The Odds of Making a Pair Hand in Poker

The Need for Understanding Poker Percentages

The greater understanding you gain of poker mathematics, the more naturally inclined you’ll be to make +EV decisions. This ability will win you money over the long run.

You’ll understand better when you may be ahead or behind. So, you’ll know when to take more of an aggressive or defensive approach to playing your hands.

As such, it’s essential to become accustomed to how different hands match up to each other, both preflop and postflop.

In Conclusion

By understanding the concept of poker equity and getting loads of practice, your off-table study will allow you to thrive when at the table. Complex mathematical calculations and fundamental winning concepts regarding equity calculations will become second nature, thus intuitively allowing you to have a better idea of how to proceed in a hand through any number of different scenarios.

Be sure to study the above charts until the information contained becomes ingrained, and you’ll have a firm grasp on hand vs range equity calculations.

Do you sometimes struggle with odds calculations in poker?

In this guide, we’ll assume that readers already know how to perform basic odds calculations but are looking for ways to speed up and simplify the process.

The faster we can figure out our odds, the more time we can spend on what matters - making the best decision. Sometimes players are so overwhelmed with the maths that they forget to think strategically about the situation they find themselves in.

Any Hand Can Win!

Firstly, it’s essential to realise that, before the flop in Texas Hold’em poker, no hand has completely dead equity.

In other words, say your opponent has Pocket Aces. Any two cards you’re dealt still has a chance of improving enough to crack those bullets!

Does this mean that you should play every hand before the flop? No, absolutely not! Many players frequently expand their preflop starting hand range to include too many hands. This “preflop looseness” is often the most pertinent single determining factor in why these players lose most of their money at the table:

Loose players will often get involved in the following situations –

• Where they’re dominated
• Or have kicker problems
• Or have the lower end of a flush or straight when their opponent holds a better one

So, (yes!) any hand CAN win preflop.

But don’t always try to beat the odds and test your luck this way. You’ll find yourself in a world of hurt all too frequently if you do.

Preflop Poker Odds: Any Hand Can Win!

Preflop Probabilities in Poker

Texas Hold’em starts with players receiving two cards each. To understand the odds of being dealt a particular hand, we’d begin by multiplying 52 unknown cards (1st card dealt) by 51 unknown cards (2nd card dealt).

Then we’d take the product of 2,652 and divide it by 2 to see that there are 1,326 different hole card combinations in poker.

NOTE: This last step of dividing by 2 is because the order of the two cards is irrelevant: 8♥7♥  is still the same hand as 7♥8♥.

Next up, say you wanted to find out the per cent chance of a specific hand. You must determine the number of combinations there are of that hand. Then divide the result by 1,326.

Let’s take a brief look into the poker combinatorics of receiving specific hands in poker:

• A paired hand will have SIX total combinations
• A non-paired hand will have SIXTEEN total combinations
  • Off-suit non-paired hands will have TWELVE combinations
  • Suited non-paired hands will have FOUR combinations

For example, there are six combinations of Pocket Aces. We would take 6 divided by 1,326 (total hand combinations possible) to determine getting Aces every 1 in 221 hands, or about 0.5% of the time.

Does a full house beat a straight?

Yes – a full house beats a poker straight. The only hands which can beat a full house are four of a kind, straight flush or royal flush. When two people have a full house, the highest three of a kind wins. If that rank happens to be the same, the one with the highest matching pair wins the hand.

5. Flush

Preflop Poker Equities: Having the Right Odds

When you’re in the big blind, you’ll need to call a raise with a significantly greater number of hands. This frequency will be larger than you would if you were (let’s say) on the button and facing a raise.

The reason for this is that you already have 1bb invested in the pot. So, you have better odds to call and see a flop.

That said, two additional factors you should consider are the following:

1. You’ll be out of position each postflop betting round.
2. How strong your opponents are with their post-flop play?

If you’re in the big blind, a player on the button raises to 2.5x, and the small blind folds. You would need to call 1.5bb to win 4bb currently in the pot:

• 2.5bb open raise + 0.5bb small blind + 1 big blind you already put in the pot

So, you’d need to have 1.5/(4 + 1.5) = 27% equity against the button’s range of hands to call.

But you’re out of position. So, you might need anywhere from 5% to 7% additional equity to account for this. (So, hands that have 32% or more equity against the button RFI range.)

If you’re starting out, note that it’s better to overfold from the big blind than to play too many hands from this position.

Beginning players will make too many post-flop mistakes, which will, in turn, make their winrate suffer dramatically.

How Does 888 Payout?

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Implied Odds Analysis of a Pair

The implied odds of one pair type hands cannot be relied on in Hold’em. As a general rule, one-pair type hands are typically medium strength at best. While a top pair is frequently the best hand, it can’t play for large amounts of chips. By the time our opponent wants to invest most of his stack, he’ll have our top pair dominated.

For this reason, one-pair hands are susceptible to suffering from reverse implied odds rather than benefiting from implied odds.

WHAT USE ARE POT-ODDS THEN?

This is not to say that preflop pot odds should be ignored entirely when making non-all-in decisions. As discussed above, some analysts attempt to mix pot odds with equity-realisation in the hope of generating more reliable estimates regarding good preflop ranges.

Although highly speculative, such estimates might allow us to at least perceive whether specific scenarios are close, and perhaps even generate ideas regarding how to adjust our preflop ranges against different opening sizes.

Let’s see an example of how this works before we proceed to discuss potentially more reliable methodology.Consider the following two scenarios with 100bb effective stacks:Scenario 1BTN open raises to 2bb. SB folds. Hero is in the BB. In terms of pot-odds, he needs 22% equity to make the call.Scenario 2BTN open raises to 3bb. SB folds. Hero is in the BB. In terms of pot-odds, he needs roughly 31% equity to make the call.Now firstly note that in Scenario 1, every possible big blind holding has at least 22% equity against a standard BTN raise-first-in range (48% of holdings, or so). If we were to follow pot-odds blindly, this means that we should never fold BB against a BTN min-raise.

Hopefully, we understand intuitively without the use of maths, that’s it’s probably not a good idea to defend garbage holdings such as 32o when OOP. The raw pot odds calculation does at least help us to see that we should likely be defending an extremely wide range of holdings, however.How would an analyst improve the quality of the decision using equity-realisation estimates? In some cases, they might start with a blanket assumption such as “we only expect to realise 65% of our equity while OOP”. They might then use this to make calculations regarding how much equity a holding would need to compensate for its reduced equity-realisation. In scenario 1 we’d need (22/0.65) roughly 34% equity, while in scenario 2 we’d need (31/0.65) roughly 48% equity.If such were the case we’d defend about 84% of holdings in scenario 1 and a mere 25% of holdings in scenario 2. (Based on which holdings have the required equity when facing a 48% BTN raise-first-in range). Of course, that is not to say that these values are anywhere near accurate, but it does demonstrate that we should be using significantly different defending strategies as a result of even a small change in open-raise sizing. This was an example of an elementary calculation to illustrate the concept. Analysts might look to increase the level of accuracy by assigning every specific preflop combination its own equity-realisation factor. (Some hands realise their equity better than others.) Regardless of the complexity, however, there are reasons why such equity realisation techniques can never give us precise preflop ranges.

The reasons are as follows - 1. These techniques assume that expectation of a preflop defend is determined by a hand’s equity which is demonstrably not the case.

2. These techniques ignore (or at least heavily simplify) the postflop game tree - overlooking essential concepts such as implied-odds (as discussed above).Even so, to this day, preflop pot odds are often used by poker analysts as a way of making broad generalisations regarding preflop play.

K

Kicker – Cards that don’t directly formulate a hand but still contribute to the overall strength of a hand since they are used as side cards. In scenarios where two players have the same hand, the best kickers will win.

2. Bet Sizing with Confidence

In No Limit cash games, players have the ability to bet whatever they have in front of them. It's this very freedom that gets a lot of players into trouble. So, bet sizing is the second most important subject on our list of Texas Hold'em 5 Golden Rules.

Bet Sizing – Pre-Flop

One of the best tips for correctly sizing your bets is to follow what's happening at your table. If the standard pre-flop raise is 2.5xBB, as a beginner this is the line you should take. If you try to be clever and raise an odd amount, it could backfire. Your bet size has to be familiar and make sense to your opponents. By raising unusual amounts, all you're doing is making it harder for players to make a decision. Making it difficult for your opponents to think, post-flop, can be a good thing. However, pre-flop it normally results in that loose call you just don't want or need.

Bet Sizing - Post-flop

If you were the raiser pre-flop, a c-bet (continuation bet, after a pre-flop raise) is almost mandatory. You should size your c-bet between 50% and 70% of the pot. The size of your bet will help define the strength of your hand. This is especially true when playing at the lower levels. Most inexperienced players will see a big c-bet as strength. You will be able to get the hand over – whether or not you've hit the flop.

You want your opponents to know (or think) that you have them beat. If you bet too small, you could end up facing a re-raise or a check-raise, depending on your position. Bet too big and you could find yourself pot-committed to a hand that is probably going to be the loser.

Here's a simple example of proper c-bet sizing:

You're UTG+1 in a 9-Max $1/$2 No Limit Hold'em cash game. You get dealt Pocket JJ and raise the table standard of 2.5xBB. It gets folded around to the Button who calls. Both Blinds fold. The flop comes down Ad-6h-2s. Now, the Ace is a scare card, but you feel that the BTN player would have 3-bet with a strong Ace, and would have tossed a weak one. Bet too small here and a savvy opponent could raise you, representing the Ace, and bluff you off the pot. You bet 2/3 pot with confidence and get the fold.

It's not always that easy, and your opponent could have called you with a suited Ace. And, if the board comes down 7d-8d-9d and you're holding As-Ks in a multi-way pot, a c-bet could be like throwing down a drain. However, the c-bet is a standard and necessary play. And a correctly sized c-bet will usually get the intended result – a fold and you winning the pot.

Bet Sizing - Bluffs

Let's say that you want to bluff in a $20 pot. You feel that there is an excellent chance that your opponent would fold. If you bet $20, you could be in for trouble if you're wrong and this guy decides to call – or worse come over the top. This would be a poor bet size if your opponent would fold to a $10 bet. Because if the bluff fails, you would lose an extra $10, needlessly.

Bet Sizing - Value

Now, let's spin the bottle 180 degrees. When you have the nuts, you should try to bet for value. For example, you've got to the river, heads-up, with Ad-Ks on a board that reads: Ac-Kh-7h-3d-2s. You're quite certain that your opponent has the Ace, at the very least. If the pot is $50, and you bet $20, your opponent snap calls with two pair, you've probably left some money on the table. They might have called off another $10-$20! So, that's a classic bet sizing mistake.

The player that tends to be successful in games like Hold’em is the player that makes fewer bet sizing errors. Of course, you don't get to see your opponents’ cards before sizing your bets. But, by using the information you have on an opponent and how the hand was played, you'll be able to figure out the right amount to bet.

For example, a loose caller might be more likely to call you down with middle pair. Therefore, when you have a strong hand, your bet-sizing can be a little bigger for value – versus a tighter opponent who would be more inclined to fold.

If you have a straight, you’ll hold five consecutive cards which are not all the same suit. For example, 8-7-6-5-4 in different suits. The highest possible straight sequence is A-K-Q-J-10.

R

Rabbit Hunt – Seeing the remaining community cards after folding. This has no impact on the game but allows players to see if they would have hit their hand or not.

Ragged – Often used to describe a non-coordinated board texture.

Rap – A term used interchangeably with “tap”, potentially used to describe the act of tapping the table twice as the visual signal for checking in a live game.Rainbow – Used to describe a board texture (or sometimes starting hand) where every card is of a different suit.Raise – To “raise” means to increase the size of the wager on the current street. For a full breakdown of all the legal options check out the glossary entry under “Action”.Rake – A small amount taken from the pot each hand as payment for running the poker game.

Rakeback – A percentage of rake paid which is given back to the players as a reward. It sometimes comes in the form of a VIP system.

Range – The term “range” is used to describe a distribution of possible holdings that a player might hold. This important concept is discussed in this glossary entry.Range Advantage – This term is used when one player has a better range than his opponent. There are different variables that contributed to range advantage; they are discussed in this glossary entry.Rank – The term “rank” simply refers to a card’s value/number. I.e. Jack, Four, Ace etc etc.Ratholing – Describes the action of leaving a ring game and then rebuying in for a smaller amount of chips. In this glossary entry, learn why ratholing is considered unethical.Razz – The lowball version of seven card Stud. Check out this glossary entry for a description of the rules.Read – Sometimes used interchangeably with the term “tell”. It indicates that we have a good vision over the type of holdings our opponent is likely to show up with. “Normally I would have folded, but I had a read that villain likes to bluff, so I made the call”.Rebuy – To purchase additional chips. Predominantly applies to cash games although rebuy tournaments do exist.Redraw – A possible draw has completed on the board texture but we are drawing to an even bigger hand. This is best understood with the examples in this glossary entry.

Regular - A poker player who regularly plays in a certain game. Usual denotes an opponent of above average skill level.Represent – When we don’t have a certain holding but we look to represent that we do through our actions. The term can also be used to analyze the meaning behind villain’s actions. Villain bet large on all three streets: he is definitely representing something big.Reverse Implied Odds – An adjusted pot odds calculation taking into account chips we might lose on the later streets after we complete our draw. Check out the glossary entry for a full breakdown.

Re-raise – To re-raise means to raise after there has already been a raise on the current street. Check this glossary entry for the rules that govern re-raising in poker.

Ring Game – This term is used interchangeably with “Cash Game”. Since not all poker games are actually played with real money, the term “ring game” might be considered more applicable in some contexts.River – Refers to the final betting round in Hold’em, Omaha and Stud variants.

River Rat – A player who gets lucky and sucks out on the river. Especially applies to players who are clearly calling too wide on the earlier streets.Rock – Refers to a player type who only enters the pot with an extremely tight range. This term might be sometimes used interchangeably with the word “nit” although some assign the two words completely different meanings.

Rolled Up - A Stud term that indicates being dealt three of a kind on third street, i.e. rolled up trips.Royal Flush – The best possible hand in poker. We hold the Ten, Jack, Queen, King and Ace, all of the same suit.

Run – A term used to describe the fall of cards over a period of time. “Running good” and “running bad” are terms commonly used to describe a lucky and an unlucky streak respectively.Rundown – The term “rundown” is generally used to describe connected starting hands in Omaha variants. For example, the starting hand T987 is referred to as a “Ten-high rundown”. Learn to distinguish between different types of rundown in this glossary entry.

Run it Twice – After all remaining players are all-in, the final board cards are dealt twice – half the pot being awarded to the winner of each runout. This is a useful tool for reducing variance. Check out this glossary entry for a description on whether running it twice makes sense.Runner Runner – Making a strong made hand after catching consecutive running cards. For example, we hold three hearts on the flop and catch running hearts on both the turn and river to make our flush.