📐 What Is Equity?
Equity is your share of the pot based on your probability of winning. If you will win the pot 60% of the time when all cards are dealt out, your equity is 60% of the pot — regardless of what action happens next.
Equity is always calculated against a specific range of hands. You rarely know your opponent's exact cards, so equity is a weighted average across all possible holdings in their range.
Hand vs. Hand Equity
Against a single known hand, equity is straightforward. Consider \(\text{A}♠\text{K}♦\) vs. \(\text{Q}♥\text{Q}♣\) all-in pre-flop:
- AK (two overcards) has approximately 46% equity
- QQ (a pair) has approximately 54% equity
Against a range, equity is computed as the weighted sum over all hands in that range:
$$\text{Equity vs Range} = \sum_{h \in \text{Range}} P(h) \times \text{Equity}(h)$$where \(P(h)\) is the probability (or frequency) of each hand in the range.
🔢 Expected Value (EV) Formula
Expected value is the average outcome of a decision, weighted by probability. The general formula is:
$$\text{EV} = P(\text{win}) \times \text{Win Amount} - P(\text{lose}) \times \text{Lose Amount}$$where \(P(\text{win}) + P(\text{lose}) = 1\) (assuming no tie for simplicity).
Worked Example
You are all-in with \(\text{A}♥\text{K}♠\) against \(\text{J}♥\text{J}♣\). The pot is $200. You have 46% equity.
$$\text{EV} = 0.46 \times \$200 - 0.54 \times \$0 = \$92$$Your EV in this situation is $92. Since you invested $100 (half the pot), this is slightly -EV as a pure chip equity calculation, but in practice AK vs JJ is a standard flip that is often unavoidable.
📞 EV of a Call
The EV of calling a bet is:
$$\text{EV(call)} = \text{Equity} \times (\text{Pot} + \text{Call}) - \text{Call}$$Rearranging: if \(\text{Equity} > \frac{\text{Call}}{\text{Pot}+\text{Call}}\) then the call is +EV. This is exactly the pot odds condition.
Example 1: Value Hand Call
You hold top pair (TPTK) with ~70% equity. Pot $100, villain bets $60.
$$\text{EV(call)} = 0.70 \times (100 + 60) - 60 = 0.70 \times 160 - 60 = 112 - 60 = +\$52$$This is a very profitable call.
Example 2: Flush Draw Call
You hold a flush draw with ~35% equity. Pot $120, villain bets $40.
$$\text{EV(call)} = 0.35 \times (120 + 40) - 40 = 0.35 \times 160 - 40 = 56 - 40 = +\$16$$Positive EV — the draw justifies calling.
Example 3: Bluff-Catcher Call
You hold a medium pair (bluff-catcher) with ~40% equity. Pot $200, villain bets $200.
$$\text{EV(call)} = 0.40 \times (200 + 200) - 200 = 0.40 \times 400 - 200 = 160 - 200 = -\$40$$Negative EV. Against a pot-sized bet you need 50% equity; 40% is not enough here.
💰 EV of a Bet
Calculating the EV of betting is more complex because villain can fold, call and lose, or call and win. The full formula:
$$\text{EV(bet)} = P(\text{fold}) \times \text{Pot} + P(\text{call}) \times \text{Equity} \times (\text{Pot} + \text{Bet}) - P(\text{call}) \times (1-\text{Equity}) \times \text{Bet}$$Simplified by combining the call terms:
$$\text{EV(bet)} = P(\text{fold}) \times \text{Pot} + P(\text{call}) \times [\text{Equity} \times (\text{Pot} + \text{Bet}) - (1-\text{Equity}) \times \text{Bet}]$$Worked Example: Semi-Bluff Bet
You hold a flush draw (35% equity) on the flop. Pot $100. You bet $70. Villain folds 50% of the time.
$$\text{EV(check)} = 0.35 \times 100 = \$35 \text{ (just your equity)}$$ $$\text{EV(bet)} = 0.50 \times 100 + 0.50 \times [0.35 \times (100+70) - 0.65 \times 70]$$ $$= 50 + 0.50 \times [59.5 - 45.5]$$ $$= 50 + 0.50 \times 14 = 50 + 7 = \$57$$Betting has an EV of $57 vs. checking's EV of $35. The semi-bluff bet is clearly correct.
🎯 Equity Realization
Raw equity and realized equity are different. Equity realization is the fraction of your raw equity that you actually capture through play. It depends on:
- Position: In-position players realize more equity — they can control the size of pots and see free cards more often.
- Playability: Hands with high playability (sets, suited connectors) realize more equity than hands that are difficult to play post-flop (offsuit broadway hands).
- Stack depth: Deep stacks favor hands with high implied odds (suited connectors, small pairs). Short stacks favor raw equity (big pairs, big aces).
The equity realization factor (ERF) adjusts raw equity:
$$\text{Effective Equity} = \text{Raw Equity} \times \text{ERF}$$| Situation | Approximate ERF | Notes |
|---|---|---|
| In position, deep stacks | 1.0–1.2 | Can over-realize equity |
| In position, 100BB | 0.95–1.05 | Near-full realization |
| Out of position, 100BB | 0.75–0.90 | OOP penalty |
| BB vs SB 3-bet, OOP | 0.70–0.85 | Significant OOP penalty |
| Multi-way pot | 0.60–0.80 | Hard to realize equity |
This is why GTO solvers call certain hands even when raw equity appears to be below pot odds — the effective equity after accounting for position and playability may still be positive.
💡 Practical Usage
You cannot run exact EV calculations at the table in real time, but you can develop a feel for EV through these habits:
- Estimate equity using outs and the Rule of 2/4. This gives you a quick equity number to plug into the EV formula.
- Identify the two main scenarios when betting: villain folds (you win the pot) vs. villain calls (you go to showdown). Estimate the probability of each.
- Check against pot odds first. If your equity clearly beats pot odds, it is +EV to call without a full EV calculation.
- Consider equity realization when calling pre-flop from out of position. Your raw equity may be sufficient but your effective equity after position discount may not be.
- Review hands off the table with an equity calculator (e.g., Equilab, Flopzilla) to calibrate your estimates.