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 explore a core mathematical concept that directly relates to whether you should continue playing a drawing hand: calculating Outs.

When you haven't made a strong hand on the flop but have the potential to improve to a strong hand on the subsequent turn or river, you hold a Draw. Outs are the cards remaining in the deck that haven't been dealt yet, which can complete your draw and likely win you the pot.

Accurately calculating outs is the foundation for evaluating the value of your draw and making correct decisions in conjunction with pot odds (which we will discuss in the next chapter). If you have many outs, your draw is valuable; if you have few outs, chasing the draw might 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, totaling 5 cards. This means there are 52 - 5 = 47 unknown cards remaining in the deck.

1. Flush Draw:

   • Definition: You hold two cards of the same suit, and the flop contains two more cards of that suit (four suited cards in total). You need one more card of that suit to complete the flush.
   • Calculation: There are 13 cards of each suit. You have seen 4 of them. Therefore, there are 13 - 4 = 9 cards of that suit remaining 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.

2. Open-Ended Straight Draw (OESD):

   • Definition: Your hand and the community cards form four consecutive ranks, needing a card on either end to complete the straight.
   • Calculation: You need one card at either end of the sequence. 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 Kings and 4 Eights 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 Tens and 4 Fives in the deck. You have 8 outs.

3. 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 one specific rank. 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 Jacks remaining 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 Queens in the deck. You have 4 outs.

More Complex Situations: Combo Draws

When you have multiple types of draws simultaneously, you need to add their outs together, but be careful not to double-count cards that satisfy both draws.

• Flush Draw + Straight Draw:

  • Example (Source File): You hold A♦ 5♦, and the flop is 2♦ 3♦ 8♣.
    • 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 Fours in the deck.
    • Overlap? We need to check: among the 4 Fours, is one also a Diamond? Yes, the 4♦. This 4♦ completes both the straight and the flush (even a straight flush!). Since we already included it in the 9 flush outs, when calculating the straight outs, we only count the remaining 3 non-Diamond Fours (4♠, 4♥, 4♣).
    • Total Outs: 9 (Diamonds) + 3 (non-Diamond Fours) = 12 outs.
    • Note: The source file mentioned 13 outs, possibly by double-counting the 4♦ for both the flush and straight, or by considering other very weak backdoor draws. Strictly speaking, the direct outs are 12. Another calculation method is: 9 (Diamonds) + 4 (any Four) - 1 (the double-counted 4♦) = 12 outs.

• Flush Draw + Pair (Improving to Trips or Two Pair):

  • Example: You hold A♠ K♠, and the flop is Q♠ 8♠ 2♦.
    • Flush Draw: 9 Spades (♠).
    • Top Pair Draw: You need an Ace or a King to make top pair. There are 3 remaining Aces and 3 remaining Kings in the deck.
    • Overlap? The A♠ and K♠ are already included in the 9 flush outs.
    • Total Outs: 9 (Spades) + (3-1=2 non-Spade Aces) + (3-1=2 non-Spade Kings) = 9 + 2 + 2 = 13 outs.