To become a winning poker player, you must master the fundamental math concepts at the core of the game. In Texas Hold’em, understanding the math behind draws is critical to success at the poker table.
It’s always exciting to see a flush or straight draw materialize on the flop, but you need to know the odds of those draws becoming made hands on later streets. Let’s take a look at the mathematics of poker draws in this article.
What Are The Odds of Hitting a Draw in Poker?
When you flop a draw in Texas Hold’em, you have two more streets (the turn and the river) that give you the opportunity to make your straight or flush. Here’s a glance at the odds of completing some of the most common drawing hands.
What Are The Odds of Hitting a Gutshot Straight Draw?
A gutshot straight draw happens when you have four outs to hitting a straight. For example, if your preflop hole cards are A♠ Q♥, and K♦ T♠ 3♣ hits the board on the flop, you have a gutshot straight draw. You need to see one of the four jacks in the deck to hit the board on the turn or river to complete your straight.
The odds of hitting a gutshot straight draw on the turn is 8.5%, or 10.75-to-1 odds against. If you miss the draw on the turn, you have an 8.7% chance (10.5-to-1 odds against) of making the straight on the river.
When you flop a gutshot straight draw, you have a 16.5% chance of completing the straight on either the turn or river (5.06-to-1 odds against).
What Are The Odds of Hitting an Open-Ender?
An open-ended straight draw gives you eight outs to make a straight. For instance, if you hold J♦ T♣ preflop, and the flop comes 9♦ 8♣ 2♠ , you have an open-ended straight draw. Any queen or seven completes the straight in this example.
With eight outs available, you have a 17% chance of completing an open-ended straight draw on the turn (4.88-to-1 odds against). If your draw doesn’t complete on the flop, you have a 17.4% chance (4.75-to-1 odds against) of seeing the straight complete on the river.
When you flop an open-ended straight draw (or a double gutshot draw), you have a 31.5% chance of making the straight on either the turn or river (2.17-to-1 odds against).
What Are The Odds of Hitting a Flush Draw?
When you flop a flush draw, you have four cards to a flush. If you hold A♥ K♥ preflop, for instance, and 9♥ 5♥ 2♠ comes on the flop, you’re looking for one of the remaining nine hearts in the deck to come on the turn or river to make the flush.
With nine outs, you have a 19.1% chance (4.22-to-1 odds against) making your flush on the turn. If the turn misses, you have a 19.6% chance (4.11-to-1 odds against) hitting the flush on the river.
If a flush draw appears on the flop, you have a 35% chance of making the flush on either the turn or river (1.86-to-1 odds against).
What Are The Odds of Hitting a Flush and Straight Draw?
Combo draws give you out to both flushes and straights, making them some of the strongest hands in Texas Hold’em.
If you’re lucky enough to flop both an open-ended straight draw and a flush draw, you have 15 outs to make your hand. For example, if you hold T♥ 9♥ preflop, and the flop comes Q♥ J♣ 2♥, you’re looking for any heart to make a flush. You can also make a straight with a king or an eight.
With 15 outs on the flop, you have a 31.9% chance of making your hand on the turn (2.13-to-1 odds against). If the turn is a miss, you still have a 32.6% chance to make your flush or straight on the river (2.07-to-1 odds against). A 15-out draw has a 54.1% chance of coming in on either the turn or river (0.85-to-1 odds against).
If you flop a gutshot straight draw and a flush draw, you have 11 outs to make your hand. An 11-out hand has a 23.4% chance of coming in on the flop (3.27-to-1 odds against). If the flop is a miss, you have a 23.9% chance of hitting one of your outs on the river (3.18-to-1 odds against).
With a gutshot straight plus flush combo draw, you have a 41.7% chance of making your hand on either the turn or river (1.4-to-1 odds against).