Heads-up Match-ups in Hold'em: Complete Equity Analysis

Understanding heads-up match-ups is crucial for making correct decisions in Texas Hold'em. Whether you're facing an all-in situation or trying to determine if your hand can profitably call a bet, knowing the approximate equity of various hand confrontations will dramatically improve your decision-making.

Why Heads-up Match-ups Matter

In poker, you're constantly evaluating whether your hand is strong enough to continue. Understanding common match-ups helps you:

1. Make correct all-in decisions preflop
2. Estimate your equity in multi-way pots
3. Choose optimal betting lines based on your equity
4. Avoid costly mistakes in marginal situations

Categories of Match-ups

Poker hands can be categorized into several groups, and understanding how these groups fare against each other is essential.

The Classic Match-up Categories

1. Overpair vs Underpair (e.g., AA vs 22)
2. Pair vs Two Overcards (e.g., JJ vs AK)
3. Pair vs One Overcard (e.g., 99 vs AJ)
4. Overcards vs Undercards (e.g., AK vs QJ)
5. Dominated Hands (e.g., AK vs AQ)
6. Suited Connectors vs Premium Pairs (e.g., 76s vs AA)

Complete Match-up Table: Preflop Equities

Here's a comprehensive table of common preflop match-ups and their equities:

Premium vs Premium Hands

Pair vs Overcards (Classic "Coin Flip")

Pair vs Two Undercards

Overcards vs Undercards (Non-Paired)

Dominated Hands (Same High Card)

Suited Connectors vs Premium Pairs

Understanding the Numbers

The 80/20 Rule

When a pair faces two undercards that don't share suits or straight possibilities:

• Pair: ~80% equity
• Undercards: ~20% equity

Example: 99 vs 72o = 81% vs 19%

This is called being "crushed" - the undercards need to hit two pair or better to win.

The Coin Flip Range

The classic "race" or "coin flip" occurs when medium pairs face high cards:

• Pair: 52-57% equity
• Overcards: 43-48% equity

Key Range: 22-99 vs AK are all roughly coin flips, with the pair being a slight favorite.

The Domination Factor

When hands share a high card, the better kicker provides ~70-75% equity:

• Better kicker: ~73-76%
• Dominated kicker: ~24-27%

Example: AK vs AJ = 75% vs 25%

Detailed Analysis: The Mathematics Behind Match-ups

Calculating Outs and Equity

Let's break down the classic JJ vs AK match-up:

AK's Outs to Win:

• 6 outs to pair an Ace or King (3 Aces + 3 Kings)
• Additional straight possibilities (connecting with board)

On the Flop:

• 47 unknown cards
• 6 outs = 6/47 = 12.8% per card
• Two chances (turn and river) = roughly 6 × 4 = 24% (using rule of 4)
• Add backdoor straight possibilities: ~3-5%
• Plus the chance of making two pair or better
• Total: ~46% equity

JJ's Equity:

• Win if board doesn't help AK significantly
• Improve to a set (~12% chance)
• Total: ~54% equity

The Impact of Suits

Suited hands gain approximately 2-3% equity due to flush possibilities:

Multi-Way Match-up Considerations

When more than two players are involved, equities distribute differently:

Three-Way All-In Example

Scenario: AA vs KK vs QQ

Key Insight: The best hand loses significant equity in multi-way pots, while middle hands gain equity.

Three-Way with Different Hand Types

Scenario: AA vs AK vs 76s

Position and Match-up Strategy

Early Position Strategy

When you're likely to face strong hands:

Fold these match-ups if you're behind:

• Any pair below 99 vs likely overpair
• Dominated ace (AJ-, AT-)
• Weak suited connectors (75s-)

Continue with:

• Premium pairs (TT+)
• Premium broadway (AK, AQ)
• Strong suited connectors in position (JTs+)

Late Position Strategy

When opponents' ranges are wider:

You can profitably race with:

• Any pocket pair
• Ace-high (AJ+)
• Suited broadway
• Suited connectors (76s+)

Advanced Match-up Concepts

Blocker Effects

Having specific cards affects your opponent's possible hands:

Example: You hold AK

Your opponent CANNOT have:

• AA (only 3 aces remaining)
• KK (only 3 kings remaining)
• AK (only 9 combos instead of 16)

This changes equity calculations:

• Facing a 3-bet range, your AK has better equity because it blocks premium pairs

Range vs Range Equity

Professional players don't think about single hands but ranges:

Example Calculation:

Your 3-bet range from the button:

• AA-TT (premium pairs)
• AK, AQ (broadway)
• Some suited connectors

Villain's 4-bet range:

• AA-JJ
• AK

Aggregate equity calculation:

Overall range equity: ~55%

If you're getting 2:1 pot odds, you need 33% equity, so calling is profitable.

Practical Applications

1. Tournament Situations

ICM Considerations: Sometimes fold even profitable match-ups near bubble:

Example:

• 10 spots from money
• You have TT vs likely AK (coin flip)
• Folding preserves guaranteed min-cash
• Math may say fold despite +chip EV

2. Cash Game Decisions

Pure chip EV: Always take +EV match-ups:

Example:

• You have 99
• Opponent shows AK
• Pot odds give you 2:1
• You need 33% equity
• You have 56% equity
• Always call

3. Stack-to-Pot Ratio (SPR)

Different match-ups play better at different SPRs:

Common Match-up Mistakes

Mistake 1: Overvaluing Dominated Hands

Bad: Calling all-in with AJ vs a tight range Why: You're often dominated by AK, AQ

Fix: Fold dominated aces against tight players

Mistake 2: Folding Profitable Races

Bad: Folding 88 vs AK getting 2:1 Why: You have 55% equity, need only 33%

Fix: Embrace coin flips when you're getting proper odds

Mistake 3: Not Considering Implied Odds

Bad: Folding 76s to a small raise in position Why: You have good equity vs overpairs if you hit

Fix: Call with suited connectors in position with deep stacks

Match-up Reference Quick Chart

Hand Strength Tiers

Tier 1 (80%+ equity vs random):

• AA, KK, QQ

Tier 2 (70-80% equity vs random):

• JJ, TT, AKs, AKo

Tier 3 (60-70% equity vs random):

• 99, 88, AQs, AQo

Tier 4 (50-60% equity vs random):

• 77, 66, AJs, KQs

Tier 5 (40-50% equity vs random):

• 55, 44, AJo, KQo, JTs

Conclusion

Mastering heads-up match-ups gives you a massive edge in poker. Key takeaways:

1. Pocket pairs are ~80% vs two undercards
2. Pair vs overcards is roughly 55/45 (pair favored)
3. Domination scenarios are ~75/25
4. Suited hands gain ~2-3% equity
5. Multi-way pots significantly change equities
6. Always compare equity to pot odds

Study these match-ups until they become intuitive. Use equity calculators to practice, and soon you'll instinctively know whether you're ahead or behind in any situation.

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Practice Exercises:

1. Calculate the EV of calling with 99 vs AK getting 2:1 odds
2. Determine minimum fold equity needed for an AK bluff vs likely pairs
3. Compare three-way equity of AA vs KK vs QQ

Recommended Tools:

• Equilab
• Flopzilla
• PokerCruncher
• Hold'em Resources Calculator