Postflop Math
Basic Situations
1. Facing a Bet:
Decision to call or fold depends on:
- Equity of the hand vs opponent's range
- Pot Odds
- Implied Odds
- Reverse Implied Odds
2. We Bet:
Decision to bet (value or bluff) depends on:
- Equity of the hand vs opponent's range
- Fold Equity — probability that the opponent will fold
Formulas
Formula 1 — Profit by Equity:
Profit = Equity − Pot Odds Share
Example:
- In an all-in we have 55% equity, invested 45% of the pot
- ➡ Profit = 10%
Formula 2 — With Implied Odds:
Profit = Equity − Pot Odds Share + Implied Odds − Reverse Implied Odds
Equity Realization (Realization Factor)
The percentage of theoretical hand equity actually realized in winnings.
Influencing factors:
- Position (better in position)
- Playability of the hand
- Stack depth
- Range advantage
- Opponent skill level
- ICM pressure (bubble factor)
Pot Odds
Pot Odds = Your Call / (Pot Before Call + Your Call)
Table
| Bet Size | Required Equity |
|---|---|
| 25% | 17% |
| 33% | 20% |
| 50% | 25% |
| 67% | 28% |
| 75% | 30% |
| 100% | 33% |
Fold Equity
Probability that opponent folds to our bet
Calculated via break-even bluff formula:
FE > Bet Size / (Bet Size + Pot)
Implied Odds
Potential future profit if we hit our hand
Formula:
1 / Equity × Call – (Pot Before Call + Call)
Reverse Implied Odds
Situations where hitting our draw still loses to a stronger hand
Examples:
- Low flush draws on paired boards
- Medium straights on two-tone boards
Poker Terminology
| Term | Definition |
|---|---|
| SPR | Stack-to-Pot Ratio |
| Effective Stack | The smaller stack between players in the hand |
| Bluffcatcher | A hand that only beats bluffs |
| Dynamic Board | Board with many possible draws |
| Fast Play | Aggressive fast play of a strong hand |
| Blocker | Card in our hand reducing probability of opponent holding certain hands |
| Capped Range | Range without the strongest hands, excluded based on action history |
| Polar Range | Contains very strong and very weak hands (no middle) |
| Linear Range | Gradual decrease in hand strength (no sharp drops) |
ChipEV and ICM
| Model | Used For | Considers |
|---|---|---|
| ChipEV | Current profit in chips | Only stack size and equity |
| ICM | Final profit in $ | Payouts, position, other stacks |
Bubble Factor (BF):
BF = Loss in equity share if lose / Gain in equity share if win
ICM pressure effects:
- Lower BB call frequency
- Change in postflop lines
- Requirement for greater "ICM premium" in %
Conclusion
Mathematics and logical understanding of the game are the basis for long-term progress. Key skills:
- Seeing profitability of actions through formulas
- Realizing equity and using fold equity
- Avoiding intuitive mistakes
- Mastering terminology to “think like a player”
Goal: turn these concepts into automated in-game skills.
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