Chapter 3: Understanding Your "Outs" - Calculating the Path to Victory
In the previous two articles, we learned about the importance of the flop and how to read board texture. Now, let's discuss a core mathematical concept that directly relates to whether you should continue playing a drawing hand: calculating Outs.
When you don't have a strong made hand on the flop but have the potential to improve to a strong hand on the turn or river, you are holding a Draw. Outs are the cards remaining in the deck that will complete your draw and likely win you the pot.
Accurately calculating your outs is the foundation for evaluating the value of your draw and making the right decisions in conjunction with pot odds (which we will discuss in the next article). If you have many outs, your draw is very valuable; if you have few outs, chasing the draw can be an expensive mistake.
How to Calculate Outs for Common Draws?
A standard deck of poker cards has 52 cards. On the flop, you know your 2 hole cards and the 3 community cards, for a total of 5 cards. This means there are 52 - 5 = 47 unknown cards left in the deck.
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Flush Draw:
- Definition: You hold two cards of the same suit, and there are two cards of that suit on the flop (four cards of the same suit in total). You need one more card of that suit to complete the flush.
- Calculation: There are 13 cards in a suit. You have seen 4 of them. Therefore, there are 13 - 4 = 9 cards of that suit left in the deck.
- Conclusion: A standard flush draw has 9 outs.
- Example: You hold A♥ K♥, and the flop is 7♥ 2♥ 9♠. Any heart (♥) will give you the nut flush. There are 9 hearts left in the deck. You have 9 outs.
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Open-Ended Straight Draw (OESD):
- Definition: Your hand and the community cards form four consecutive cards, and a card at either end will complete a straight.
- Calculation: You need a card at either end of the straight. For example, your hole cards are T♣ 9♣, and the flop is Q♦ J♠ 3♥. You need a K or an 8 to complete the straight. There are 4 Ks and 4 8s in the deck.
- Conclusion: A standard open-ended straight draw has 4 + 4 = 8 outs.
- Example: You hold 8♠ 7♠, and the flop is 9♥ 6♦ 2♣. You need a T or a 5 to complete the straight. There are 4 Ts and 4 5s in the deck. You have 8 outs.
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Gutshot Straight Draw:
- Definition: Your hand and the community cards form four cards to a straight, missing one card in the middle.
- Calculation: You need a specific rank to complete the straight. For example, your hole cards are T♣ 9♣, and the flop is Q♦ 8♠ 2♥. You need a J to complete the straight.
- Conclusion: A gutshot straight draw has only 4 outs (there are 4 Js left in the deck).
- Example: You hold A♦ K♠, and the flop is T♥ 7♣ J♦. You need a Q to complete the straight. There are 4 Qs in the deck. You have 4 outs.
More Complex Scenarios: Combo Draws
When you have multiple draws at the same time, you need to add their outs together, but be careful not to double-count cards that complete both draws.
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Flush Draw + Gutshot Straight Draw:
- Example (from source): You hold A♦ 5♦ on a 2♦ 3♦ 8♣ flop.
- Flush Draw: You need any diamond (♦) to complete the flush. There are 9 diamonds left in the deck.
- Gutshot Straight Draw: You need any 4 to complete the A-2-3-4-5 straight. There are 4 4s in the deck.
- Overlap? We need to check: of those four 4s, is one of them a diamond? Yes, the 4♦. This card gives you both a straight and a flush (a straight flush!). We already included it in the 9 outs for the flush draw, so when calculating the straight outs, we only count the remaining 3 non-diamond 4s (4♠, 4♥, 4♣).
- Total Outs: 9 (diamonds) + 3 (non-diamond 4s) = 12 outs.
- Note: The source material mentioned 13 outs, which might have double-counted the 4♦ or considered other very weak backdoor draws. Strictly speaking, there are 12 direct outs. Another way to calculate this is: 9 (diamonds) + 4 (any 4) - 1 (the double-counted 4♦) = 12 outs.
- Example (from source): You hold A♦ 5♦ on a 2♦ 3♦ 8♣ flop.
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Flush Draw + Overcards (to make a pair):
- Example: You hold A♠ K♠, and the flop is Q♠ 8♠ 2♦.
- Flush Draw: 9 spades (♠).
- Top Pair Draw: You need an A or a K to make top pair. There are 3 As and 3 Ks left in the deck.
- Overlap? The A♠ and K♠ are already included in the 9 outs for the flush draw.
- Total Outs: 9 (spades) + (3-1=2 non-spade As) + (3-1=2 non-spade Ks) = 9 + 2 + 2 = 13 outs.
- Example: You hold A♠ K♠, and the flop is Q♠ 8♠ 2♦.
Caution! Tainted Outs
Sometimes, a card that appears to be one of your outs might complete your draw but simultaneously give your opponent a stronger hand, causing you to lose the pot. These are known as "tainted outs" or outs that need to be "discounted."
- Example (from source): You hold 9♦ T♦, and the flop is A♦ 8♦ J♠.
- Draw: You have an open-ended straight draw (needing a Q or a 7). Your outs are the 4 Qs and 4 7s, for a total of 8 outs.
- Potential Taints:
- If a Q♥, Q♠, or Q♣ comes, you make a K-high straight (K-Q-J-T-9). However, any opponent holding KT would make a higher, Ace-high straight (A-K-Q-J-T)!
- If the 7♦ comes, you make a J-high straight (J-T-9-8-7) and also a flush. But if an opponent holds K♦ Q♦, or any K♦X♦ or Q♦X♦, they will have a higher flush.
- If a 7♥, 7♠, or 7♣ comes, you make a J-high straight, which is relatively safer.
- Assessment: In this example, your 8 straight outs are not all "clean." The Qs are particularly risky. You might need to discount the Qs as outs, or even ignore them completely, especially in a multi-way pot or against a tight opponent. The 7s are less risky but still have potential dangers.
Quick Estimation of Equity: The Rule of 2 and 4 (The 4/2 Rule)
Calculating your exact equity requires complex math or software, but at the table, we need a quick way to estimate it. The Rule of 2 and 4 is a widely used approximation method:
- On the flop (two cards to come): Your equity is approximately Outs x 4 (%).
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On the turn (one card to come): Your equity is approximately Outs x 2 (%).
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Examples:
- You have a flush draw on the flop (9 outs). Your equity is about 9 x 4 = 36%. (The exact value is ~35%).
- You have an open-ended straight draw on the flop (8 outs). Your equity is about 8 x 4 = 32%. (The exact value is ~31.5%).
- You still have a flush draw on the turn (9 outs). Your equity is about 9 x 2 = 18%. (The exact value is ~19.6%).
This rule is very accurate with a small number of outs. The more outs you have, the slightly larger the error, but it's sufficient for a quick estimation.
Summary
Accurately calculating your outs (and considering potential taints) is the first step in evaluating the strength of your draw. It's the bridge connecting the board texture to your hand's potential. By mastering outs calculation and the Rule of 2 and 4, you have the tools to quantify the value of your draws.
In the next article, we will combine our knowledge of outs with Pot Odds to learn how to make mathematically optimal decisions to call, raise, or fold.