Poker Odds Calculator
Calculate Texas Hold em hand probabilities for pre-flop, flop, turn, and river. Enter values for instant results with step-by-step formulas.
Formula
Probability = Outs / Remaining Cards
Poker odds are calculated by counting outs (cards that improve your hand) divided by unseen cards. The 'Rule of 2 and 4' gives quick estimates: multiply outs by 2 for one card to come, by 4 for two cards to come. This calculator uses Monte Carlo simulation for full probability distributions.
Worked Examples
Example 1: Flush Draw on the Flop
Problem: You hold A♥ K♥. Flop is 7♥ 3♥ J♠. What are your odds?
Solution: You have 4 hearts, need 1 more for a flush\nRemaining hearts: 13 - 4 = 9 outs\nOuts for top pair (3 aces, 3 kings): 6 more outs\nTotal outs: ~15\nProbability on turn: 15/47 = 31.9%\nProbability by river: ~54.1% (Rule of 4: 15 × 4 = 60% rough)\nPot odds needed: Less than 2:1
Result: 15 outs | ~54% to improve by river | Strong draw
Example 2: Pocket Pair on the Turn
Problem: You hold Q♠ Q♣. Board is 9♦ 5♥ 2♣ K♠. Should you continue?
Solution: Current hand: One Pair (Queens)\nThe K on the turn is concerning — opponent could have K-x\nOuts to improve: 2 queens for a set = 2 outs\nProbability: 2/44 = 4.5% on the river\nYour pair of queens is still strong against most hands\nBut proceed cautiously against aggression
Result: 2 outs | 4.5% to improve | Medium hand strength
Frequently Asked Questions
What are poker outs and how do I count them?
Outs are the unseen cards that will improve your hand to a likely winner. For example, if you have 4 cards to a flush after the flop, there are 9 remaining cards of that suit (13 total minus 4 you can see) — so you have 9 outs. Common counts: flush draw = 9 outs, open-ended straight draw = 8 outs, gutshot straight draw = 4 outs, two pair to full house = 4 outs, one pair to two pair or trips = 5 outs. The 'Rule of 2 and 4': multiply outs by 2 for the turn probability, or by 4 for turn + river combined probability.
What are pot odds and how do I use them?
Pot odds compare the current size of the pot to the cost of calling a bet. If the pot is $100 and you must call $20, your pot odds are 5:1 (or you need to win 16.7% of the time to break even). Compare this to your equity (chance of winning): if your hand has a 25% chance of improving to the best hand, you should call because 25% > 16.7%. This is the mathematical foundation of poker — make calls when your equity exceeds the pot odds required, and fold when it doesn't. Over thousands of hands, this approach is profitable.
How do poker probabilities change from pre-flop to river?
Pre-flop, you have just 2 cards and 5 community cards to come — huge uncertainty. Getting dealt pocket aces: 0.45%. Flopping a set with a pocket pair: 11.8%. Making a flush from a suited hand: ~6.5% by the river. On the flop, with 3 community cards revealed, probabilities crystallize: a flush draw completes ~35% of the time (turn + river). On the turn with 1 card to come, probabilities are roughly halved: flush draw ~19.6%. On the river, your hand is final — no more improvement possible.
What are the odds of common poker events?
Pocket aces: 1 in 221 (0.45%). Any pocket pair: 1 in 17 (5.9%). Suited connectors (like 8-9 suited): 1 in 46 (2.1%). Flopping a set: 11.8%. Flopping two pair: 2.0%. Flopping a flush: 0.8%. Making a flush by the river with 4 suited cards on flop: 35.0%. Runner-runner flush (needing 2 cards): 4.2%. Being dealt suited cards: 23.5%. Royal flush by the river: 0.003% (1 in 30,940). Bad beat (set over set): ~1 in 100 when both have pocket pairs.
What is the difference between odds and probability?
Probability is expressed as a number between 0 and 1 (or a percentage), representing the likelihood of an event. Odds compare favorable outcomes to unfavorable ones — odds of 3:1 means 3 wins for every 1 loss, which is a probability of 3/(3+1) = 75%. Casinos often express odds differently from true probability to build in their house edge.
How do poker hand probabilities work?
In a standard 52-card deck, there are 2,598,960 possible 5-card hands. Royal flush: 4 (0.000154%); straight flush: 36 (0.00139%); four of a kind: 624 (0.024%); full house: 3,744 (0.144%); flush: 5,108 (0.197%); straight: 10,200 (0.392%); three of a kind: 54,912 (2.11%); two pair: 123,552 (4.75%); one pair: 1,098,240 (42.3%); high card: 1,302,540 (50.1%).