Definition
Essential mathematical formulas used in poker calculations.
Pot Odds
Formula:
Pot Odds = Call Amount ÷ (Pot + Call Amount)
Example:
- Pot = $100, Villain bets $50, you must call $50
- Pot Odds = $50 ÷ ($100 + $50 + $50) = 50/200 = 25%
| Bet Size (% of pot) | Pot Odds Needed |
|---|---|
| 25% | 17% |
| 33% | 20% |
| 50% | 25% |
| 66% | 28% |
| 75% | 30% |
| 100% | 33% |
| 150% | 38% |
Equity Required
Break-even Formula:
Required Equity = Risk ÷ (Risk + Reward)
Expected Value (EV)
Formula:
EV = (Win% × Amount Won) - (Lose% × Amount Lost)
Example:
- 40% to win $200, 60% to lose $100
- EV = (0.40 × $200) - (0.60 × $100) = $80 - $60 = +$20
Rule of 2 and 4
| Situation | Multiply Outs By |
|---|---|
| Flop to Turn | 2 (approximation) |
| Flop to River | 4 (approximation) |
| Turn to River | 2 (approximation) |
Exact Formulas:
Flop→Turn: Outs × 2.13
Flop→River: Outs × 4 - (Outs - 8)
Turn→River: Outs × 2.17
Common Outs Table
| Draw | Outs | Turn% | River% | Both% |
|---|---|---|---|---|
| Gutshot | 4 | 8.5% | 8.7% | 16.5% |
| Two overcards | 6 | 12.8% | 13.0% | 24.1% |
| Open-ended straight | 8 | 17.0% | 17.4% | 31.5% |
| Flush draw | 9 | 19.1% | 19.6% | 35.0% |
| Flush + gutshot | 12 | 25.5% | 26.1% | 45.0% |
| Flush + OESD | 15 | 31.9% | 32.6% | 54.1% |
Implied Odds
Formula:
Implied Odds = Call Amount ÷ (Pot + Call + Expected Future Winnings)
Minimum Defense Frequency (MDF)
Formula:
MDF = Pot Size ÷ (Pot Size + Bet Size)
| Bet Size | MDF |
|---|---|
| 33% pot | 75% |
| 50% pot | 66.7% |
| 66% pot | 60% |
| 100% pot | 50% |
| 150% pot | 40% |
Bluff-to-Value Ratio
Formula:
Bluff Frequency = Bet Size ÷ (Pot + Bet Size)
| Bet Size | Bluff Frequency |
|---|---|
| 33% pot | 25% bluffs |
| 50% pot | 33% bluffs |
| 66% pot | 40% bluffs |
| 100% pot | 50% bluffs |
Combinatorics Quick Reference
| Hand Type | Combos |
|---|---|
| Unpaired (suited) | 4 |
| Unpaired (offsuit) | 12 |
| Unpaired (total) | 16 |
| Pocket pair | 6 |
| Pair with 1 blocker | 3 |
| Pair with 2 blockers | 1 |
💡 Key Takeaway: Memorizing key formulas and common scenarios speeds up decision-making at the table.