📊 Poker Odds & Probabilities

Master the math behind poker for better decisions

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Why Poker Odds Matter

Understanding poker odds and probabilities is crucial for making mathematically correct decisions. While poker involves luck, the best players use odds to minimize losses and maximize winnings over time.

🎯 Expected Value (EV)

The average amount you can expect to win or lose on a decision over many repetitions.

💰 Pot Odds

The ratio of money in the pot compared to the amount you need to call.

🎪 Implied Odds

Future bets you expect to win if you hit your hand.

Basic Poker Probabilities

Poker Hand
Probability
Odds
Description
Royal Flush
0.000154%
649,740 to 1
A♠ K♠ Q♠ J♠ 10♠
Straight Flush
0.00139%
72,193 to 1
Five suited cards in sequence
Four of a Kind
0.0240%
4,165 to 1
Four cards of same rank
Full House
0.1441%
694 to 1
Three of a kind + pair
Flush
0.1965%
509 to 1
Five cards same suit
Straight
0.3925%
255 to 1
Five cards in sequence
Three of a Kind
2.1128%
47 to 1
Three cards same rank
Two Pair
4.7539%
21 to 1
Two different pairs
One Pair
42.2569%
2.4 to 1
Two cards same rank
High Card
50.1177%
1.2 to 1
No matching cards

How to Calculate Pot Odds

Pot odds help you determine if a call is mathematically correct.

Example 1: Simple Pot Odds

Pot: $100
You need to call: $20

Pot Odds = $100:$20 = 5:1

If your equity is better than 16.7% (1/6), the call is profitable.

Example 2: With Multiple Callers

Pot: $150
You need to call: $30

Pot Odds = $150:$30 = 5:1

Same 16.7% break-even point.

Texas Hold'em Hand Odds

Flush Draw

4 cards to flush on flop

35% (2.9:1)

Turn or river

Open-Ended Straight Draw

4 cards to straight

32% (2.1:1)

Turn or river

Gutshot Straight Draw

4 cards with gutshot

17% (4.9:1)

Turn or river

Set Mining

Pocket pair vs overcards

12% (7.5:1)

Flop set

Overcard on Flop

Ace-high vs lower board

2.2:1

Improve to pair

Backdoor Flush

2 suited cards

23% (3.3:1)

Turn and river

Expected Value Examples

Coin Flip Situation

You have 50% equity. Pot: $200. Call: $100.

EV = (0.5 × $200) + (0.5 × -$100) = $50

Expected profit of $50 per decision.

Bluff Example

You bluff with 20% equity. Pot: $100. Bet: $50.

EV = (0.2 × $150) + (0.8 × -$50) = -$10

Expected loss of $10 - bad bluff!

Poker Odds Calculator Tips

🎯 Break-Even Percentage

Convert odds to percentage: 3:1 = 25% (you need 25% equity to break even).

💰 Implied Odds

Factor in future streets. If you'll win $200 more when you hit, your effective odds improve.

📊 Reverse Implied Odds

When hitting your hand might cost you more money later (like drawing to a flush with many suited cards on board).

🃏 Hand Reading

Use odds to narrow opponent ranges. If they always fold to aggression, you can bluff more.

Practice Your Poker Math!

Use our interactive tools to practice calculating odds and making better decisions.