Poker Lesson #12: Poker Odds for Beginners, Part II

Poker Lesson #12:
Poker Odds for Beginners, Part II
by Oliver Butterick

In the first article, I talked about how to count your outs when you have a drawing hand, and how to calculate pot odds. This article will show you how to calculate the odds of making a drawing hand.

How “outs” and the “nuts” work together, and why it is important to play cards that can make the “nuts”:

In the QJ of Hearts example from the previous article, the number of outs changed based on your opponents’ holdings. This is because only your straight and straight flush outs are to “the nuts.” Any cards that will make your hand the winning can be referred to as “clean” outs. Outs to the nuts are always clean outs, since if you make the nuts, then you will definitely have the winning hand. Usually, you won't have to make the nuts in order to win, and so the problem is that you don’t always know which of your outs are “clean” and which are “dirty.”

For example: You have K-10 of Spades, and the flop comes 8-8-3, with two spades. Your opponent comes out betting, and you think that he has a 8, and that he is betting so that it will be expensive if someone wants to try and catch a flush. So, you figure that you have nine outs to make a flush, but this is not correct, for a reason that is deceptive. Even if you are correct in determining that your opponent had an 8, one of your spade outs might make him a full house, if it is the same as his kicker.

Let’s say that he has 9-8, with no spades in his hand. This means that if the 9 of spades comes, you will make your flush at the same time your opponent makes his full house, a very bad situation to be in! In this case, you only have eight “clean” outs, and you won’t know which one is the “dirty” out.

Or your opponent could have 9s-8. Now, he can’t catch the 9 of spades, because it is already in his hand. In this case, you don’t have any “dirty” outs, but you still have eight “clean” outs, since the 9 of spades will not be coming up.

Matters could be better: your opponent could have 10-8, in which case, since YOU have the 10 of Spades, you no longer have any “dirty” outs, and all nine of your outs are “clean.”

But matters could also be a lot worse. Your opponent could have 8-8 (making four of a kind), and you will have zero “clean” outs. This means that none of the cards in the deck will improve your hand enough to make the winning hand. This is called “drawing dead,” a situation that you want to avoid if at all possible. Remember that you will never be drawing dead as long as you have “outs to the nuts.”

Example of Drawing Dead: You have A-K and your opponent has A-A, and the flop comes:

A-9-6, with no flush possibilities for you.

In this situation, A-K is drawing dead because there are no cards that will come so that it can surpass A-A. Even if a King comes on the turn AND on the river, you will still make a smaller full house than A-A. Though this specific situation is very rare, it is important to be aware when you might be drawing dead.

Odds of making your hand

There are two ways to go about learning the odds of making your hand- both involve counting your outs.

Strategy #1: Doing the Math

This involves counting your outs, determining which ones are clean, and calculating the odds that you will hit one of them. We’ll start with calculating the odds of making your hand with only one card to come (after the turn and before the river), since that is much simpler than calculating your odds after the flop.

Step 1—Count Your Clean Outs

In determining which of your outs are “clean,” you will have to look back at the information that you have gathered throughout the course of the hand, the course of your session, and the course of your poker career.

Over the course of the hand, did your opponent raise pre-flop or call a pre-flop raise? Did your opponent bet, raise or call a bet after the flop? Regardless of the answers to these questions, there is information buried in there somewhere. Also, what is the position of your opponent? These factors will help you narrow down the range of hands that your opponent could possibly have.

Over the course of your session, what information have you gathered about this opponent? Is he tight or loose? Is he passive or aggressive? Is he on tilt? All of this information can be added to the information that you received during the hand. Or better, this information will provide a context for the hand. If you have no context yet (say you just started your session, or you are involved in a pot with a player that just sat down), then assume more or less that your opponent plays like you do, but be wary of ruling out potential hands just because you wouldn’t play them.

Finally, think back over the course of your poker career. As you add to the poker database in your brain, you will see many people play hands differently than you would. Categorize these plays and see if you notice trends. If there is a strong trend of how a certain hand is played, then knowing this will help you defend against it better—also, it can be a good learning tool. For example, if your regular play is to go all-in when you flop trips (three of a kind when two of them are on the board), and you notice that 1) usually nobody calls you unless they have trips or a full-house, and 2) that almost everyone else will play trips much more slowly, then maybe there is a better way for you to play the hand.

Step 2—Set up your odds

The first number of your odds—the number of unsuccessful possibilities —will be 46 minus your number of outs. This is because after the turn, you have knowledge of six out of the total of 52 cards in the deck (your two cards, the flop, and the turn), meaning that there are 46 cards left in the “deck.”

Wait a minute!?!? The dealer dealt out a bunch of cards to all the players on the table, INCLUDING the cards that your opponent is holding right now. Surely, you shouldn’t count those as being in the deck, right? Wrong. This is because all of the cards that were dealt out are (or at least should be) unknowns, and you don’t know whether the other players were dealt your outs or not.

Think of it this way: what are the odds that the first card dealt is the Ace of Spades? 51:1, right? Well, what if I asked you, what are the odds that the 26th card from the top is the Ace of Spades? As long as you don’t know anything about any of the other cards, the odds are still the same: 51:1. When determining the odds that the river card will improve your hand, you are really asking the same question.

The cards were shuffled and cut, the dealer dealt out 18 cards, 2 to each of the 9 players at the table; then he burned a card, dealt 3 cards for the flop, burned another card and dealt the turn. Now the 25th card is on the top of the deck, waiting to be burned so that the 26th card can become the river. The only thing that has changed is that you now know that 6 cards either are or are not the Ace of Spades, and you can adjust the odds accordingly.

This is one reason why it is important not to expose your cards during the course of the hand, AND to pay attention if someone else does. One way or another, these exposed cards will affect your odds if you are in the hand.

So, let’s say that you have 8 outs to make an open-ended straight. Your non-outs are 46-8, which equals 38.

Therefore, you’re the odds of making your straight on the river are 38:8. Since 38 is really close to 40, and it is safer to round up the number on the left side than it is to round it down, we’ll approximate your odds as 40:8, which can be reduced to 5:1. It’s not as hard as it looks, it just takes a little practice.

So how would we go about calculating your odds after the flop if you had two cards to come? This is much more confusing, and is good as little more than an academic exercise at this time.

Step 1—Count Your Outs

Lets say that you once again have an open-ended straight draw, so you have 8 outs.

Step 2—Calculate your odds by working in reverse

We’ll use probabilities for this step, and convert back to odds later. First, what is the probability that you will NOT make your draw on the turn? 39 out of 47. Then, what are the chances of you missing your draw on the river? 38 out of 46. Now, you make fractions out of these: 39/47 and 38/46 and multiply them together, getting 1482/2162, which, calculated to a percentage, is 68.5%. This is fairly close to 66%, so we’ll say that you will miss your draw 2/3 of the time, which means you will make your draw 1/3 of the time. In this case, the odds of hitting your straight draw on one of the two cards to come is a little worse than 2:1

That was pretty confusing, and involved multiplying and dividing some big numbers.

Strategy #2: Memorize the Odds

Although memorization is not the most palatable alternative for most, it is a lot easier than multiplying and dividing large numbers, and will save you a lot of work in the long run.

Here is a chart of post-flop odds:

Outs	Odds on the flop for the turn	Odds on the turn for the river	Odds on the flop for the turn and river
1 Out	46.00 to 1	45.00 to 1	22.50 to 1
2 Outs	22.50 to 1	22.00 to 1	10.88 to 1
3 Outs	14.67 to 1	14.33 to 1	7.01 to 1
4 Outs	10.75 to 1	10.50 to 1	5.07 to 1
5 Outs	8.40 to 1	8.20 to 1	3.91 to 1
6 Outs	6.83 to 1	6.67 to 1	3.14 to 1
7 Outs	5.71 to 1	5.57 to 1	2.59 to 1
8 Outs	4.88 to 1	4.75 to 1	2.18 to 1
9 Outs	4.22 to 1	4.11 to 1	1.86 to 1
10 Outs	3.70 to 1	3.60 to 1	1.60 to 1
11 Outs	3.27 to 1	3.18 to 1	1.40 to 1
12 Outs	2.92 to 1	2.83 to 1	1.22 to 1
13 Outs	2.62 to 1	2.54 to 1	1.08 to 1
14 Outs	2.36 to 1	2.29 to 1	0.95 to 1
15 Outs	2.13 to 1	2.07 to 1	0.85 to 1
16 Outs	1.94 to 1	1.88 to 1	0.75 to 1
17 Outs	1.76 to 1	1.71 to 1	0.67 to 1
18 Outs	1.61 to 1	1.56 to 1	0.60 to 1
19 Outs	1.47 to 1	1.42 to 1	0.54 to 1
20 Outs	1.35 to 1	1.30 to 1	0.48 to 1
21 Outs	1.24 to 1	1.19 to 1	0.43 to 1

In the third and last article in this series, I will put everything together, using some examples to demonstrate how you would use this information in order to make good poker decisions

Oliver can be reached at oliver@babblog.com.