Poker is a game where you’re trying to find long-term profits through many variables and unknowns in any given situation. Therefore, it’s essential to understand the “odds” and the various mathematical calculations that you can and should be making. This will only allow you to play more profitably and help you make better, sound, +EV decisions during any given hand.

It used to be that players either played primarily by “feel” or by “maths”. But, in a game that’s becoming tougher and tougher to beat, it’s vital to mesh both concepts together.

In this “new age” of poker, players must have both a solid foundation of optimal mathematical poker, while developing a robust and intuitive sense as to what is the best play to make in any situation.

One of the most common situations that comes up in poker is draws. These are situations where you have 4-cards towards a straight or flush. To play draws profitably, you first must understand odds:

(1) percentages of your hand improving;

(2) pot odds, and finally

(3) implied odds.

This article is going to illuminate everything you need to know surrounding this, most notably on what implied odds are and how they can help transform a losing call into a profitable one.

NOTE: If you know the basic concepts of outs, calculating basic equities and pot odds, you can skip these first few sections until “What Are Implied Odds?”.

What Are “Outs” In Poker?

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

FLUSH DRAW OUTS:

If you have a flush draw (4 cards to a flush), because there are 13 cards of each suit in a standard 52-card deck, there are 9 remaining outs for you to hit your flush.

OPEN-ENDED STRAIGHT DRAW OUTS:

If you have an open-ended straight draw (i.e. 6-7 on K-8-5) or double gutter (i.e. J-9 on K-T-7, you have 8 outs total to improve to your made hand of a straight.

GUTSHOT STRAIGHT DRAW OUTS:

If you have a gut-shot straight draw (i.e. 5-6 on 9-8-2), then you would have 4 outs to improve your hand.

How to Use Outs to Calculate Your Odds (Equity)

After the flop is dealt in Texas Hold’em Poker, you know 5 of the 52 cards in a deck – the 2 hole cards in your hand and the 3 community cards on the table.

This means that if ever you have a hand with a draw after the flop, you can easily calculate the odds you’d have of improving your hand either on the turn or the river.

To start with, you must recognise that after the flop, there are 47 unknown cards in the deck.

From here, just divide the number of outs you have by the total number of unknown cards in the deck and you will get discover the chances of improving on the very next card.

For example, if you had a flush draw, you would divide 9 outs by 47 unknown cards to see the likelihood of improving your hand to a flush on the turn (19.1%).

If you wanted to know the odds to improve on either the turn or the river, you would add together (the likelihood of improving only on the turn) + (the likelihood of improving only on the river) + (the likelihood of improving on the turn and river):

= ((9/47) x (38/46))  + ((38/47) x (9/46)) + ((9/47) x (8/46))

= (0.191 x 0.826) + (0.801 x 0.196) + (0.191 x 0.174)

= 0.158 + 0.157 + 0.033

= 0.348

= 34.8%

NOTE: If you wanted to calculate your chances of improving from the turn to the river, remember to change the number of unknown cards in the deck from 47 to 46.

The Rule of 2 and 4

As you can see, the above mathematical equitation would be quite a complicated ordeal to go through during a poker hand, just to find approximate equities and per cent chances of improving.

Luckily, there is a more straightforward process you can use to get decent approximations:

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

To put this into an example, let’s use the same flush draw situation from above. Multiplying 9 outs by 4 is 36%. This percentage isn’t too far off from the 34.8% we got from doing the actual, more-time-consuming calculations above.

Similarly, to find the approximate odds of us hitting our flush on the very next card, we would multiply our 9 outs by the number 2 to discover that there’s about an 18% chance of this happening (again, close to the 19.1% chance we calculated above for hitting it on the turn).

What Are Pot Odds

blackboard filled with mathematical equations

 

The next step of playing draws profitably (and relating this to mathematics in poker) is to see if you’re “getting the right price” to continue. Suppose the pot is $40 on the flop, and your opponent goes all-in for $20. Can you call profitably with your draw?

Well, in this case, you must risk $20 to potentially win $60 (the pot + your opponent’s bet). This number leads to pot odds of 3 to 1 ($60 to $20), meaning that you must win just over 25% of the time for this to be a profitable call. Because a flush draw here has about 36% equity with nine outs and two cards to come, you should call here, as you’ll profit in the long-term.

However, let’s suppose now that your opponent went all-in on the turn (betting $20 into a $40 pot). Then, you’d only have one more card to improve to a flush. This time, you’d only have 18% equity, meaning you could not profitably call here (as above, we can see we needed 25%). If you do call, then you will lose more money in the long-term than otherwise.

Is there any situation where you can make a profitable flop or turn call when NOT getting the correct pot (expressed) odds, though? The simple answer is yes, and it has to do with implied odds!

What Are Implied Odds?

Implied odds consider the money you could potentially/additionally win on future streets, in case your draw hits.

Taking the above example, imagine that your opponent bet $20 into $40 on the turn, but also had $40 left in his stack. Yes, you’re getting 3 to 1 pot odds, but this doesn’t account for the additional $40 that you could win from villain’s stack on the river.

With this additional factor, you’d be risking $20 to win $60 in the pot, PLUS potentially $40 more (or $20 to win $100 total). This situation means you’re now getting 5 to 1 odds, meaning you’d need 16.67% equity to call profitably. Seeing as you’d have about 18% equity with one card to come, you can call here with confidence, knowing that you’ll be making money in the long run.

The Likelihood of Your Opponent Paying You Off

Using the concept of implied odds, you can calculate a few additional factors that will enhance your mathematical and decision-making abilities:

  1. Whether it’s still profitable to call if your opponent is only going to call a future bet a certain percentage of the time (i.e. if you donk bet the river once your draw comes in).
  1. The exact amount of money you’d have to win on a future street to make your current call profitable.

EXAMPLE #1

Let’s continue with the previous example and say that instead of our opponent calling a $40 river bet all the time when we improve, he’ll only call it 50% of the time.

Can we still profitably call the turn based on implied odds?

Now, we’d be immediately risking $20 to win ($60 in the pot + $40 in our opponent’s stack, but only 50% of the time):

= $20 to win ($60) + (50%)($40)

= $20 to win ($60 + $20)

= $20 to win $80

= 4 to 1 pot odds

= 20% equity we need to call.

With only 18% equity, we should not be calling here, then, based on the assumption that our opponent will only call a future bet 50% of the time if our draw comes in.

EXAMPLE #2

Using implied odds, we can calculate how big of a bet we’d need to win on the river to make our call break-even (or profitable). This scenario is one of the beautiful things about No Limit Hold’em: being able to choose appropriate bet-sizings in any given situation to try and influence or bring about the desired result. (This topic is especially relevant in deep-stacked situations.)

For this, we must work backwards, and start by realising that, with a flush draw, we have 18% equity.

This fact means that we would need to have ~4.6 to 1 odds to call.  (To determine this, take 100% divided by 18% (or the equity you have), and then subtract 1 from this answer to get the X : 1 ratio.

4.5 to 1 = X to $20 (money we’re risking to call)

4.5 to 1 = $90 to $20

Therefore, if we need to win $90 to make this call breakeven, and there’s $60 in the pot that we would win now, that means that we only need to have our opponent call a $30 river bet to not lose money from calling with our draw on the turn.

Important Considerations Regarding Implied Odds

Even though you should now be able to calculate implied odds for future streets quickly, there are a couple things that you should always remember:

  • Flop Implied Odds: Multiplying your outs by 4 will give you the chance of improving your hand on either the flop or the turn. When you’re relating this equity to the immediate pot odds or implied odds you’re getting, do keep in mind that you’re not necessarily guaranteed to see both cards for the same price. After you call the flop, your opponent might continue betting on the turn, charging you even more for your draw. (Multiply your outs by 2 for the chances of improving on the immediate next card, but by 4 for either the turn or the river to improve your hand.)
  • Being Out of Position: Suppose you face a turn bet while out of position, and don’t have the right pot odds to call with your draw, but you do have the right implied Well, the thing is that being out of position is going to make it harder for you to extract the required value from your opponent. Checking to your opponent is often the easiest/simplest way to go from one betting round to the next, as it allows you to balance your ranges accordingly (mix in both bluffs and value bets). If your plan is to donk bet from out of position when your draw gets in, then it would be essential to turn some hands in your range into bluffs to stay balanced. Additionally, it’s ultimately going to be less easy to have your opponent pay you off when you’re out of position: (1) either you’ll check and risk your opponent checking back; or (2) you’ll bet allow your opponent the opportunity to fold and not pay you off.
2 poker players at table

 

NOTE: On the opposite end of the spectrum, if you’re in position with a draw: (1) either your opponent will check to you, in which case you can bet for value; or (2) your opponent will continue betting into you, wherein you’ve gained an extra bet and can then decide to either call or raise.

  • How Likely Is Your Opponent to Bluff? If your opponent likes to bluff (i.e. on the river with all sorts of weak holdings), this can help your cause in calling with draws based on implied odds, even when out of position. If you hit your draw and check to villain, he’ll have the ability to fire again as a bluff, allowing you to profit more wholly from the implied odds you were getting on the previous street.
  • How Likely Is Your Opponent to Continue Betting When the Obvious Draw Gets There? If your opponent plays very weak-passive when obvious draws come in, it’s going to be tough to get paid the correct amount you need to gain on the next street. As a result, calling with implied odds isn’t always the best idea, as you can’t count on extracting the extra bet from villain. (On a separate note, this would mean you could exploit your opponent by bluffing more frequently with weaker hands when draws come in, as they’re going to be overfolding in such spots.)
  • How Obvious Is Your Draw? If your draw is well-disguised (like a double gutshot straight draw), your opponent will have an easier time value betting a merged range when you get there. (Simply because it’ll be more difficult for your opponent to put you on that hand). Oppositely, if a flush draw ever completes (usually these are the most apparent draws; same with 4-to-a-straight), some opponents will tend to shut down their betting completely, fearing that you could have improved your hand. Therefore, always consider how obvious your draw is when calculating implied odds, in addition to your opponent’s betting tendencies when noticeable draws get there.
  • Are There Any Other Draws That You Could Bluff at on the River to Try and Win the Pot, In Case Your Draw Doesn’t Get There? Let’s say that you have a gutshot straight draw and decide to call the turn, based on implied odds. You don’t hit your specific card on the river, but the river does make a 3-flush now evident on the board. This situation is perfect for betting, as you would with a flush (either by donk betting out of position or betting when checked to in position). This move will balance your range for the times you’re calling the turn in the same situation with a flush. You didn’t improve your hand, but you have a good chance of scaring your opponent off and taking down the pot if you bluff.

An Alternative Option: Raising with your Draws

Sometimes, it can be ideal to raise with your draws, instead of relying solely on expressed odds and implied odds to help you profit when you hit. Raising the flop or turn (usually with your weakest draws, like a low flush draw, or a gut shot to the nuts – something with no current showdown value) can sometimes be a +EV play:

  • Such is the case when your opponent c-bets too frequently and folds when faced with aggression.
  • The same is true when your opponent overfolds when facing raises, specifically check-raises.
  • It is often best to raise with your draws when out of position (as it can be challenging to get that extra bet with implied odds otherwise, when you’re out of position, as previously discussed).
  • You gain fold equity by raising, meaning you could (1) win the pot right now if your opponent folds; or (2) build a bigger pot to win for the times when you do make your draw.

In Conclusion

Your opponent having more money remaining in their stack for future betting rounds can help turn a losing call into a profitable one (when taking this above-described concept of implied odds into account).

Always consider how strong your draw is when continuing (and if raising would be a more profitable play instead). Also, contemplate the likelihood of extracting future value from your opponent if and when your draw does get there.

Good luck in using this concept of implied odds in practice at the felts.

About the Author
By
Matthew Cluff is a poker player who specialises in 6-Max No Limit Hold’em games. He also periodically provides online poker content for various sites.
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