## Calculating Outs and Odds; Part I, Count your Outs

by ~ May 9th, 2008. Filed under: Instructional posts.

* Modified July 4th, 2011 *

For some reason there often seems to be confusion regarding odds in poker. I think partly this is due to the fact that there are a variety of different aspects to odds as well as different methods of for calculating or viewing them. As a bit of a project I thought that I’d try to organize and summarize the various aspects that I’ve come across.

But before looking at odds, we have to be able to count your chances.

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**Outs, what are they and how do you count them**?

Outs are chances or different possibilities that your hand might improve.

You hold

A8, the flop comes K65.

What are your chances of getting a flush? To get a flush you need one more spade. There are 13 spades in a deck, 4 are known (you have two and two are in the flop) so there are 13 – 4 = 9 remaining spades. Each chance is called an “out”, so you have 9 outs to make the flush. It doesn’t matter whether someone else had or has a spade in their hand. Unless someone tells you that they folded a spade or you’re watching televised poker you won’t know if another spade has been seen, so for calculating your outs it doesn’t matter. (Obviously if you’re playing Stud or some other game where you can see other cards that are gone then those cards have to be deducted from your total outs)

What if you suspect your that opponent has paired the king? In that case if an Ace comes you will be beating him with your higher pair. There are 4 Aces in the deck, and you have one so 4 – 1 = 3 aces as outs. If, as you suspect, your opponent has paired the King, then if you get an Ace *or *if you get a spade, you will be beating him so you can add the outs, 9 spades + 3 Aces = 12 outs.

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Let’s look at straights. You hold

98 and the flop is A76.

Now if a 10 or 5 of any suit comes, you will have a straight. There are four 10s and four 5s so 4 + 4 = 8 outs to get a straight.

Say you hold

98 again but the flop this time is A65.

Now only a 6 fills your straight (these are called “inside” or “gut shot” straight draws). Four 7s = 4 outs to fill the gut shot straight.

Or, you hold

98 the flop is J75.

Now, a 7 fills your 56789 straight, but a T fills your 789TJ straight. This is the “double gutshot” or “double belly buster” straight draw with four 7s and four Ts to fill a straight so 4 + 4 = 8 outs.

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Try one more. This time you have

98 and the flop is A76.

You think you will win if you hit a flush or a straight. To get there, you have nine outs for the flush draw (KQJT65432). Then any 10 or 5 will give you a straight. However, you have already counted T and 5 in your flush outs, so now you can only count TTT for three more 10s and 555 for three more 5s as outs. Nine flush outs plus three other 10s and three other 5s gives you 9 + 3 + 3 = 15 outs in total.

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**Clean outs, Tainted outs
**

Sometimes not all of your outs are always going to win for you if they hit. Say you have

98 and the flop is A76.

This time, your opponent knocks over his cards in his excitement and you see that he holds two more Aces for a set of Aces. Now the 6 is not an out; do you see why? In fact, if you didn’t know your opponent had AA (or 77 for that matter) you would be in big trouble if the 6 hit because your big hand is almost dead to his bigger hand. Your only hope in that event is a straight flush.

More often, something like

98 on a A76 flop will come up.

Of your eight outs for making a straight, only six are clean outs as the T and 5 would give someone a flush if they do indeed hold the flush draw. Sometimes these are referred to as “tainted” outs. They can be counted as partial outs, so you could value them as 1/2 outs each. Six clean outs plus two tainted outs for a total of seven outs.

Say instead you hold the

54 on the A76 flop. Your opponent has T9.

Here an 8 or 3 will give you a straight so there are eight possible useful cards. However an 8 gives your opponent a diamond flush. If the one of the other 8s comes, your opponent will hit a T9876 straight which will beat your 87654 straight. Even if you don’t know exactly what your opponent holds, the uncertainty of having the winning hand if an 8 comes means that it is dangerous to consider any 8 as a full out. I would ignore the 8 entirely and value the 88 or 8 as 1/2 outs. Four 3s as outs, three 8s as 1/2 outs = 4 + 1.5 = 5.5 outs.

As it turns out, your opponent has nine outs with the flush draw, plus the other three 8s for a gut shot straight draw or 9 + 3 = 12 outs. He’s also ahead of you at the moment, though neither of you know that at the time. If you did know each other’s cards (if one of you is all in and the cards have been turned over) you would see that a 5, 5, 4 or 4 will give you a pair which is currently enough to beat his hand. The 5 or 4 gives him the flush so they are not outs for you, but the others give you four more outs. That’s unless he gets a T or a 9 to beat your lower pair.

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**Partial Outs**

In the last examples the tainted outs were counted as 1/2 outs because their value may be questionable. There are other situations where you will encounter partial outs.

This will happen often on the flop because you have the turn and river cards yet to come. For example, you have

98 and the flop is A72.

This time if* both the turn and river car*ds are spades you can still hit a runner-runner flush. How often does a runner-runner flush come in? There are ten remaining spades. On the turn there are 52 total cards – 5 known cards = 47 cards remaining. Assuming that you caught a spade on the turn, at the river there are 9 more spades remaining and 52 total – 6 known cards = 46 remaining cards. Therefore, the chances of the turn being a spade are 10 in 47, and if it is, the chance of the river also being a spade is 9 in 46. The math calculation is (10/47)(9/46) = 4.16% or slightly better than a 1 in 25 chance (actually closer to 1 in 24). Not particularly good odds; runner-runner flushes are usually valued as one or perhaps 1.5 outs.

The 7 also gives you three cards to a runner-runner straight draw. The chances to hit the straight are similar to the flush, so you could count the straight draw as another 1 or 1.5 outs. If however the flop has a 6 instead of a 7 such as A62 you have a gap in the straight draw. As we saw with the gutshot draw earlier on the chances of hitting drop. The chances of hitting are so remote I wouldn’t even consider the runner-runner gutshot draw as an out unless you get to see the turn for free and the turn card is part of your straight.

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Okay, that took longer than I expected just to cover outs, so I’ll start discussing odds in another blog posting. If you have questions, or you think that I’ve missed something, feel free to send an email or leave a comment.

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The rest of the series:

- Calculating Odds and Outs; Part II, Pot Odds
- Calculating Odds and Outs; Part III, Odds on the River

- Calculating Odds and Outs; Part IV, Using Percentages
- Calculating Odds and Outs; Part V, Bet sizing, and Expressed and Implied Odds

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