What Are Push-Fold Charts?

Push-fold charts are strategy tables specifically designed for single-table tournament (SNG) late-game scenarios (typically when effective stacks are below 15bb). Based on hand strength, position, stack depth, and ante size, they clearly instruct a player whether to push (shove) or fold preflop, or whether to call when facing a shove from the small blind. These charts are not made up arbitrarily; they are the product of extensive mathematical simulations (e.g., Nash equilibrium solving) aimed at approximating theoretically optimal offensive and defensive strategies.

In the shallow-stack phase of SNGs, there is almost no room for postflop play, and most pots are decided preflop. Hence, simplifying the decision to a binary "push or fold" model is both practical and easy to memorize and execute quickly. Common sources include the book Kill Everyone, software like SNG Wizard, and PokerStrategy.

The Math Behind Push-Fold Charts

The core of push-fold charts is the Nash equilibrium from game theory. Assuming all players are rational and only consider pot odds and stack depth, there exists a set of strategies such that any unilateral deviation would reduce the player's own expected value (cEV). In SNGs, due to the step-like prize structure, the bubble and ICM (Independent Chip Model) significantly affect decisions. However, classic push-fold charts usually assume cEV (chip EV) optimality, i.e., they ignore ICM distortions. Therefore, players need to adjust when using them on the bubble or near the money.

The typical calculation process: given blind levels, antes, and effective stack size (in bb), solve for which hands the small blind can push with positive expectation when the big blind calls with an optimal range based on pot odds. The big blind's calling range is determined by pot odds. The two ranges interact until they stabilize. For example, with blinds 500/1000, ante 100, and an effective stack of 8bb, the small blind might push with about 40%-50% of hands, while the big blind calls with about 20%-25% of hands.

Practical Examples

Suppose a 9-player SNG with blinds 500/1000 and ante 100 (total pot per hand: 500+1000+9*100=2400). You are in the small blind with an effective stack of 8000 (8bb). According to a push-fold chart (for SB at 8bb), the recommended pushing range is approximately: 22+ (pairs), A2s+, A7o+, K9s+, KTo+, Q9s+, QTo+, J9s+, JTo+, T9s+, 98s+, etc. This accounts for roughly 35%-45% of all hands.

Suppose you hold A♣8♦. This hand is in the range (since A8o is stronger than A7o), so you should push. If the big blind is a loose-passive player (a wide calling range), you may need to tighten your pushing range because they are more of a "calling station." Conversely, if the big blind is tight-passive, you can push a wider range.

Another example: you are in the big blind, and the small blind pushes. You have 8000 chips. According to the chart (BB facing SB shove, 8bb effective stacks), the typical calling range is: 22+, A2s+, A9o+, KJs+, KQo+, QJs+. If you hold K♥J♦, this hand is not in the recommended calling range (KJs is, but KJo is not), so you should fold.

Common Misconceptions

1. Blindly following the chart, ignoring opponent tendencies
   Push-fold charts assume opponents also play optimally. In reality, opponents may be too tight or too loose. Against a very tight player, you can significantly expand your pushing range; against a loose caller, you need to tighten up. Following the chart rigidly means handing your strategy over to a static model.

2. Neglecting ICM factors
   Near the money (on the bubble) in SNGs, the "survival value" of chips is higher than their fair value per chip. Even if a hand has positive cEV according to the chart, you may need to fold to avoid the risk of elimination. For example, on the bubble, the pushing range for a short stack should be tighter, while a big stack can afford to loosen up.

3. Ignoring positional differences
   The same hand is treated very differently in different positions. The UTG pushing range is the tightest, the button the widest, and the small blind in between. Beginners often confuse charts for different positions.

4. Believing the chart is always correct
   Push-fold charts are simplified models that assume fixed antes, no dead money effects, and rational players. In practice, changing antes, player behavioral deviations, and different stages all affect the optimal strategy. The chart is a starting point, not an end point.

Summary

Push-fold charts are among the most powerful teaching tools for the short-stack phase of SNGs. They simplify complex game theory into memorable tables, helping players make reasonable decisions quickly. However, strong players incorporate ICM, opponent tendencies, and dynamic game considerations to adjust the charts dynamically.

Beginners are advised to first memorize common stack depths (e.g., 10bb, 8bb, 5bb) for push/call ranges on the button, small blind, and big blind. Then, refine through actual play reviews. The ultimate goal is to internalize the chart so it becomes instinct, while also knowing when to deviate.