is where knowing whether your holding is above or below the line tells you which kind of decision you are making: one that needs no read at all, or one that depends on the player across from you.

For everything the model leaves out, use the other free tools here. The M-ratio calculator tells you how much pressure the blinds are putting on you in the first place. The ICM calculator applies the Independent Chip Model, which turns chip stacks into a share of the prize pool, and alongside the bubble factor calculator it handles the prize pool considerations that a heads up chip model cannot see.

Here is the case worth sitting with. Pocket deuces have a Sklansky-Chubukov number of 49.1 small blinds. A2s comes in higher at 59.3. A2o, the same two cards in different suits and a hand nobody would claim is better than a pocket pair, sits at 46.1, close behind the deuces. And KQs, a hand that has to improve just to beat a pair of deuces at showdown, has a number of 87.1, comfortably the largest of the four.

The resolution is that the number was never asking how strong your hand is. It is asking what the calling range costs you once your hand is face up. Two things feed into that: how much of the deck can profitably call at all, and how far ahead those hands are when they do. A wide calling range costs you very little if the hands in it are barely ahead of you. A narrow one is brutal if the hands in it have you crushed.

Work through the calling side. Your opponent has already posted 2 and has to put the rest in to call. When your stack is deep, they are risking a lot to win a pot that is only a little more than what they are putting in, so the equity they need runs close to half. Around the depth where the deuces cross over, about 48% is all it takes for a call to show a profit, and the bar creeps closer to half as stacks get deeper still. That is the bar your hand has to clear on their side of the table.

Now hold that bar against pocket deuces. A pair of deuces is a favorite over most unpaired hands, but only just: 51 to 52% is a typical margin. That is barely on the right side of a coinflip and barely above the threshold they need. So when they can see the deuces, an enormous slice of the deck becomes a profitable call. At the deuces' own number, roughly 57% of all combinations can call and show a profit. Plenty still folds, but the majority of the deck stays in. Most of what calls is only a hair behind, so those calls cost you little beyond the 2 you would otherwise have collected. The damage comes from the rest of the calling range: every bigger pair calls as well, and against a bigger pair the deuces are drawing to two outs.

KQs is in a different position entirely. Much less of the deck can call it profitably, so turning it face up still folds out a great deal. What does call is the bigger pairs and the bigger aces, plus a band of small pairs that are barely a coinflip with it. Fewer calls, and less lost to the calls that arrive. That is why the shove keeps beating a fold up to a much deeper stack, and why KQs outranks a pocket pair here despite having to improve to beat one.

Once you see the mechanism, the rest of the table stops looking strange. AKs at 553.1 sits above QQ at 479.0. AKo at 333.1 edges past JJ at 320.5. AQo at 193.6 and 99 at 192.4 finish level, which is surprise enough for a hand that is behind the pair before the flop. ATs at 140.0 sits above 77 at 135.8. Big unpaired cards keep outranking pairs that are ahead of them before the flop, over and over, and the reason is in the calling range. What can profitably call a big unpaired hand face up is mostly pocket pairs, and a pair against two big cards is a race rather than a beating. What calls a pair is chiefly a bigger pair, and a bigger pair leaves it drawing to two outs. Being called often by a coinflip is cheap. Being called rarely by a hand that has you crushed is not.

Notice what is not doing the work here. ATs is dominated by the bigger aces that call it, meaning they hold an ace as well but with a better card beside it, and a dominated hand is a long way behind rather than a coinflip. So the big unpaired hands are not outranking pairs because they dominate their callers. They outrank them because most of what calls them is only racing, while what calls a pair has it beaten badly.

So read the column for what it is. It is a ranking of how difficult your hand is to play against when your opponent knows exactly what it is. That lines up with raw hand strength at the very top, where aces can never be punished and KK runs to 954.1, and it comes apart in the middle, which is exactly the part of the chart where you actually make decisions.

The frequency line under the grid is the quickest summary of what stack depth does to your options. These are the shares of all 1326 two card combinations that are unexploitable shoves, as the tool reports them.

• 5 small blinds, which is 2.5 big blinds: 82.2%
• 10 small blinds, 5 big blinds: 60.8%
• 15 small blinds, 7.5 big blinds: 49.6%
• 20 small blinds, 10 big blinds: 41.5%
• 25 small blinds, 12.5 big blinds: 34.5%
• 30 small blinds, 15 big blinds: 30.6%
• 40 small blinds, 20 big blinds: 25.2%
• 50 small blinds, 25 big blinds: 21.1%

Read down that list and the shape of short stack poker is right there. At the shallowest depths the great majority of hands you can be dealt are shoves that no opponent on earth could punish, which is the arithmetic behind the old advice that at a few big blinds the cards barely matter. The share falls fast through the middle depths, then flattens out: from 40 to 50 small blinds it moves only a few points, because by then the hands still qualifying are the ones that little of the deck can call profitably, and those hold up for a long way.

Two cautions on those percentages. They count combinations, so 82.2% does not mean 82.2% of the boxes in the grid. And a combination dropping out of the shaded set does not become a fold, it just stops carrying the guarantee.

The other shove or fold tool on this site, the push/fold chart, is a Nash equilibrium solve: a set of strategies, one for each seat, where no player can improve by changing their own, computed at a 9-handed table for both the shover and the callers. The two tools look similar and answer genuinely different questions.

• Nash asks what is best when your opponent is also playing well but cannot see your cards. It gives you a strategy, seat by seat, including what to call with.
• Sklansky-Chubukov asks what is safe when your opponent is playing perfectly and can see your cards. It gives you a boundary, for one seat, and only for shoving.

The assumptions differ sharply, so the two charts will not line up hand for hand, and the seats other than the small blind have no counterpart here at all. One relationship does hold, and it is the useful one. An opponent who cannot see your cards can only respond worse than one who can, so a shove that beats folding face up also beats folding against a hidden opponent, whatever strategy that opponent is playing, equilibrium included. A hand at or below its number is therefore never a fold in a small blind equilibrium either, and the equilibrium shoving range is the wider of the two, usually by a long way. The distance between them is what having your cards hidden is worth.

So put them to different jobs. Nash is the strategy you study in order to play well. Sklansky-Chubukov marks, hand by hand, the deepest stack at which one particular action, shoving that one hand, cannot be punished, which is what you fall back on when you want a decision you can defend without knowing anything at all about the player across from you.

If you are new to either idea, the introduction to tournament poker covers the ground that both charts assume you already have.

The value of the model comes from how narrow it is, so the limits are not fine print. They are the terms of the guarantee.

• Heads up only, small blind against big blind. This is not a 9-handed opening chart, and nothing here accounts for players still to act behind you. The one full ring spot it does describe is the small blind after everyone else has folded, where there is nobody left behind you.
• Shove or fold only. No raising small, no limping, no flop, turn or river. If a smaller raise is available and sensible, the model has nothing to say about it.
• The pessimism is on purpose. A face up opponent is a worse opponent than you will ever face, so the numbers understate what you can profitably do. Above the number the shove is often still right, it just is not bulletproof.
• It is a bound, not a strategy. It cannot tell you what to do with a hand past its number, and it says nothing whatsoever about calling an all in.
• The premium numbers are a statement about the model, not advice. A 954.1 small blind stack in a heads up match does not happen. What KK's number really tells you is that shoving it is never in danger, not that anyone should be reasoning about stacks that size.
• Chips only. There is no prize pool in this model, so nothing here knows about pay jumps, the bubble, or a satellite. Those change the correct play far more than a marginal shove decision does, and they need ICM or a satellite bubble calculation instead.

The numbers on this page come from our own solve, not from retyping a published table, and the first thing to do with any such solve is check it against the source everyone knows.

For the pocket pairs from kings down to sevens, the published table gives 954, 478, 320, 241, 193, 160 and 134. Ours gives 954.1, 479.0, 320.5, 240.7, 192.4, 160.2 and 135.8. Every one of the seven lands within 2 of the published figure, across figures running from over nine hundred down to the low hundreds. Agreement that tight across that spread is a good sign that the two are computing the same quantity by the same definition.

Equities are produced by a Monte Carlo engine, which means hands are dealt out and counted rather than enumerated exhaustively. That is why the last digit is not meaningful and why the tool stops at one decimal. Treat any two hands a tenth apart as tied, and near the top of the chart, where our figures sit up to 2 away from the published ones, treat a gap of a point or so the same way. The differences that matter here are much larger than the noise: the gap between KQs at 87.1 and KQo at 59.7, or between JTs at 36.4 and T9s at 23.4, is real and worth acting on.

At the far end of the ranking the numbers get small and the message is blunt. The bottom of the table is a run of offsuit rag hands only a few small blinds deep, with 32o last of all 169. At those depths even the worst hand in the deck is a shove nobody can punish, and a little above them it is not, which is about as compact a summary of desperation poker as you will find.

It is the largest stack at which open shoving a given hand from the small blind, heads up, is still at least as good as folding, even though your opponent can see your two cards and responds perfectly. At or below that stack the shove is unexploitable: no strategy your opponent could adopt makes it worse than folding. Above it, the shove may still be correct against a real opponent, but the guarantee no longer applies.

The published table has always used small blinds, and this page follows it, so the slider and the grid are set in small blinds. The same model in big blinds gives exactly half of every figure, and the ranked table above shows both columns so you can read whichever unit you count your stack in. If you count in big blinds, double the figure before you set the slider. If a number looks twice as large as you expected, that is the unit, not a mistake.

There is not one. AA shows an infinity symbol in the grid and "any stack" in the table. Once stacks are meaningful, no hand in the deck holds enough equity against aces for a call to show a profit, so a face up shove either takes the blind uncontested or is called by a large underdog. However deep you are and however clearly your opponent sees the hand, shoving aces is never worse than folding, so no crossing point exists. It is the only hand in the deck with that property.

Because the model keeps asking the question long after the situation stops occurring. KK comes out at 954.1 small blinds, which is a stack nobody has ever had heads up. That figure is not advice about deep play, it is a way of saying that a face up KK shove never breaks down at any depth you could ever face. The part of the chart worth studying is the region where marginal hands cross the line, not the top of it.

Because the ranking is about what the calling range costs you, not about which hand wins when two of them race. Around that depth your opponent needs only about 48% equity for a call to profit, and pocket deuces are a bare 51 to 52% favorite over most unpaired hands, so once the deuces are face up a huge slice of the deck clears that bar: roughly 57% of all combinations can call profitably at the deuces' own number of 49.1. Most of those calls are near coinflips and cost you little, but every bigger pair is in the group too, and against a bigger pair the deuces are drawing to two outs. A2s at 59.3 is called by far less, because ace high runs well ahead of the unpaired hands that would like to call, and because holding an ace yourself removes some of the ace combinations that could call you.

Because much less of the deck can profitably call KQs face up. Turning it over folds out a great deal, and what does call is the bigger pairs and the bigger aces, plus a band of small pairs that are barely a coinflip with it. Pocket deuces are ahead of KQs before the flop, but they are only barely ahead of everything else, which lets almost the whole deck call them. KQs holds up to 87.1 small blinds and the deuces stop at 49.1. The column is not a hand strength ladder.

Not as a general opening chart. The solve is small blind against big blind with nobody else in the hand, so it says nothing about opening from early position with players still to act behind you. One full ring spot does fit exactly: when everyone folds to you in the small blind there is nobody left to act, and that is the situation this model describes, whatever the size of the table. Antes are not in the model, and they cut both ways, adding dead money for you to collect while giving the big blind a better price to call, so treat an ante table as a spot the chart does not price exactly. For a multi way shove or fold decision use the Nash push/fold chart, which is solved seat by seat at a 9-handed table.

No, and this is the most common misreading of the chart. Crossing the number means the unexploitable guarantee has lapsed, not that shoving has become a mistake. Real opponents cannot see your cards, so they misjudge in both directions, and that uncertainty pays you. Above the number the decision goes back to being a normal poker decision that depends on the player, the format and the stakes.

They do not. Sklansky-Chubukov is a bound on shoving from the small blind and nothing else. Calling ranges are a different problem, and they are part of what a Nash equilibrium solve produces, so use the push/fold chart for the calling side.

It reproduces it closely. For KK through 77 the published numbers are 954, 478, 320, 241, 193, 160 and 134; this solve gives 954.1, 479.0, 320.5, 240.7, 192.4, 160.2 and 135.8, with every one of the seven within 2. Equities come from a Monte Carlo simulation, so the final digit carries no information and the tool displays one decimal, with whole numbers from 100 upwards. Treat two numbers a tenth apart as the same answer.

Most of them, and it changes quickly with depth. At 5 small blinds, which is 2.5 big blinds, 82.2% of all 1326 combinations qualify. At 10 small blinds it is 60.8%, at 20 it is 41.5%, and by 50 small blinds it is down to 21.1%. That decline is why shove or fold play feels almost card independent at the shallowest stacks and gets steadily more selective as you get chips.

Two things. As a table aid they give you a class of shoves you can make without any read at all, which is worth a great deal when you have no history with the player and no time to think. As a study aid they are better still, because working out why KQs outranks a pocket pair trains you to ask what can call you and what those calls cost, and that question carries into spots far away from the small blind. For the wider tournament context, the lessons put it to work.