Atlassino Academy · Poker in the room · Lesson 7 of 13
Outs and the exact odds
An out is a card that puts your hand ahead. Here is how to count outs, the exact chance they come by the river, and the cards that help the other hand more.
You hold A♥ K♥, the flop is 9♥ 7♥ 2♣, and the other player shows 7♠ 7♦. How many of the cards still to come put your hand ahead?
The short answer
8. Every heart still unseen finishes your flush, but the 2♥ also pairs the board and gives three sevens a full house: that heart gives you a flush, which ranks above three sevens, but it lifts the other hand higher still. Counted over every turn and river, the clean outs give your hand 24.6% of the pot by the river, well under the figure a table of outs prints for a flush draw against a hand you cannot see.
From your seat
- Cards you have not seen47
- Cards that finish your flush9
- Chance of the flush by the river, from the table35.0%
In training mode
- Cards left45
- Clean outs8
- Dirty outs1
- Exact share of the pot by the river24.6%
The cards are the same in both pictures. Only the other hand changes, from hidden to face up, and with it the cards left in the deck, the count of outs and the share of the pot.
Leoformer dealer · rules and maths
Dealing poker, I heard “nine outs” about every flush draw at the table. Some of those nine were the very cards that would fill up the other player’s hand. So I ask people to count the cards that put their hand ahead, not the cards that finish their draw: most of the time the two counts are the same, and the times they differ are the hands that cost the most.
What an out is, and how to count one
An out is a card still to come that puts your hand ahead of the hand you are up against. A clean out does that outright. A dirty out would put your hand ahead of the other hand as it stands, but the same card lifts the other hand higher still, so it is not an out. Counting outs takes three steps.
- List the cardsEvery card that would finish your draw: the rest of the suit, or the ranks that complete the straight.
- Take away what you seeCards in your hand and on the board are already dealt, and cannot come again.
- Check against the other handPut the card on the board and count both hands with it: it is an out only if your hand comes out ahead.
Three draws come up again and again on the flop. A flush draw is four cards of one suit, two in your hand and two on the board, waiting for a fifth. A straight draw open at both ends is four cards in a row, finished by a card at either end. A straight draw with one gap is finished only by the rank that fills the gap.
A flush draw
Your handThe boardA straight draw open at both ends
Your handThe boardA straight draw with one gap
Your handThe boardThe board and your hand change from tile to tile. The count under each tile is the cards still unseen that finish the draw, counted from your own seat, where the other hand is hidden.
The exact odds, and where the rule of 4 and 2 slips
Once you have the outs, the chance that one of them comes is counted, not guessed. From the flop two cards are still to come, the turn and the river; from the turn one card comes. An operator’s guide to poker odds says that the odds change throughout a game as cards come out of the deck, and that no player can predict which card comes next.
| Outs | Flop to river, exact | Rule of 4 | Turn to river, exact | Rule of 2 |
|---|---|---|---|---|
| 4 outs | 16.5% | 16%−0.5 points | 8.7% | 8%−0.7 points |
| 8 outs | 31.5% | 32%+0.5 points | 17.4% | 16%−1.4 points |
| 9 outs | 35.0% | 36%+1.0 points | 19.6% | 18%−1.6 points |
| 12 outs | 45.0% | 48%+3.0 points | 26.1% | 24%−2.1 points |
| 15 outs | 54.1% | 60%+5.9 points | 32.6% | 30%−2.6 points |
The rule of 4 and 2 multiplies the outs by four on the flop and by two on the turn. The rule of 4 is roughly the turn’s chance plus the river’s chance, and adding the two counts twice every turn and river that both bring an out; the more outs, the more of those, so on a big draw the rule runs high. The rule of 2 counts one card and comes out a little low.
On 15 outs the rule of 4 is 5.9 points high: the longer bar is the rule, the shorter one the exact count.
That table is for a hand you cannot see, the way a real table plays: the 47 and 46 unknown cards include the other player’s two. In training mode the other hand is face up, so its two cards are out of the deck as well: 45 cards are left on the flop, 44 on the turn, and the exact share counts every turn and river for both hands.
Two draws in one hand
A hand can hold a flush draw and a straight draw at once. Every card that finishes either draw is an out, and a card that finishes both draws is still one card: count the suit, add every card of the ranks that finish the straight, and take away the cards that sit in both lists.
A flush draw and a straight draw open at both ends
Your handThe boardCards of the suit, plus cards that finish the straight, minus the cards in both lists, makes the outs.
A flush draw and a straight draw with one gap
Your handThe boardCards of the suit, plus cards that finish the straight, minus the cards in both lists, makes the outs.
The suit and the straight change from the first picture to the second; in both, the cards in both lists are counted once.
Fifteen outs on the flop come by the river 54.1% of the time with the other hand hidden, which is the draw where the rule of 4 slips the furthest.
Dirty outs: cards that help the other hand more
Back to the hand this lesson opened with: A♥ K♥ on 9♥ 7♥ 2♣ against 7♠ 7♦. Every card of the deck can be put on the turn and checked against both hands, and the deck below shows what each card does.
| Suit | A | K | Q | J | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ♠ spades | · | · | · | · | · | · | · | T | · | · | · | · | · |
| ♥ hearts | Y | Y | O | O | O | B | O | B | O | O | O | O | D |
| ♦ diamonds | · | · | · | · | · | · | · | T | · | · | · | · | · |
| ♣ clubs | · | · | · | · | · | · | · | · | · | · | · | · | B |
- O a clean out: puts your hand ahead
- D a dirty out: lifts the other hand higher still
- B Y T on the board, in your hand, in their hand
- · not an out
Every heart finishes your flush. The 2♥ also pairs the board, three sevens become a full house, and that heart is the one marked D.
On the turn the same hand can pick up more dirty outs. With 9♥ 7♥ 2♣ K♠ on the board, the king of spades gave your hand a pair of kings: another king now makes three kings for your hand and a full house for the other hand.
| The hands | From your seat: cards that finish the draw | Clean outs | Dirty outs | Exact share |
|---|---|---|---|---|
| A♥ K♥ against 7♠ 7♦board 9♥ 7♥ 2♣ | 935.0% by the table | 8 | 1 | 24.6% |
| A♥ K♥ against 7♠ 7♦board 9♥ 7♥ 2♣ K♠ | 919.6% by the table | 8 | 3 | 18.2% |
| 8♥ 7♥ against A♥ K♥board K♣ 9♥ 6♥ | 1554.1% by the table | 8 | 5 | 31.2% |
From your seat, the count of cards that finish your draw cannot tell which of them help the other hand more, or which of them sit in the other hand. Against the hand shown, the clean outs are fewer and the exact share is lower.
Whether calling a bet is worth it at these numbers is a different question, and lesson 7.8 takes it up with the same counts.
Mayaformer floor supervisor · manners, money and breaks
Knowing the exact chance of a card tells you what that card is worth to your hand. It does not bring the card, and on any one hand the cards decide: a session can go against you for a long time with every count right. Practise the counting here, at home.
Decide before you sit down how much money and how much time the session gets, and stop when either one runs out. A draw that missed is not a reason to put more in.
If it stops being fun
If gambling stops being entertainment, help is available. 19+ in most of Canada; 18+ in Alberta, Manitoba and Quebec. More on responsible gaming.
The lesson on one card
That is the lesson. Here it is on one card: print it, or keep it on your phone.
| Outs | Flop to river, exact | Rule of 4 | Turn to river, exact | Rule of 2 |
|---|---|---|---|---|
| 4 outs | 16.5% | 16% | 8.7% | 8% |
| 8 outs | 31.5% | 32% | 17.4% | 16% |
| 9 outs | 35.0% | 36% | 19.6% | 18% |
| 12 outs | 45.0% | 48% | 26.1% | 24% |
| 15 outs | 54.1% | 60% | 32.6% | 30% |
19+ (18+ in AB, MB, QC) · Set a limit before you sit down · Play responsibly · the line for your province is at Helplines by province
Practice: count your outs
Every hand in the practice run shows the board, your hand and, in training mode, the other hand face up. First you count the clean outs; then, on the same hand or another, you name the share of the pot your hand has by the river. Level 1 deals clean draws, level 2 two draws in one hand, level 3 hands with dirty outs among the cards still to come.
Nothing is bet here, and no card is dealt: each hand stops at the moment you count.
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Level 3 · Dirty outs
The board on the flop
Your hand
The other hand, face up in training mode
Two cards to come: the turn and the river.
How many clean outs does your hand have against the hand shown?
- 9 outs That counts the 2♥ as clean. With that card on the board the other hand ends up higher than yours, so it is not an out.
- 8 outs 3♥, 4♥, 5♥, 6♥, 8♥, 10♥, J♥ and Q♥: each of these cards puts your hand ahead of 7♠ 7♦. 2♥ would put your hand ahead of 7♠ 7♦ as it stands, but lifts the other hand higher still: a dirty out, not counted.
- No outs at all There are outs. The other hand is ahead now, but 3♥, 4♥, 5♥, 6♥, 8♥, 10♥, J♥ and Q♥ still put your hand ahead.
A♥ K♥ on 9♥ 7♥ 2♣, against 7♠ 7♦. Put each card still unseen on the board and count both hands with it: only the cards that leave your hand ahead are outs.
Every hand in the practice run is worked out the same way: each card still unseen is put on the board in turn, both hands are counted with it, and the exact share of the pot counts every turn and river that can still come.
How the practice run works
Where the answers come from. Each hand is a board, your hand and the other hand, chosen to show one thing, and the answer is worked out when the page is built: every card still unseen is put on the board in turn and both hands are counted with it, and the exact share of the pot counts every turn and river that can still come, a tie as half. The wrong answers are named mistakes: the whole suit counted, one end of a straight counted, a card that finishes both draws counted twice, a dirty out counted as clean, one card counted instead of two, one card in fifty-two, the table figure for a hidden hand, or the rule of 4 and 2.
One strip, and no rounds. Every square on the strip is one moment of this lesson, and all of the squares are there from the start. Your first answer fills the square it belongs to; when the squares of one level are full, the next level begins by itself, with no button in between. Practising a moment you got wrong turns its cross into “fixed in practice” and does not change the count, because only first answers count.
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Check yourself
Mayaformer floor supervisor · manners, money and breaks
Three quick ones. Pick an answer, then check it. No timer, no points: just whether it stuck.
Back to the question we opened with. Against three sevens, 8 of the 9 hearts put your hand ahead; the dirty one is the heart marked D in the deck above.
Further reading
19+ (18+ in AB, MB, QC) · Play responsibly · the helplines are further up this page
Further reading
- Poker odds · OLG PlaySmartWhat odds mean, why they change as cards come out, and why one hand says nothing about the next.
How it’s worked out
Numbers, sources and hosts
Where this happens. Every hand on this page is a hand of Texas hold’em at a table in a poker room. At a real table the other hands are face down; the practice run shows the other hand face up, as a training mode, so that clean and dirty outs can be counted card by card.
Numbers. The chances in the table of outs count the cards themselves: the chance that at least one out is among the cards to come, with 47 unknown cards on the flop and 46 on the turn. The share of the pot against a hand shown counts every turn and river that can still come from the cards left, for both hands, a tie counting as half. Every figure carries a machine-readable key and is recomputed by the same engine on every build.
The words. No document we could read defines an out, a dirty out or the rule of 4 and 2; the definitions on this page are ours, and so are the counts.
What is deliberately absent. There is no money on this page and no decision to call or fold: the share of the pot a call needs is lesson 7.8. How often starting hands come and how far ahead they are before the flop is lesson 7.6; the strongest hand a board allows and blockers are lesson 7.9; the showdown and kickers are lesson 7.5; the order of hands is lesson 7.1. The fee the room charges, from the pots or for the seat, and what it does to a table over a month, is lesson 7.10; tilt and when to leave is lesson 7.13. Nothing here is counted per hour.
Sources. Every claim drawn from a document carries a button with the sentence it rests on, the publisher who wrote that sentence and the date we read it.
Hosts. Leo and Maya are illustrated characters. Their backstories, a former dealer and a former floor supervisor, are written for the course: neither is a real person, and neither speaks for any casino. The rules and numbers on this page come from the sources it cites, not from their experience.
No promise. Poker in a poker room is played against the other players at the table, not against the house, and the room charges for the seat, a rake from the pots or a session fee. Knowing what a card is worth to your hand tells you that before the card comes; it does not make the card come, and on any one hand the cards decide.
Odds change as the cards come out
That means that the odds will change throughout any game, as cards are removed from the deck.
However, even the most skilled players can’t predict which card will be dealt next.
OLG PlaySmart · Poker — odds · read
In Poker, the odds of drawing any card is 1 in 52, but those odds change as cards are dealt.
Odds change as the cards come out
That means that the odds will change throughout any game, as cards are removed from the deck.
However, even the most skilled players can’t predict which card will be dealt next.
OLG PlaySmart · Poker — odds · read
In Poker, the odds of drawing any card is 1 in 52, but those odds change as cards are dealt.
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