Mathematics: Odds & Outs for Advanced Players

Introduction

In this article

• The checklist for evaluating draws
  
• How to correctly discount outs
  
• The value of backdoor draws
  

One of the most important tools of an aspiring poker professional is the concept of odds and outs, as you have already learned in Bronze section. This article is designed to deepen your understanding of the nuances behind various types of draws and will teach you how to precisely apply this concept to your game.

You will learn the role that backdoor draws play and the number of outs you can give yourself. You will learn to discount outs and properly evaluate and play various draws, such as gutshot draws, two pair draws, top pair draws, and combinations of these draws.

This article will give you a more comprehensive understanding of odds and outs and teach you to accurately determine the number of outs you can depend on. This will ultimately help you in virtually any game situation and lead to more profitable decisions at the table.

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Overview to odds and outs for advanced players

Playing according to odds and outs

Let's look at the chart from the Bronze section before we get started. There are a few changes that need to be made.

You can see the odds and outs of various undiscounted draws. An exception worth noting is the gutshot draw. You can call with 7:1 instead of 11:1 odds in some situations, which we will discuss later in this article.

We will start by clarifying what this article is all about: How do you best play according to odds and outs? Look at the following example:

Pre-flop: Hero is CO with 9, 8
UTG+2 calls, MP2 calls, 1fold, Hero calls, 2 folds, BB checks

Flop: (4,5 SB) Q, J, 4 (4 players)
BB checks, UTG+2 checks, MP2 bets, Hero ???

You decided to enter the hand with a suited connector after two limpers and flopped a gutshot draw. First, you need to ask how many outs you have. A gutshot, as you learned in the Bronze articles, has 4 immediate outs.

Now you need to decide whether or not calling is profitable. To do this you must calculate the pot size, which is currently 5.5 SBs after MP2 bet the flop.

Then you ask yourself how much it is going to cost to see the next street. You probably won't run into a check/raise, since no one raised before the flop. You can therefore expect to see the turn card for 1 Small Bet.

Finally, you compare the pot odds with the odds and decide whether calling or folding is the better choice. The odds and outs chart shows you need 11:1 odds to call; you are only getting 5.5:1 and fold.

The example shows you how helpful it can be to have a kind of checklist handy when playing according to odds and outs. The following points are decisive:

• How many discounted outs do you have?
• How big is the pot?
• How much will it cost to stay in the hand?
• Compare the odds and pot odds -> call or fold

You determine your chances of winning the hand and compare them to the amount you can expect to win vs. the amount you must pay to stay in the hand. You can then determine whether or not calling is profitable.

Counting your outs isn't always as easy as in this example, however. You will now learn what discount outs means and how to do so.

The last example showed you that determining the actual cost of staying in the hand requires some strategic thinking. The relative position of the players at the table plays an essential role. Let's make a small change to our example:

Pre-flop: Hero is BB with T, 8
UTG+2 calls, MP2 calls, 3 folds, SB calls, Hero checks

Flop: (4 SB) A, J, 7 (4 players)
SB bets, Hero ???

You hit the same gutshot draw and the player in front of you bets. The major difference: You are now in a different position. There are also two opponents behind you. It's very possible that the costs of staying in the hand will go up. You can expect to pay app. 1.5 SBs for the turn card on average.

How do you play backdoor draws?

The next two sections will teach you what to pay attention to with different drawing hands, when and why to discount, and how to calculate the pot odds needed to call. We will start with backdoor draws.

Having a backdoor draw means you need to hit outs on the turn and on the river to complete. You can either have a backdoor flush draw, BDFD, or a backdoor straight draw, BDSD.

This means you are only using one of your hole cards to as part of your draw. For example, if you have A K on a 4 J T flop, you need a on both the turn and the river to make a flush.

The following chart shows you how many outs you can give yourself with a 1 card backdoor flush draw.

Outs for a 1 card backdoor flush draw 1 Card BDFD 3 or more opponents Less than 3 opponents A 2 2 K 1.5 1.5 Q 0.25 1 9+ 0 0.75 <9 0 0.5

The column on the left corresponds to the strength of your hole card, the two on the right to the number of outs you can give yourself based on the number of opponents active in the hand.

Pre-flop: Hero is BU with K, 7
Hero raises, SB calls, BB calls.

Flop: (6 SB) 4, Q, 8 (3 players)
SB checks, BB checks, Hero bets, SB raises, BB folds, Hero ?

You raised from the button with K7o and both blinds called. The blinds check to you and you make a continuation bet in position. Then the Small Blind check/raises. Call or fold?

• How many discounted outs do you have?
  You hold an overcard and a K high BDFD. Since you only have one opponent, you use the column titled "Less than 3 opponents" and look at the corresponding "K" row in the left column; you have 1.5 outs. The K also gives you three good outs, which we will discover in the section on one pair draws. You also have a 1 card BDSD with your 7, which gives you an additional 0.25 outs (which will be outlined in the next section). You have a total of 4.75 outs.

• How big is the pot?
  9 SB.

• How much will it cost to call?
  Since the BB has already folded, you are heads up. You must pay exactly 1 SB to play.

• Compare the odds and pot odds -> call or fold?
  You have 4.75 outs, meaning you need 9:1 pot odds to call. There are 9 SBs in the pot, so you call.

Not counting your backdoor draw outs, you have 3 outs for your overcard, meaning you need 15:1 odds to call. The 9 SBs in the pot wouldn't be enough and you would have to fold.

We can take things even further. You can expect the Small Blind to bet on the turn; he has shown a lot of strength so far. Since this is very likely, you can add this bet into your calculations. These "new" pot odds are referred to as implied pot odds.

You can see that backdoor draws are not worth much alone, but they do add value to a hand and can make the difference in close call-or-fold decisions.

The main difference between 1 and 2 card backdoor flush draws? The value of a 2 card BDFD does not depend so heavily on the strength of your high card, meaning you can give yourself 2 full outs for a 2 card BDFD.

Pre-flop: Hero is MP3 with J, 9
Hero raises, 3 folds, BB 3-bets, Hero calls.

Flop: (6,5 SB) 4, A, 6 (2 players)
BB bets, Hero ???

You raise from MP3 with J9s and the Big Blind 3-bets. You call, only to miss the flop completely. You can only continue to play according to odds and outs. Time to look at the checklist.

• How many discounted outs do you have?
  Since the opponent is an unknown, you assume his 3-Bet comes right from the BB "Defense Chart". You can't give yourself outs for your jack or nine, since your opponent is likely to have hit the ace or have a higher pocket pair. The J high BDFD is all you have - a total of 2 outs.

• How big is the pot?
  7.5 SBs.

• How much will it cost?
  You are heads up and must pay exactly 1 SB to stay in the hand.

• Compare the odds and pot odds ->call or fold?
  You need 22:1 pot odds to call with 2 outs. You are only getting 7.5:1 and fold.

The chart shows you the difference. A 2 card BDFD always gives you 2 outs, whereas you can rarely give yourself 2 full outs with a 1 card BDFD. But there are a few other advantages, as well.

First, a 2 card flush is naturally better hidden (4-suited vs. 3-suited board), which means you can expect to get paid off more often, meaning you have higher implied odds.

If there are 4 cards of the same suit on the board, your opponent only needs to hold one card of that suit to have a flush. This is half as many cards as he would need on a board with 3 flush cards. You are therefore, as shown in the table, beat much more often when holding a 1 card flush.

Backdoor straight draws require a closer look. Aside from 1 and 2 card BDSDs, there are three other kinds of BDSDs. Let's look at an example.

You hold J 9.

• Flop: T 3 2 -You have a 0-gap BDSD. The three cards that represent the draw are connected without gaps.
• Flop: 8 3 2 - You have a 1-gap BDSD. The 3 cards have a gap.
• Flop: 7 3 2 - You have a 2-gap BDSD. The 3 cards have two gaps.

The difference between these types is mainly the fact that 0-gap BDSDs have better chances of turning into an OESD on the turn, whereas the 1-gap and 2-gap BDSDs require specific outs to complete.

The following chart gives you the number of outs you have with various BDSDs. It is important to differentiate between rainbow and suited flops, since a flush would have you beat.

Outs for BDSDs BDSD Rainbow Board 2-suited Board 0-gap BDSD 1.5 1 1-gap BDSD 0.75 0.5 2-gap BDSD 0.25 0

You can clearly see that BDSDs (and BDFDs) are only valuable as "back-up." You would need 22.5:1 pot odds to call with 2 outs on the flop, meaning you will almost never be able to call with a BDSD alone. These draws can, however, make the difference in close call-or-fold decisions with other draws.

How do you play strong draws according to odds and outs?

Flush draws, like backdoor draws, can be placed in one of two categories: 1 and 2 card flush draws. You don't really need to discount your outs with a 2 card flush draw. Discounting may be theoretically necessary, but you will almost always have the right pot odds to call (at least to the river) with a 2 card flush draw.

1 card flush draws are another story, as it is more likely that another player also has a card of that suit.

Pre-flop: Hero is BB with 4, 4
BU raises, SB calls, Hero calls.

Flop: (6 SB) J, A, 6 (3 players)
SB bets, Hero ???

Your flush draw with 9 undiscounted outs isn't worth much in this example. You have the third lowest heart and two other players have shown strength. After heavy discounting you can count on 3.5 outs.

As you can see, 1 card flush draws depend very heavily on the strength of your hole card. The following chart will show you how to discount your outs with 1 card flush draws.

Outs for a 1 card flush draw 1 card flush draw Less than 3 opponents 3 opponents More than 3 opponents A 9 K 8 7 4.5 Q 7 6 4 J 4.5 0 8+ 4 0 <8 3.5 0

You see your hole card on the left and the corresponding number of outs you can count on to the right, based on the number of opponents involved in the hand. Keep in mind, if you have the K and the A is on the board, your K is as good as an A (in the chart), since you are drawing for the nut flush.

2 card OESDs don't need to be discounted, either. The only thing you are worried about is possible flush.

Pre-flop: Hero is MP3 with J, 9
MP2 calls, Hero raises, 3 folds, BB calls, MP2 calls.

Flop: (6.5 SB) T Q, 2 (3 players)
BB bets, MP2 calls, Hero raises, BB calls, MP2 calls.

Turn: (9.25 BB) 4
BB bets, MP2 calls, Hero ???

You hit an OESD on the flop and raise the BB's donk bet in order to possibly get a free card. The BB seems to know what you're up to and donks again on the turn. Raising again won't help much. You have to continue playing according to odds and outs.

• How many discounted outs do you have?
  Neither of your hole cards can be considered outs as the Queen represents an overcard. The BB very likely has you beat. You do, however, have 8 undiscounted outs with your OESD. A quick look at the board shows a possible flush draw. With 2 opponents in the hand it is rather likely that one of them has it.

  Looking back at the hand so far, you see that MP2 has been passive the whole time, first limping, then calling a raise, and smooth-calling the rest of the way. Aside from bad made hands and other draws, a flush draw is a definite possibility. The BB is less likely to have a flush draw, but his donk bets could also be explained by a hand like middle pair + flush draw. In other words, even though the 8 or K would complete your draw, you cannot be certain that hitting these outs will give you the best hand. These are so-called tainted outs and need to be discounted. You discount 0.5 outs per opponent, leaving you with 7 discounted outs in this example.

• How big is the pot?
  9.25 BBs.

• How much will it cost?
  Since you are last to act, so there won't be any raises behind you. Staying in the hand costs 1 BB.

• Compare the odds and pot odds -> call or fold?
  You need 6:1 odds to call with 7 outs, which means you can easily call with the 9:1 odds you are getting.

When the board is 2 suited and you have ...

• two opponents: you discount your tainted outs by 50%.
• more than two opponents: you discount your tainted outs by 100%.

How do you play weak/medium draws?

Gutshots are interesting in certain respects. For one, they rarely hit - you only have 4 outs. On the other hand, your hand is very well disguised, which means you have good implied odds.

This section will take a different approach to draws. You will learn how to give yourself implied odds depending on the situation at hand. If you aren't familiar with implied odds, you can learn more by clicking here.

Pre-flop: Hero is BU with 7, 6
Hero raises, SB folds, BB calls.

Flop: (4.5 SB) 8, Q, 4, (2 players)
BB checks, Hero bets, BB raises, Hero ?

You can only continue playing according to odds and outs after the BB's check/raise.

• How many discounted outs do you have?
  You can be sure that your 4 gutshot outs are clean. You also have a 0-gap BDSD with the 8. This gives you an additional 1.5 outs. You can give yourself 1 full out for the BDSD, since a 5 would complete your gutshot. You can't give yourself outs on your hole cards, since the BB is sure to have a strong hand when he isn't bluffing; he has a polarized range. All in all, you have 5 outs.

• How big is the pot?
  7.5 SBs.

• How much will it cost?
  You are last to act and have to pay exactly 1 SB.

• Compare the odds and pot odds -> call or fold?
  You have 5 outs, which means you need 8.5:1 pot odds to call. You theoretically have to fold, since you are only getting 7.5:1. This is where the implied odds come into play. The Big Blind's check/raise suggests that he will be leading out on the turn regardless of what comes. You can therefore add 2 more SBs to the total pot size when calculating the pot odds. Your opponent is very likely to have a made hand, but he will rarely be able to beat a straight. You can expect to win an additional 2 BBs (4 SBs) on average when you do complete your gutshot. Your implied odds to call on the flop are therefore 11.5:1, which are more than enough to stay in the hand with 5 outs.

Flop: Hero calls.

Turn: (4.25 BB) J
BB bets, Hero ???

Your draw does not hit on the turn. Again, you must make a decision.

• How many discounted outs do you have?
  You still have 4 outs, but now you have different odds on the turn. The ratio of helpful cards to non-helpful cards has changed. There are now 46 unknown cards and 42 non-helpful cards, which gives you 10.5:1 odds.

• How big is the pot?
  5.25 BBs.

• How much will it cost?
  Again, you are last to act and would have to pay 1 BB.

• Compare the odds and pot odds -> call or fold?
  The odds have improved slightly to 10.5:1. The pot odds, however, have deteriorated. You are only getting 5.25:1. You can't assume that he will bet again on the river. If he has been bluffing, he will probably give it up. He could also check/call with a weak made hand, in which case you would only win 1 additional BB. All in all, you can expect to win 1 additional BB and can give yourself app. 6:1 implied odds, which still aren't enough. You fold.

The following chart shows the implied odds you get with various gutshot draws. You will see different columns for Rainbow or 2-Suited boards and the respective required pot odds to make a call.

Pot Odds needed for a Gut-Shot Gutshot Board Pot Odds on Flop Pot Odds on Turn 2-Card Gutshot Rainbow Board 7:1 10:1   2-suited Board 9:1 10.5:1 1-Card Gutshot Rainbow Board 10:1 10.5:1   2-suited Board 14:1 14:1

Pre-flop: Hero is BU with J, T
MP2 calls, MP3 raises, Hero calls, 2 folds, MP2 calls.

Flop: (7.5 SB) 5 , Q, A (3 players)
MP2 bets, MP3 calls, Hero ?

You cold call after a limp and a raise before the flop and hit a gutshot draw. MP2 donks after limping pre-flop and the PFA calls. You will rarely be ahead in such a situation; MP2's donk bet into the PFA will rarely be a bluff. He will often have a strong draw (flush) or a strong made hand (Q or A). And even if he only has a 5, he still has you beat.

Once again, we consult our checklist to determine the value of moving forward with the hand.

• How many discounted outs do you have?
  Your hole cards are not worth much with two overcards on board. The clubs indicate potential flush draws and the action supports this possibility. Your 2-card gutshot gives you 4 outs, but you need to discount (due to the possible flush draw). All in all, you can give yourself 3.5 outs.

• How big is the pot?
  9.5 SBs.

• How much will it cost?
  You are on the button and are last to act, so you must pay 1 SB.

• Compare the odds to the pot odds -> call or fold?
  You have a 2-Card gutshot on a 2-suited board. You determined that you have 3.5 outs, so you are looking for 12.5:1 pot odds. Once again, you can give yourself implied odds. The table shows you can give yourself 9:1 implied odds, meaning you can call with 9.5:1 pot odds.

Always keep your implied odds in mind with gutshot draws. They are what give these otherwise weak draws potential.

Discounting outs and calculating implied odds with two pair draws depends entirely on the situation at hand. The key is determining which of your outs complete better hands.

Pre-flop: Hero is BB with 7, 5
MP3 raises, CO folds, BU calls, SB calls, Hero calls.

Flop: (8 SB) Q, T, 5 (4 players)
SB checks, Hero checks, MP3 bets, BU calls, SB folds, Hero ?

In this hand, you hit bottom pair on the flop. You certainly are not ahead with so many opponents in the hand and can only continue playing according to odds and outs. You have 5 discounted outs, which correspond to 8:1 odds.

The 7 in your hand really doesn't have any straight draw potential, nor do your diamonds have any chance at a backdoor flush. Calling is easy with 10:1 odds in this case. Let's look at the next example.

Pre-flop: Hero is BB with J, 5
MP3 raises, CO folds, BU calls, SB calls, Hero calls.

Flop: (8 SB) Q, T, 5 (4 players)
SB checks, Hero checks, MP3 bets, BU calls, SB folds, Hero ?

You hit bottom pair with J5s. This time, however, you will have to discount your outs differently:

• How many discounted outs do you have?
  Your outs on the 5 are pretty clean, since the 5 of clubs is on the board. Your J, on the other hand, isn't so clean. You have to discount the J. Against two opponents you should discount him by half. A J on the turn would also allow redraws for a straight and complete 2 gutshots (AK and 89). You should therefore also discount your remaining J outs by 50%. Your J does give you a 0-gap BDSD. A look at the chart shows you that this is worth 1 more out. All in all, a total of 4.5 outs.

• How big is the Pot?
  10 SBs.

• How much does it cost?
  You're last to act, so it costs 1 SB.

• Compare the odds to the pot odds -> call or fold?
  You have 4.5 outs, which corresponds to 10:1. You are getting 10:1 pot odds so you call.

Discount your outs by 50% when you are facing at least than two opponents and your outs could complete other draws or allow redraws.

The last two hands show why. The 7 was actually a better kicker than the J, because it didn't allow any redraws or complete any draws. You have reverse implied odds with the J, since you can't count on all your outs (the extent of which depends on the number of opponents in the hand).

We will not go into great detail here, since there is a complete article devoted to this topic in the Silver section. We will look at examples to get used to using the checklist instead:

Pre-flop: Hero is Button with J, T
UTG+1 calls, 3 folds, MP2 calls, MP3 calls, 1 fold, Hero calls, SB folds, BB checks

Flop: (5.5 SB) 3, 5, 9 (5 players)
BB checks, UTG+1 bets, MP2 folds, MP3 calls, Hero???

You obviously can't see yourself ahead. UTG+1 bets into the field and will usually have hit the board or at least have a strong draw. Time to go through the checklist.

• How many discounted outs do you have?
  You discount your overcard outs by 50%, since you aren't sure how many of them are clean. Aside from your overcards, you have a BDSD. The chart shows you can give yourself 1 out with a 0-gapper on a 2-suited board, giving you a total of 4 outs.

• How big is the pot?
  7 SBs.

• How much will it cost?
  In most cases you will have to pay 1 SB.  The only player left to act behind you is the BB who has not been very active so far. Given the previous preflop action he will most likely have directly bet any playable hand.

• Compare the odds to the pot odds -> call or fold?
  You have 4 outs, which correspond to 11:1 odds. You are only getting 7:1, so you fold.

Important: Do not confuse this with the gutshot draw, in which case you had 7:1 implied odds. This applies specifically to gutshots, which almost always give you the nuts. A top pair draw isn't so strong. Opponents can easily catch up by the river.

So, although you have 1-2 BB implied odds on the one hand, you have 1-2 reverse implied odds on the other (negative IOs). This means you will pay your opponent off every time you hit and he catches up. You would have top pair and he could be bluffing, so you will be showdown bound. The IOs and RIOs negate each other.

Examples

You've now seen how to evaluate different draws on various boards and how to discount your outs as precisely as possible. We will now look at a few examples to help you get a feel for putting this theory to practice. We will also take a look at various combodraws.

In this example, we take another look at the situation from the section on 1-Card flush draws.

Pre-flop: Hero is BB with 4, 4
BU raises, SB calls, Hero calls.

Flop: (6 SB) K, A, 5 (3 players)

You called with pocket fours in the BB after the BU tried to steal and the SB cold called. You have a flush draw and an underpair on the flop.

• How many discounted outs do you have?
  A flush draw usually gives you 9 outs, but it isn't worth much with 4 high. You have 3.5 outs after discounting.

  You also have two outs for a set. You need to discount these outs since a player could already be holding a flush. Discount them by half to 1 out. You also have a 2-gap BDSD. Look at the column "Rainbow Board", since the suit helps you. You see you have an additional 0.25 outs.

  Altogether, you have 3.5 + 1 + 0.25 = 4.75, about 4.5 Outs. In this case you should tend to round down, since this hand doesn't have much potential anymore and you'll find yourself in rather awkward situations (just imagine your flush draw arrives).

Flop: (6 SB) K, A, 5 (3 players)
SB checks, Hero checks, BU bets, SB calls, Hero ?

• How big is the Pot?
  8 SBs.

• How much does it cost?
  You are last to act and have to pay 1 SB to see the turn.

• Compare the odds to the pot odds -> call or fold?
  You have 4.5 outs, which correspond to 9.5:1 odds. You are getting 8:1 and thus fold.

Flop: (6 SB) K, A, 5 (3 players)
SB bets, Hero ???

• How big is the pot?
  7 SBs.

• How much will it cost?
  This is an interesting question. The PFA is still behind you and could make it more expensive. The SB has also shown interest in the hand. What would happen if he 3-bets a raise from the BU? You are sandwiched. You can expect further action from either/both opponent(s). Staying in the hand will cost more than calling the SB's donk bet. You will have to pay 1.3-1.5 SBs on average.

  This changes the pot size accordingly. You get (6+1.5*2)=9:1.5, or 6:1 pot odds when staying in the hand costs 1.5 SBs.

• Compare the odds to the pot odds -> call or fold?
  You have 4.5 outs, which correspond to 9.5:1 odds. You fold, since you are expecting to get 6:1 pot odds.

Pre-flop: Hero is BB with J, 9
CO raises, BU calls, SB calls, Hero calls

Flop: (8 SB) 2, T, Q (4 players)
SB checks, Hero checks, CO bets, BU folds, SB raises, Hero ?

You call in the Big Blind with J9o, as do the BU and SB, after a steal raise from the CO. On the flop, you hit an OESD and 1-card flush draw.

You might consider raising for value with such a draw, but this is not the best move, since you can't be sure that any of your outs will give you the best hand. You might get the CO to fold, but the SB has shown a lot of strength with his check/raise. You should continue playing passively according to odds and outs.

• How many discounted outs do you have?
  You can't give yourself any outs on your hole cards with this much action. Your 1-card flush draw is Q high flush draw, since your J is as good as a Q with a Q on the board. The chart shows this gives you 7 outs when facing 2 opponents (the BU folded). You can't give yourself the full 6 outs on your OESD (the two were already counted towards the flush draw). The flop is 1-suited, but another card of that suit would give you a flush. You have a total of 10 outs.

• How big is the pot?
  11 SBs.

• How much will it cost?
  You can expect to see the turn card for 2 SB despite the heavy action on the flop. The CO is just making a contibet. He has position on most players and the board is pretty scary. Still, he will often have a weak hand. The SB is also showing a lot of strength by check/raising out of position. The CO knows this, as well, and will need a very strong hand to 3-bet, especially after he sees you call. Since, however, the CO will certainly not just call 100% of the time, you will have to pay a little over 2 BBs on average. You should estimate your costs at app. 2.2 SBs.

• Compare the odds to the pot odds -> call or fold?
  You have 10 outs, which correspond to 5:1 odds. You are getting 11:2.2 = 5:1 pot odds and can call.

Pre-flop: Hero is MP2 with 7, 7
Hero raises, MP3 calls, 3 folds, BB calls.

Flop: (6,50 SB) 3, 5, J (3 players)
BB checks, Hero bets, MP3 raises, BB calls, Hero ?

You bet your pocket pair after seeing one overcard on the flop. The player in MP3 raises in position and the BB cold calls. You have to see yourself behind against at least one of your opponents, especially after a cold call. You can only continue playing according to odds and outs.

• How many discounted outs do you have?
  You have 2 outs for a set. The board is drawless aside from an OESD with 64. Discounting is not necessary here. You also have a 2-gap BDSD. A 6 and a 4 would give you a straight. According to our chart, this gives you 0.25 outs, giving you a total of 2.25 outs.

• How big is the pot? 
  11.5 SBs.

• How much will it cost?
  You are last to act and would have to pay exactly 1 small bet.

• Compare the odds to the pot odds -> call or fold? 
  You learned how to calculate odds in the Bronze section. You have 2.25 outs, so you have odds of (47:2.25) ~ 20:1. The pot size is 11.5 SBs. You can give yourself implied odds on the set, since the board is basically drawless. You can expect to win an additional 2 BBs when you hit a set on average; a showdown will be likely given the action so far. You have 15.5:1 SB implied odds, which is not enough for a call. You fold.

The main reason you switch to odds and outs mode here: The BB's cold call. You simply have to see yourself behind.

Pre-flop: Hero is MP2 with K, J
Hero raises, 4 folds, BB calls.

Flop: (4.5 SB) 3, Q, 7 (2 players)
BB checks, Hero bets, BB raises, Hero ?

You made a standard continuation bet on the flop and the BB raised. There is little sense in 3-betting with K high; time to look at the checklist:

• How many discounted outs do you have?
  You hold an overcard, a king. You should discount this card to half giving you 1.5 outs. If you hit the king, you’ll usually win, but could still be dominated in some situations. Hands like KQ and QJ lie in this range, Q7 or Q3 are, however, rather unlikely. Similarly, monsters like 77 and 33 are possible. But because the board is so dry, draws become unlikely. Either your opponent is bluffing, or he’s holding a made hand. With that, a queen becomes probable, but in a few, very few situations, you can also win with a jack. That’s why you shouldn’t completely discount the jack, you can give yourself 1 out.

  Over and above this, you still have 2 backdoor draws: A king-high-BDFD, from which you can give yourself 2 outs, and one 1-gap-BDSD, with which you can give yourself 1 out on a rainbow board. With the 2.5 outs on your hole cards, you come out with a total 5.5 outs.

• How big is the pot?
  7.5 SBs.

• How much will it cost?
  You are heads up and have to pay exactly 1 SB.

• Compare the odds to the pot odds -> call or fold?
  You have 5.5 outs, which correspond to 7.5:1 odds. You are getting 7.5:1 and thus have a marginal call.

Pre-flop: Hero is BU with A, 9
MP3 raises, 1 fold, Hero 3-bets, 2 folds, MP3 caps, Hero calls.

Flop: (9 SB) 3, 5, 7 (2 players)
MP3 bets, Hero ???

• How many discounted outs do you have?
  At first glance, this board looks pretty good; you have 2 overcards, two 2-Gap BDSDs and a backdoor nut flush draw. However, you need to discount your overcards heavily. Your A is dominated by AT-AK, your 9 could be dominated by TT+. You have to discount your 6 overcard outs by 50%. You can give yourself 0.25 outs on the BDSD with the 9, even though the board is two suited, since you are only facing one opponent. You will also end up splitting with another A rather often. You can give yourself 2 full outs on your BDFD. All in all, you have 5.5 outs.

• How big is the pot?
  9.5 SBs.

• How much will it cost?
  You are heads up and have to pay exactly 1 SB.

• Compare the odds to the pot odds -> call or fold?
  You have 5.5 outs, which correspond to 7.5:1 odds. You are getting 9.5:1 and can call.

Pre-flop: Hero is MP3 with T, 9
Hero raises, 2 folds, SB calls, BB calls.

Flop: (6 SB) 3, Q, K (3 players)
SB checks, BB checks, Hero bets, SB raises, BB 3-bets, Hero ?

You raise with suited connectors from MP3 and both blinds call. You hit a gutshot on the flop and make a contibet. Unfortunately, both blinds decide to start some action. Capping for a free card won't work often, you can only continue to play according to odds and outs.

• How many discounted outs do you have?
  Your gutshot on a rainbow flop gives you 4 outs. You have to discount your hole cards completely.

• How big is the pot?
  12 SBs.

• How much will it cost?
  You must pay 2 SB to call.

• Compare the odds to the pot odds -> call or fold?
  The pot odds are at 13:2, or 6.5:1, in the case of the SB calling (which is quite likely given the pot size and the previous action). If it gets capped on the flop you would be getting 15:3 pot odds, so 5:1. Your pot odds will therefore deteriorate with further action. You have a clean gutshot, which gives you 7:1 implied odds. You are only getting 6.5:1 pot odds at best however, which is why you have to fold your hand.

Conclusion

This article should have given you a deeper understanding of odds and outs. You learned to discount outs and evaluate backdoor draws. You also have a checklist you can use on the flop or turn in situations, in which you can only continue playing according to odds and outs.

You now have an important tool that will give you an edge against the other players at the table.

Test yourself with a quiz:

Test Your Knowledge With The Quiz: Odds and Outs for Advanced Players

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