Once you know about odds in poker, understanding * Pot Odds *&

*will help you make even better decisions.*

**Implied Odds**With all of the variables and unknowns involved in poker, it’s important to know how to make and implement the best math-based decisions possible.

Understanding poker odds – and how to calculate them – is important, but it’s also necessary to understand the concept of “implied odds”.

**DRAWS AND POKER ODDS**

Poker odds are particularly relevant when you are looking at **draws **– i.e. where you have 4-cards towards a straight or a flush and need to decide how you can best play your hand.

To play draws well, you will need to understand:

(1) the chances of your hand improving – i.e. how many “outs” you have;

(2) pot odds;

(3) implied odds.

**1. What Are “Outs” In Poker?**

An “out” in poker is any card that can come on a later street that will help improve your hand.

- If you have a
**flush draw**(4 cards to a flush: 2 in your hand and 2 on the table), as there are 13 total cards of each suit, there are only 9 other cards that will make your flush – so you have**9 outs**. - If you have an
**open-ended straight draw**(e.g. 9-8 on Q-7-6), or a**double gutter**(e.g. Q-10 on A-J-8), there are**8 outs**for you to improve to a straight. - If you have a
**gut-shot straight draw**(i.e. Q-10 on 9-8-4), there are just 4 cards that will make your straight (any of the Jacks), so you have**4 outs**.

**1.1. Using “Outs” to Calculate Your Odds**

After the flop you can see 5 of the 52 cards in a deck – your 2 hole cards and the 3 community cards on the table. There are 47 cards in the deck you haven’t seen (the fact that some of these cards are in your opponents’ hands is irrelevant).

To calculate your chances (or odds) of improving and making your draw *on the very next card*, divide the number of outs you have (let’s use the example of 9 outs, such as if you’re on a flush draw), by the total number of unknown cards left (47). So, you have a 9/47 (or 19.1%, or approximately 1 in 5) chance of improving, to a flush, __on the very next card__.

To see the odds of improving on __either on__* the turn or river*, you must calculate:

- The likelihood of improving on the turn = 9/47 = 19.1%, PLUS
- The likelihood of improving on the river = 9/46 = 19.5%, MINUS
- The likelihood of improving on
*both*the turn and the river = (9/47) x (8/46) = 3.3%

Therefore, the chance of improving on *either* the turn or the river is about** 35%**, meaning you will hit your flush about 1/3^{rd} of the time and not improve about 2/3^{rds} of the time.

NOTE: When calculating for the river, there are only 46 unknown cards instead of 47.

Doing these calculations when you’re in a hand and at the table can be quite tricky! But don’t worry, because there’s a very simple rule that gives the approximate result. This is the rule of 2 and 4.

**1.2. The Rule of 2 and 4**

This simple rule allows you to easily find your approximate chance of improving:

- With one card to come, simply multiply the number of outs you have by 2.
- With two cards to come, multiply the number of outs by 4.

Looking at the above examples, we saw that your chance of hitting the flush on the turn was **19.1%, **and improving on either the turn or river, was **34.8**%,

Using the rule of 2 and 4 you would have multiplied the 9 outs by 2 (= **18%**) to improve with one card to come, or 9 outs by 4 (= **36%**) with 2 cards to come.

While you can see these answers aren’t perfectly exact, they give you a great approximate result that saves you from having to do elaborate, time-consuming calculations when you’re at the table.

**2. What Are Pot Odds in Poker?**

Once you know your chances of improving your hand, you need to know if you’re “getting the right price” to continue with the hand. In other words, is the pot offering you the right odds to profitably take the chance on making your hand?

As an example, let’s suppose there were 100 chips in the pot and your opponent went all-in on the __flop__ for 40 chips. You’d be risking 40 to win 140 in the pot. Do you have the right pot odds to call with your flush draw?

There are two ways you can calculate this: using percentages or using ratios.

- Percentages: To determine the minimum equity (%) you need to have to call, the formula to use is amount to (bet / (pot + bet)). Therefore, 40 / (140 + 40) = 40 / 180 = 22.2%.
- Ratios: Here, we relate the amount in the pot to the amount we have to call: 140/40 = 3.5 to 1. Knowing we need around 2 to 1 (or 33% equity) in order to call with a flush draw, calling here is certainly a profitable play.

If, however, your opponent went all-in on the __turn____ (with one card to come),__ then your chance of getting your flush is now around 4:1. In this instance, because you’re not getting the sufficient pot odds you need (you’re only getting 3.5 to 1) you cannot profitably call.

BUT, sometimes you *can* make a profitable call, even when you don’t seem to be getting the correct pot odds, and this is where implied odds come in.

**3. What Are Implied Odds in Poker?**

Implied odds take into account not just the chips in the pot now, but also chips that might still come into the pot, i.e. chips that you could win on future streets.

Looking again at the above example for the turn (1 card to come), when your opponent bet 40 into the pot of 100, let’s suppose he still had an additional 90 chips in his stack that you thought you could win if you hit your flush.

You’d be risking 40 now to win the 140 in the pot *plus* potentially another 90 chips (or 230 chips total). This would be giving you pot odds of nearly 5.75 to 1 when you’re a 1 in 5 chance (4:1 against) to hit your flush. So, assuming your opponent will pay you off if you make your flush, you should call this bet and hope to win the rest of his stack on the river if you hit one of your outs.

**3.1. The Likelihood of Your Opponent Paying You Off**

Is it as easy as that? No. You will still need to use judgement to allow for a few additional factors. For example, even if your opponent has more money behind them, you must determine how likely they are to put that into the pot if you make your flush or straight.

Continuing to use the previous example, let’s suppose that when the 3^{rd} flush card comes in and you go all-in, they’ll only call 50% of the time. Can we still profitably call 40 on the turn based on implied odds?

Well, we can now only expect to win only 45 additional chips on average on the river. (Even though 50% of the time we won’t win any more money and 50% of the time, we’ll win 90 chips more, this is simply how it averages out in terms of *expected value*.)

Therefore, you’d be risking 40 to win 140 + 45 = 185, which means that the pot is offering you odds of 185/40 = 4.6 to 1. In this instance, the odds are a lot closer to the 1:5 chance you have), but it would still make it a slightly –EV (losing) call on the turn.

If your draw is **well-disguised** (like drawing to a double gutshot e.g. Q-10 on A-J-8), it won’t be as easy for your opponent to guess that the K or 7 has made you a straight. Therefore, in instances like this, the chances of your opponent paying you off are greater.

**3.2. Some other things to consider **

**Might it cost you more?**When you’re calculating “outs” with 2 cards to come, remember that you’ll have no guarantee to see both cards for the same price. After you’ve called the flop, villain might bet again on the turn, charging you even more for your draw! And, he might bet big. (Now that you understand this, YOU would bet big if you were him and saw a potential flush draw out there – to price him off drawing to it!) This is an important consideration. It’s easy to calculate pot odds and implied odds when you know exactly how much it’s costing you, but much harder when, if you don’t hit on the first card, you may have to pay again to see the second one.**Do you have bluff opportunities to**You shouldn’t play all draws passively (by only checking or calling with them). To help balance your ranges – and also to help you continue with your draws when you don’t necessarily have the correct odds to call – it’s okay to bet or raise with certain bluff combinations of draws, if you think there’s a chance your opponent will fold.*raise*on the flop or the turn?**Do you have bluff opportunities if your draw doesn’t get there?**Let’s say that you have a straight draw and called the turn, based on implied odds. Your draw didn’t get there, but the river completes a flush. This now gives you the opportunity to bluff, representing that it WAS a flush that you were going for, which is especially advantageous if you think your opponent will now fold to any aggression.

**In Conclusion**

Understanding outs, odds, and implied odds will undoubtedly improve your poker and help you enjoy it more, as you include more math-based, fundamentally sound poker strategies into your gameplay.

Now that you’ve read this article and our earlier strategy guide, * About Odds in Poker*, we suggest you next look at

*to see how it all comes together.*

__Probability in Poker – Putting It All Together (An Example)__With the help of__Matthew Cluff__