Poker Odds: Hand Probabilities, Outs and Pot Odds Explained

Poker odds tell you how likely a hand or draw is to come in. The numbers players use most: you are dealt a pocket pair once every 17 hands (5.9%), a pocket pair flops a set 11.8% of the time, and a flush draw on the flop completes by the river 35% of the time (19.6% with one card to come). Compare those odds with the pot odds you are being offered, and you know whether a call makes money in the long run.

Here’s the deal, bro: you do not need to be a maths nerd to use poker odds. You need about a dozen numbers and one shortcut (the rule of 2 and 4). This guide gives you all of them for Texas Hold’em, shows the full hand-probability tables, explains outs, pot odds and implied odds with worked examples, and finishes with the classic preflop matchups. Every figure is either from standard combinatorics or calculated for this page, and we show the working where it matters.

Poker Odds Cheat Sheet

Preflop figures come from counting the 1,326 possible two-card starting hands: 78 of them are pocket pairs, 312 are suited, 16 are AK and 6 are AA. Flop and river figures are calculated from the unseen cards (50 after your two hole cards; 47 on the flop; 46 on the turn).

Odds of Each Poker Hand

Two tables matter. The first covers a straight five-card deal, the basis of five-card draw and of video poker. The second covers the best five cards from seven, which is what you actually get in Hold’em and seven-card stud by the river.

Five-card hands (2,598,960 possible hands)

Best hand from seven cards (133,784,560 possible deals)

Notice what happens with seven cards: two pair jumps from under 5% to 23.5%, and finishing with no pair at all drops to 17.4%. That is why one pair is often not enough at showdown in Hold’em, especially in multiway pots. It is also why the hand rankings never change between five and seven cards: a flush is still rarer than a straight, so it still ranks higher.

Outs: The Building Block of Poker Odds

An “out” is any unseen card that improves your hand to what you think will be the best hand. Holding four hearts after the flop, you have 9 outs (13 hearts minus the 4 you can see). With an open-ended straight draw such as 8-7 on a 6-5-K board, any 9 or 4 completes it: 8 outs. The chance of hitting depends on how many outs you have and how many cards are left to come.

“Hit by the river” assumes you see both cards, which is only true if you are all in on the flop or the betting stops. If you face a bet on the turn as well, use the one-card column for each decision.

Counting outs honestly

• Discount tainted outs. With a flush draw on a paired board, the cards that complete your flush can also give an opponent a full house.
• Do not count outs twice. A flush draw with an open-ended straight draw has 15 outs, not 17, because two of the straight cards are also flush cards.
• Ask whether the out wins. Hitting top pair with an ace is no help if your opponent probably has a set.

The Rule of 2 and 4

A fast way to estimate your chance of hitting without a table:

• One card to come (flop to turn, or turn to river): multiply your outs by 2.
• Two cards to come (flop, all in or no more betting): multiply your outs by 4.

A flush draw (9 outs) gives about 18% for one card (true figure 19.1% to 19.6%) and about 36% for two cards (true 35.0%). The shortcut stays close for small and medium draws but overstates big ones. With 15 outs, the rule of 4 says 60% while the true figure is 54.1%. A common fix for more than 8 outs: multiply by 4 and subtract the number of outs above 8 (15 outs: 60 minus 7 = 53%).

Pot Odds: Turning Probabilities Into Decisions

Pot odds compare the size of the pot with the price of your call. To find the equity you need to break even, divide the call by the total pot after you call.

Break-even equity = call / (pot before your call + call)

Worked example 1. The pot is $100 on the turn and your opponent bets $50. The pot is now $150 and you must call $50, so the final pot would be $200. You need 50 / 200 = 25% equity. With a flush draw and one card to come, you hit 19.6% of the time. On pure pot odds, that is a fold.

Worked example 2. Same draw, but on the flop your opponent moves all in for $50 into a $100 pot. You still need 25%, and now you see two cards, so your flush draw hits 35% of the time. That is a profitable call: over 100 identical spots you would invest $5,000 and get back about $7,000 (35 wins of $200).

Read the table against the outs chart. Against a one-third pot bet you need 20%, so a flush draw (19.6% on the river) is close to break-even even without extra winnings. Against a pot-sized bet you need 33.3%, which no single draw reaches with one card to come.

Implied Odds and Reverse Implied Odds

Pot odds only count the money already in the pot. Implied odds add what you expect to win on later streets when you hit. Go back to worked example 1: you call $50 to win $150 with 19.6% equity. The expected value of the call is 0.196 x (150 + F) minus 0.804 x 50, where F is the extra money you win on the river when you hit. Setting that to zero gives F of about $55. If you are confident of winning at least $55 more on average when the flush comes in, the call becomes break-even or better.

Implied odds are strongest when your draw is disguised (a straight on a board with no obvious straight), when stacks are deep, and when your opponent tends to pay off. Reverse implied odds are the opposite trap: hands that win small pots when they are ahead and lose big ones when behind. Drawing to a low flush, or calling with a weak ace on an ace-high board, are classic examples. The money you lose when you hit and still lose can wipe out what the raw pot odds promised.

Classic Preflop Matchups

All-in equities before the flop, from a simulation of 60,000 random boards per matchup run for this guide (rounded; remaining percentage is split pots). Exact figures vary by a point or so with the specific suits involved.

The lessons generalise: a pair against two overcards is roughly a coin flip, a bigger pair against a smaller pair is about 4 to 1, and a dominated hand (sharing a card with a better kicker against it) wins only about one time in four.

How Your Odds Shrink Against More Opponents

Every equity figure above is heads-up. Add players and even the best starting hands win far less often, because each extra hand is another chance for someone to outdraw you. The table shows the share of the pot each hand wins (ties split) when it goes to showdown against random hands, from a simulation of 20,000 deals per cell run for this guide.

Two practical points follow. First, aces are still the favourite against any single opponent hand, but against eight callers they win only about a third of the time, which is why strong players raise before the flop to thin the field. Second, small pairs lose value quickly in multiway pots unless they flop a set (11.8% of the time), so they rely on implied odds rather than raw strength.

The same logic applies to cooler situations. Holding QQ, the chance that one specific opponent has AA or KK is 12 in 1,225, just under 1%. At a full nine-handed table (eight opponents), the chance that at least one of them holds a bigger pair rises to about 7.7%, roughly one hand in thirteen. That is rare enough that folding queens before the flop is almost always a mistake, and common enough that a big re-raise from a tight player deserves respect.

Converting Odds and Percentages

Poker players switch between “odds against” and percentages all the time. To convert odds of X to 1 against into a percentage, divide 1 by (X + 1). To go the other way, divide the misses by the hits.

Putting Poker Odds to Work: A Step-by-Step Routine

1. Put your opponent on a range, not a single hand. What hands bet this way on this board?
2. Count your clean outs against that range and discount any that might not win.
3. Estimate your equity with the rule of 2 and 4 (or the outs table).
4. Work out the pot odds: call divided by the final pot.
5. Adjust for implied and reverse implied odds: stack depth, how disguised your draw is, and how your opponent plays.
6. Decide: call if equity (with realistic implied odds) beats the price; otherwise fold, or raise if fold equity makes a semi-bluff worthwhile.

Common Mistakes With Poker Odds

• Using the two-card number for a one-card decision. If more betting is coming on the turn, your flush draw is 19.1%, not 35%.
• Counting dead outs. Cards that complete your draw but also improve your opponent are worth less, or nothing.
• Overestimating implied odds. Opponents do not always pay off when the third flush card lands.
• Forgetting the coin flip is still a flip. 22 against AK offsuit is only about 52.5% to 47%. Treating it as a big edge leads to bad all-ins.
• Ignoring rake. In cash games the room takes a cut of the pot, which slightly raises the equity you need to call profitably.

Poker Odds in Other Games

The method (count outs, compare with pot odds) works in every poker variant, but the numbers change. In Omaha you hold four hole cards and must use exactly two, so draws are often bigger and preflop equities run much closer together than in Hold’em. In seven-card stud you can see some of your opponents’ cards, so you count live cards rather than assuming all unseen cards are available. Our guide to types of poker explains the main variants, and the online poker guide covers how poker is offered online (both written for Australian readers but useful anywhere).

Casino poker games played against the house, such as Casino Hold’em or Three Card Poker, are a different case: there is no pot to win from other players, so pot odds do not apply, and each bet carries a fixed house edge set by the paytable. Our craps guide shows how that kind of fixed pricing works in practice, bet by bet, and why the cheapest choices there cost under half a percent.

Who This Guide Is For

If you play cash games or tournaments and want to stop guessing on draws, the cheat sheet, outs table and pot-odds table cover nearly every decision you will meet. Newer players should learn the showdown basics too: who shows first and when you must table your hand are covered in our poker showdown rules, and our explainer on slow rolling covers the etiquette side. More guides live on the Casino Bros blog.

Odds knowledge makes you a better player, not a guaranteed winner: short-term results in poker swing wildly. Set a budget you can afford to lose. In the US, help is available on 1-800-MY-RESET; in Great Britain, the National Gambling Helpline is 0808 8020 133. See our responsible gaming page for more.

FAQ

What are the odds of being dealt pocket aces?

1 in 221, or 0.45% (odds of 220 to 1 against). The same applies to any specific pocket pair. The chance of being dealt any pocket pair is 1 in 17, or 5.88%.

What are the odds of hitting a flush draw?

With 9 outs after the flop, you complete the flush on the turn 19.1% of the time, on the river 19.6% of the time, and by the river (seeing both cards) 35.0% of the time.

What is the rule of 2 and 4 in poker?

A shortcut for estimating your chance of hitting: multiply your outs by 2 with one card to come, or by 4 with two cards to come. It is accurate for small and medium draws and overstates big draws of more than about 8 outs.

How do you calculate pot odds?

Divide the amount you must call by the total pot after your call. Calling $50 into a pot that will be $200 needs 50 / 200 = 25% equity to break even.

What are the odds of flopping a set?

With a pocket pair you flop three of a kind or better 11.8% of the time, about 7.5 to 1 against. By the river, the chance of making at least a set rises to 19.2%.

What are the odds of a royal flush?

In a straight five-card deal, 4 in 2,598,960, or 649,739 to 1 against. Using the best five of seven cards, as in Hold’em by the river, it is about 30,939 to 1.

Is AK better than a pocket pair?

Against a lower pair it is roughly a coin flip: 22 has about 52.5% equity against AK offsuit, which has about 47% (the rest is ties). Against QQ, AK offsuit wins only about 43% of the time. AK is strong, but it is still a drawing hand until it pairs.

What are implied odds?

Implied odds add the money you expect to win on later streets when you hit your draw. They can justify a call that pot odds alone reject, especially with deep stacks and a disguised draw.