Dirty Outs in Poker: How to Discount Your Outs

A dirty out is a card that completes a draw but may still leave the hand beaten, while a clean out gives the best hand. Take a straight draw with 8 outs: if two of those cards also finish a flush for the opponent, only 6 outs are clean. The honest chance of winning with the draw is then 6 outs out of 46 unseen cards on the turn, which is 13.0%, not the 17.4% that all 8 outs suggest.

Counting every out as clean is the most common way to overestimate a draw. This article defines clean, dirty and blocked outs, shows the exact formula for a discounted count, builds a table of what each dirty out costs, and walks through a straight draw with real cards on the flop and the turn. Readers who need the basic definition first can start with what outs are in poker.

Clean Outs, Dirty Outs and Blocked Outs

An out is any unseen card that improves a hand into a likely winner. A clean out improves the hand to the best hand no matter which reasonable holding the opponent has. A dirty out, also called a tainted out, improves the hand but leaves it second best, usually because the same card also helps the opponent.

Dirty outs come in a few recurring forms. A card can complete a better draw for the opponent, such as a diamond that finishes a straight for one player and a flush for the other. A card can pair the board so that an opponent’s two pair or set becomes a full house. A card can also make a straight that is the lower of two possible straights, so a player holding the higher end of the same run wins.

A third idea is easy to confuse with the first two. A blocked out is a card the opponent is holding, so it can never appear on the board. Blocked outs cannot be seen, so they are estimated rather than counted, while dirty outs can be identified from the board and the opponent’s possible hands. The rest of this article concentrates on dirty outs, because they can be counted from the table cards alone.

How to Discount Outs, Step by Step

Discounting is a counting step that happens before any percentage is calculated. Subtract the dirty outs from the total, then use the clean count in the exact formulas. Applying the discount to a finished percentage, for example by taking a few points off, mixes an estimate with an exact figure and hides the logic.

The formulas with a clean count

Let c be the number of clean outs and U the number of unseen cards. With one card to come the probability is c ÷ U. With two cards to come it is 1 − [(U − c) ÷ U] × [(U − 1 − c) ÷ (U − 1)]. On the flop U = 47 (52 minus 2 hole cards minus 3 board cards) and on the turn U = 46. The opponent’s hole cards stay in the unseen count, because they are not visible.

What each dirty out costs

The table applies the flop-to-river formula to a draw that starts with 9 outs, such as a flush draw, and loses one dirty out at a time. The right column shows the rule of 2 and 4 estimate for comparison, which is the clean count times 4.

The turn-only column divides by 46, so it applies after the turn card has been dealt and one card remains. Each dirty out costs about 3 to 4 percentage points of the flop-to-river chance for a draw of this size, which is why discounting changes the outcome of a pot-odds comparison instead of acting as a rounding detail.

Worked Example: A Straight Draw With Two Dirty Outs

Suppose a player holds 10♠ 9♠ and the flop is J♦ 8♣ 2♦. The player has an open-ended straight draw: any queen gives 8-9-10-J-Q and any seven gives 7-8-9-10-J. That is 4 queens + 4 sevens = 8 outs, counted from 47 unseen cards.

The board shows two diamonds, so an opponent holding two diamonds would have a flush draw. If the opponent does hold two diamonds, the Q♦ and the 7♦ finish both the straight and the flush, and the flush wins. Those two cards are dirty, leaving 6 clean outs (Q♠, Q♥, Q♣, 7♠, 7♥, 7♣).

Flop to river, the clean estimate is 1 − (41 ÷ 47) × (40 ÷ 46) = 1 − 1,640 ÷ 2,162 = 24.1%, compared with 31.5% for all 8 outs. If the turn is a blank such as 4♥, the player faces one card with 46 unseen: 6 ÷ 46 = 13.0% against 8 ÷ 46 = 17.4%. As odds, 13.0% is about 6.7 to 1 against and 17.4% is about 4.75 to 1 against. The gap is the cost of the two dirty outs, and it matters for any comparison with the price of a call.

This count covers only the straight cards. Pairing a ten or a nine could also win against a hand with no pair, but that is a separate event with its own assumptions about what the opponent holds, and it is not counted here.

Reading the Discount at the Table

Discounting rests on assumptions about the opponent’s possible hands, so the discounted number is an estimate, not an exact probability. Against a single known holding the dirty outs can be counted exactly. Against an unknown holding, the count depends on which hands are reasonable, and different players will discount differently from the same board.

A useful habit is to scan three things after counting the raw outs. First, does the card also complete a flush or straight for a hand the opponent could hold? Second, does it pair the board in a way that could improve an opponent’s hand into a full house? Third, does it make a straight that a higher straight could beat? Each yes lowers the clean count, and each no leaves the out intact.

The discount shrinks as more of the picture is known. On the turn, only one card is left, so each dirty out affects one probability, and on the river the question disappears. It also helps to remember that overlapping draws can make some cards count twice in a raw tally, an error that carries straight into the rule of 2 and 4, which multiplies whichever outs count is used.

Common Mistakes When Discounting Outs

Counting every out as clean is the starting error. A flush draw next to a paired board, or a straight draw next to a flush draw, can easily have at least one out that deserves a second look, and ignoring that makes the draw look about 3 to 4 points better than it is.

Discounting too many outs is the opposite error. Removing a card only because some distant holding could beat it turns a sensible estimate into pessimism. A card is dirty when a plausible opponent hand beats the player after it arrives, not when a one-in-a-thousand holding does.

Applying the discount after the percentage breaks the formula. Taking points off 35.0% by guesswork rarely lands on the exact 27.8% for 7 clean outs, so the exact formula should be run on the clean count instead.

Mixing up dirty and blocked outs double counts the discount. A dirty out is visible from the board and ranges, while a blocked out is a card in an opponent’s hand. Subtracting a card for both reasons removes it twice.

Where Discounted Outs Matter

The clean count feeds directly into the price comparison. A call is break-even when the chance of winning equals the call divided by the final pot, as set out in the guide on how to calculate pot odds. A draw that clears the price with 8 outs may fall short with 6, so the discount can change whether the numbers support a call.

Discounting also separates a simple tally from a full equity calculation. A hand-versus-hand calculation, such as the one in set vs. flush draw, street by street, enumerates every runout and handles dirty cards automatically. The discount shortcut is for situations where the opponent’s exact hand is unknown, so the result is a labeled estimate.

Even a well-discounted draw is a probability, not a promise. A 24.1% draw misses about 76% of the time, and a hit still needs to be paid off, a point developed in implied odds in poker. Poker involves real financial risk, and results over short stretches are dominated by luck.

Related Concepts and the Next Step

Outs counting works best as a chain: first count the raw outs, then discount the dirty ones, then convert the clean count with the exact formula or the rule of 2 and 4, and finally compare the result with the price of the call. Readers who want the precision behind the shortcut can continue with the accuracy of the rule of 2 and 4, and readers who want the pricing side can move on to how implied odds are calculated.