This sounds like a small distinction, and in many ways it is. There are plenty of contexts where you can even get away with using the concepts interchangeably. Poker, however, is not one of them. In fact, the ability to separate the possible from the probable is arguably one of the key skills that separates solid recreational players from professionals.

Let’s take a look at a sample hand that illustrates the concept. This hand is taken from tournament play on Full Tilt Poker. You have about 40BBs and are in the SB. The table folds to you and you complete with Kh6c. The BB checks, leaving us with the following setup as we head to the flop:

From here on out, we’re going to evaluate our opponent’s hand from two perspectives: the possible and the probable. So, let’s start preflop.

Possible: All combinations that don’t involve one of our hole cards (1225).
Probable: All combinations that don’t involve one of our hole cards and aren’t premium hands (AA-JJ, AK), as most opponents will raise the SB limp with strong hands in this spot (1185).

Obviously, that’s a pretty small gap, but as the hand progresses and you get more information to work with, focusing on the probable and not the possible becomes critical. For many players, the possible becomes an enabler of bad behavior, allowing them to construct justifications for terrible plays that a consideration of the probable would never permit. Let’s return to our sample hand to see this in action.

The flop gives you top pair and has some draws:

Ks Th 5s

You bet 650 and the BB calls.

Possible: All combinations that don’t involve one of our hole cards or the flop and aren’t premium hands (1021 combos).
Probable: TT, 55, combinations with two spades, a king, a ten, a five, an open ended straight draw along with AJ, some underpairs and some complete air looking to take it away on a later street (approximately 500 combos)

Nothing earth-shattering there, but we’re starting to see the significant difference that emerges between the probable and the possible as the hand progresses and you get more information, even in a generic situation. That’s the first major flaw in thinking in terms of the possible instead of the probable: Thinking in terms of the possible doesn’t fully utilize new information. Let’s move on to the turn.

The turn is the 3d, for a board of Ks Th 5s 3d.

You bet 1250 and your opponent calls.

Now that we have new information, our possible set is based on our probable set from the previous street, and our probable set is a refinement of our possible set based on that new information. Note that there are some situations where you might want to insert additional hands into the possible set based on new information, but that’s the exception rather than the rule.

Possible: TT, 55, combinations with two spades, a king, a ten, a five, an open ended straight draw along with AJ, some underpairs and some complete air looking to take it away on a later street (approximately 500 combos).
Probable: This second bet should chase out most of the air and the weaker draws, along with most fives, the underpairs and some weaker tens. That leaves us with kings, some tens, some spade draws, QJ and a few weaker fives and draws and the occasional air (approx 325 combos).

While there’s a good amount of fuzziness involved in determining a probable range for our opponent, considering the probable instead of the possible still moves us much closer to our ultimate goal of correctly determining our opponent’s hand. Let’s return to our example.

The river pairs the board with the Tc, for a final board of Ks Th 5s 3d Tc. You check and your opponent bets 2900.

Possible: Some spade draws, QJ, a few weaker fives and missed draws, air, all kings, some tens, TT, 55 (approx 250 combos).
Probable: All kings, some tens, some spade draws, QJ and some weaker fives, missed draws and air, TT, 55 (approx 250 combos).

Those ranges appear, by all accounts, to be the same. To understand how they’re actually very different, let’s pause for a moment and think about how this hand looks to someone only considering the possible. From that point of view, your opponent could be making this bet with a very wide range that includes missed spade draws, missed straight draws, and even some smaller pairs that are now turning their hands into bluffs. That seems to suggest a relatively simple river call.

It’s important to note that there’s nothing about the above assessment that’s untrue. All of those things are possible. However, in poker what’s possible is a bit of a Rorschach test – when you focus on it, you’re likely going to only see what you want to see. In this example, even decent players are going to skew their assessment to favor a distribution that allows them to win the pot. That highlights the second critical flaw in considering the possible: you leave yourself vulnerable to making decisions based on how you’d prefer things to be rather than how things likely are.

The difference in the above ranges is, of course, in their weighting. The possible is arranged in the order of hands you’d like your opponent to have, while the probable is arranged in the order of the hands your opponent is most likely to have from a strict distributive perspective. That’s the final flaw in relying on the possible: You risk ignoring the fact that some combinations of cards are far more or less likely than others. To understand the impact distribution can have, consider the following about our example:

• Two kings remain in the deck, and 44 cards remain for the kings to combine with. That results in 87 combinations. We assumed earlier that your opponent would likely raise preflop with KK and AK, removing 9 combinations for a total of 78. Of those combinations, you beat 16 and tie with 6.
• Two tens remain in the deck, so 87 combinations.
• 11 spades remain in the deck, resulting in 55 possible spade combinations. 10 of those combinations involve a ten, so 45 missed spade draw combinations exist.
• There are 16 ways to make QJ. One of those is QJ of spades, so 15.
• There are three ways to make 55 and one way to make TT.

That leaves us with 145 combinations you’re losing to and 76 you’re beating, along with 6 ties. Even with a healthy allowance for air and missed draws, you’re still losing on this river a lot more often than you’re winning. All of the sudden, the relatively simple river call seems a lot less simple.

The point of this article isn’t really to determine whether or not you should be calling on the river – there are certainly other factors you’d need to consider before making that decision. Rather, the point is to illustrate how different a hand can look to you based solely on the manner in which you evaluate the information you receive during the hand. Considering only the possible results in decision-making bordering on pure guesswork, ignorant of new information and over-reliant on ego and emotion. Considering the probable results in guesswork as well, but an educated version steeped in deductive reasoning and an appreciation of the mathematical realities of distribution.

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Understanding these odds is only a small part of making proper all-in decisions. You’ll also need to develop a good sense for putting your opponents on a range of possible hands and an appreciation for the impact of a broad array of other situational factors. That said, these numbers are still useful for newer players and an interesting reminder of the inescapable fact that you’re just never all that far ahead (or behind) in preflop all in situations.

For equity calculations, we suggest using PokerStove (read our review of Poker Stove here).

Two overs vs two unders
Two overcards will generally be a 65 / 35 favorite over two undercards. That gap closes as the undercards get connected and suited and the overcards become less so.

Sample matchups
K9o vs 76s = 58 / 41
QJs vs 98s = 66 / 34
AKs vs 32o = 67 / 33

An over and an under vs two mid cards
This matchup usually features an over-under running slightly ahead (roughly 57 / 43). The distance closes based on suitedness, connectedness and whether or not the opposing hands share cards needed to make straights.

Sample matchups
A2s vs T9o = 58 / 42
KTo vs QJs = 56 / 44
Q3o vs 87s = 52 / 48

An over and under vs a mid and an under
The over-under will be about a 60 / 40 favorite over the mid-under hand. That gap shrinks as the mid-under hand gets more suited an connected and the over-under becomes less so.

Sample matchups
A7s vs J4o = 66 / 34
K8o vs 97s = 56 / 44
AQo vs KJs = 59 / 41

A pair vs one over and one under
The pair is generally about a 70 / 30 favorite over the over-under. The over-under gets back to just about 2 /1 when it’s suited and connected.

Sample matchups
99 vs K7o = 72 / 28
99 vs T8s = 67 / 33

A pair vs two unders
The pair is about a 80 / 20 favorite over the two unders. Suited connectors that don’t share straight cards with the overpair are the best hand in this group to take up against an overpair.

Sample matchups
KK vs 87s = 77 / 23
KK vs QJs = 82 / 18
KK vs Q3o = 88 / 12

A pair vs an underpair
A larger pair is roughly a 80 / 20 favorite over a smaller pair (slightly more depending on whether or not the pairs share suits)

An over vs an under with one shared card
Generally referred to as a ‘dominated’ matchup. The dominating hand is actually usually only about a 70 / 30 favorite, with suitedness and connectedness having a reasonable impact on the gap. Dominated matches that feature two high-low hands are much closer due to how often they end up splitting the pot..

Sample matchups
KQo vs KJs = 69 / 31
AJs vs A8o = 74 / 26
A5o vs A3o = 56 / 44
ATo vs KTo = 74 / 26
ATo vs JTs = 68 / 32
KTo vs T9s = 67 / 33

First of all, let me suggest a good rule of thumb for implied odds: figure them once and then readjust your initial assessment downward [make it more conservative]. The reasoning behind this tactic is that a lot of players find themselves calculating implied odds when they’re in situations where they might be looking for a reason to call, and therefore skewing the numbers to provide that reason. Check this natural tendency by always handicapping your calculations by a number or two; if you get 10-1 on your first run through, make your working number 8 or 9 to 1.

That said, let’s get to defining implied odds. In basic terms, determining whether or not you’re getting correct implied odds is a function of:

a) Direct pot odds [the ratio of the pot before you call to the amount you have to call]
b) The gap between direct odds and proper odds [the odds you need to call; for example, you're about 7.5-1 to flop a set with a pocket pair]
c) How much money is available for you to win [the size of your opponents stacks]
d) The probability of getting paid off if you make your hand

Here’s a quick example to illustrate how those factors work together. Let’s say you’re playing online poker and holding a flush draw and are heads up with your opponent. Each of you have $100 remaining. Let’s say the pot size on the flop is $8 and your opponent bets $5.

a) Direct pot odds: You are getting about 2.5-1 direct.
b) Odds Gap: You need about 4-1 direct, so you’re missing about 1.5 which in this case is $7.50
c) Potential win: Your opponent has money remaining greater than b)

That leaves us with one issue – d), where we have to figure whether or not your opponent is likely to pay you more than $7.50 on remaining streets if you hit on the turn. There’s no formula for figuring that out, but the looser the opponent and the more disguised your hand is, the more likely you are to get paid.

Obviously there’s often a lot more to it, but that’s the bare bones of figuring implied odds in Texas Holdem Poker. When you get comfortable with the basics, you’ll have to deal with issues like redraws and true outs, but just considering the four factors above should be enough to point you in the right direction.

In Poker, every time it’s your turn to act you have 3 choices : Fold, Call, or Raise. Which is right? In this article, I won’t deal with the Raise option. This article will cover the basics of whether you are going to continue with a hand or not, and the math that should be used in such decisions. I’m not going to cover starting hands and preflop play. I will say this though, you should be playing tight and only playing solid starters. Look around the articles here, look at the message board, and find any beginning poker book and it deals with the preflop decision to fold/call/raise.

What I want to cover is the basics of “Should I Stay Or Should I Go!” from the flop forward. In order to make this decision you need to know 2 things : What are my Pot Odds and what are my Card Odds. If you know those two things you can make a “mathematically” correct decision about staying in the hand or not.

We’ll start with calculating Pot Odds. Pot Odds are very straightforward. Pot Odds is a ratio of the money you’ll get back from the pot compared to the size of the current bet.
Pot Odds = $ In Pot / Current Bet (expressed in ratio)
If there is $100 in the pot and the bet is $10 to you, you are getting Pot Odds of 10:1. Really, that’s all there is to it. If you are a limit player, I recommend that you keep track of this in Bets rather than $. Its easier to keep track of and it makes the switch from 1 level to the next easier. Preflop and flop, keep track of the bets as SmallBets (SB). When you get to the betting on the turn, divide the number of SB by 2 to get the number of BigBets (BB) and keep counting.

Example: You are playing $1/$2 limit and are on the button. 4 limpers to you, you raise, both the Small Blind and Big Blind call as do the 4 original limpers. 7 to the flop * 2SB each = 14SB. On the flop the first limper bets, the other 3 limpers call. You are now getting 18:1 Pot odds to call. But you’ve got a big hand so you raise. Both blinds fold, the bettor raises and all 3 limpers fold. You cap and the bettor calls. There are now 25SB in the pot (14 preflop, 4 from bettor, 4 from you, and 3 from limpers). On the turn the villain bets. What are your pot odds now? Remember, cut your SB in half so,
25SB = 12.5BB + 1BB = 13.5 : 1.

Lets move next to Counting Outs. 2 paragraphs barely scratch the surface of this topic. For a thorough exercise in being able to count outs, see Sklansky/Malmuth/Miller “Small Stakes Hold ‘Em” – Its got an entire chapter on finding “hidden outs.” I’m going to give the basics with a few “be aware of” things, but this certainly won’t make you an expert (keep in mind that I did not promise to do so). My definition of Outs is “Cards that will likely make your hand the winner at showdown.”

If you have 4 to a flush then you have 9 outs to make that flush.
If you have an open-ended-straight-draw (OESD) then there are 8 outs to hit that straight.
If you have a gut-shot straight draw then you have 4 outs to hit the straight.

None of that is news to you, I’m sure. But what about if you have a flush draw and 2 overcards to the board? Say you have AsKs and the flop comes Ts 4h 6s. How many outs do you have now? If an A or K comes on the turn your hand might be good. I usually count the cards that will pair my overcards as about 1/2 out each. This is not exact, but it is close. A lot of times the preflop action or flop action will tell you if this is true or not, but if you use 1/2 for each overcard you won’t be too far off. So, in this hand I have 12 Outs (9 flush cards + (1/2 * 6 A/K left).

What about if I have an OESD and there are 2 cards of the same suit on board? How many outs is that? Again, a lot depends on the read you have of your opponents, how many opponents are left in the hand, and action preflop and on the flop, but I want to give you something to start with that you can refine with more reading and more experience. Lets say that you have JhTd and the flop is Qs Ks 6c. So you have 6 outs to the nuts (three non-spade 9 and 3 non-spade A). But you can’t just eliminate the 9s and As because its not a certainty that someone is on the flush draw. So the As and the 9s can be treated as half-outs as well. Again this isn’t exact but it is a good approximation unless the betting tells you that someone is on a flush draw. So you have about 7 outs (not likely that pairing your J or T is going to be good). Lets say you have pocket Aces (yippie!). There are 2 villains (one is the BB who protected against your raise) in the hand against you. On the flop, the BigBlind comes out betting, villain 2 folds, you raise and BigBlind reraises. You suspect that villain has 2-Pair. How many outs do you have against his 2 pair? You have the two other aces in the deck, and for the turn you have three outs to pair the board (of the card he didn’t pair). So you’ve got 5 outs now, and assuming that he doesn’t hit his full house on the turn, you’ll have 8 outs on the turn. Whether or not to call depends on the pot odds and what we calculate the card odds to be, but just make sure that you count all your outs!

Card Odds : Card Odds is a description of the probability that any of the card(s) that you need to make the best hand will come. It is expressed as a ratio where the first # represents how often it WON’T happen against how often it will happen. It is generally expressed as N : 1.

Card Odds = (#unseen cards – Outs) / Outs (expressed as a ratio). So if you have a flush draw on the flop, you have 9 outs. 47 unseen cards after the flop (52 – 2hole cards – 3 flop cards = 47). Odds that you’ll hit your flush on the next card = (47-9) / 9 = about 4:1. That’s all there is to this as well. It’s not tough, it just requires some practice.
Flop an OESD, what are your card odds to hit the straight on the turn? 8 outs, so COdds = (47-8)/8 = 4.875 (or about 5:1)

There are plenty of charts out there that show card odds for 2 – 25 outs. I’m not going to include one here for the sake of brevity, but now you know how to do the calculation yourself.

Card Odds vs. Pot Odds : Should I continue with this hand? That is the eternal question in Poker. How many times have you thought “I don’t think I’m ahead, but man if I can just catch that (fill in card need here) I can take this pot down!!!” I do it all the time. I hate folding. I prefer action! Most people do. But I like winning money more than I like action, so before I toss more chips into a pot hoping to catch my 2 outer I do the math to determine if I should or not. The most basic way to determine if you should continue in a pot or not is this : Are the odds I’m getting from the pot bigger than the my card odds? If the answer is “yes” then you should continue in the hand. If the answer is “no” then you shouldn’t continue in the hand (there is exception to this that deals with something called “implied odds” that I’ll discuss in a later article). Lets look at an OpenEndedStraightDraw (OESD). Here is the scenario:

You are in the BB with J8o. 4 players limp (including the SB) and you check. (5players, 5SB to the flop). The flop comes (Ts 3c Ah). It gets checked around and the turn comes 9d. So now there are 5 players and 2.5BB in the pot. The SB checks, you check and 1st limper bets. All limpers call (including the SB) and its up to you to act. What do you do? The pot is now offering you 7.5:1 odds (2.5BB + 5BB = 8BB). The odds that you’ll hit your OESD are about 4.75:1. This is a CLEAR call.

Lets change it a bit though to show a fold. Lets say that when Limper 1 bets, everyone folds to the button who raises and the SB folds. What are your pot odds now? 2.5BB + 1 + 2 = 5.5BB in the pot, but its going to cost you 2BB to call, so you are only getting 2.75 : 1 pot odds. The odds of hitting the OESD are still 4.75 : 1, so this is a fold (NOTE : Its possible that Implied Odds could make this a call, but that is for a later article).