Flush Draw Odds Example

Blinds are $50/$100 in a no limit holdem game. You're the big blind and a player from middle position doubles it to $200. Everyone folds to you. You peek down at a suited Queen Two of Hearts. You decide to call and the flop comes...

Ace of Hearts King of Hearts Seven of Spades

...you check and he goes all-in for his last $150.

Lesson 1: Should I really have called a preflop raise with that?
From a pot odds standpoint, you only had to call $100 more into a pot of $350. So your pot odds were 3.5 to 1 (around 22%). Heads up, there are very few hands where he would beat you more than 22% of the time. Even if he had Ace King of Hearts, you'd still be correct in calling there. The worst that he could have is pocket Queens, Kings, or Aces, which would ruin your call.

Lesson 2: I realize that I have a nut flush draw, but I also have a backdoor straight draw! How should I factor that in?
Since you might make a flush in making your straight, we have to discount the hearts in figuring out your chance to runner, runner a straight. You'd need a non-heart Ten and a non-Heart Jack. Your chance of getting either of those on the turn would be 6/47 and the chance of getting the other one on the river would be 3/46. Multiply them together to get the % chance. Comes out to a whooping 0.83%. You can add that on top of your existing chance to hit your flush (since we didn't use hearts in the calculation) to come up with your chance of winning.

Lesson 3: What are my pot odds to call the bet?
You've got your chance of winning the pot somewhere around 36% (we'll round up to account for the chance of making runner, runner two pair or trips). You would be calling $150 to win a potential pot of $600. That's pot odds of 6 to 1.5 which is 4 to 1 or 20%.

Lesson 4: So should I call or fold?
You have a 36% chance of winning with the pot telling you that you should call any bet where you have more than a 20% chance of winning. 36% > 20% so you should call. If you ran into this situation over and over in your poker career, you would make money if you called every time it came up. Sure you would lose more often than you win but since you make a lot when you win and lose a little when you lose, it's correct to call.

Lesson 5: Isn't there a chance that I could make my flush and still lose?
Sure is. If they have a set, you can't count the Nine of Hearts as an out. You also would have to figure out the chance of a board pair on the river if you made your flush on the turn. These are slim chances though, and since we don't know what they have, we don't factor them in. We could do all the calculations for every possible hand they have, figure out the chances of them boating over our flush in some cases or our runner, runner straight making them a straight too in other cases and every other case and possibility. All that would accomplish though is a difference of a couple percent. The call here is so clear that we don't need the headache.

A lot of info to soak up, right? That's only half of the equation. We could also attach a dollar figure to these percentages to find out how much, on average, we win or lose by making the play. This is useful when evaluating more than one choice, like calling, folding, or raising. So far we've only focused on call/fold situations. Including an estimated average is the next step. That term is called expected value (or EV).

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