Poker Calculator Hand Vs Hand

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Learning how to calculate the odds of winning a poker hand is essential for every player. In this article we'll provide you with some techniques that you can use to calculate the odds of winning a poker hand on the fly, we'll equip you with a tool that can do that for you and provide you with some useful information that you can memorize.

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Poker Odds and Outs Calculations

  • More Articles about Poker Odds: The Building Blocks of Poker: A Beginner's Guide to Pot Odds; More Beginner Poker Tools: Poker Odds Calculator (odds of winning at each point in a hand) Which Hand Wins Calculator (determine which poker hand wins).
  • Next street analysis narrows a range down as you proceed through a hand to analyze turn and river decisions. Assign a range into eight groups. Intelligent auto-selection into groups. Instant heads up range vs range equity calculations preflop, 'vs equity' hand list, anod more. Graphs, reporting, export, customizable calculator and a whole lot more.
  • Jun 07, 2017  In this hand the caller flops top pair with KQ but faces a jam. Bart uses the opportunity to go over how to easily calculate your equity vs a range in your head. If you want to call in with a hand.
  • The Best Poker Hands Calculator. You can use this calculator while playing or reviewing past hands to work out the odds of you winning or losing. Have fun letting your friends know that they made a less than optimal move against you in a home game. Or prove that you made the right play based on the odds shown in the 888poker Poker Calculator.
  • This is a discussion on Hand Equity vs Opponents Range within the online poker forums, in the Learning Poker section; Hello Guys, I would just want to ask on how do you calculate (manually) your.

Let's start with the basics. With the exception of the very strong holdings like some flushes, quads etc. almost every poker hand can improve. Outs are the cards that will improve your hand if they show up at a later street. For example, if you're holding AQ on a Q34 board you can still improve to two pair or trips if you hit on of the three Aces remaining in the deck or one of the two remaining Queens.

How do we know if one of our opponents isn't holding one of those cards? Well.. we don't and that's why we're forced to ignore that possibility in our calculations.
Here are some common examples of drawing hands in no-limit hold 'em and the number of outs that they can hit to improve:
  • Gutshot Straight Draw (examples: JT on Q93, 57 on 69A etc.) - 4 outs
  • Open Ended Straight Draw (examples: 98 on T72, KQ on JT5) - 8 outs
  • Flush Draw (examples: AhQh on 2c7h9h, 4d6d on JdKd8s) - 9 outs

Pot Odds

Pot Odds - the size of the pot in relation to the bet that you have to call to continue playing the hand. Pot Odds are usually represented in the form of a ratio (2:1, 3.2:1, 4:1 etc.). Pot odds are essentially the risk you have to take (call) to gain the reward (size of the pot).

Let's say that the size of the pot on the flop equals 2$. Our opponent is betting 1$. To continue playing we have to call 1$ and if we do we can win 2$ + 1$ = 3$. We're getting 3 to 1 pot odds. Now let's make it a bit more complex, pot size is 3,55$, opponent bets 2,33$. We have to call 2,33$ to win 3,55$ + 2,33$ (5,88$). Our pot odds are 5,88$ / 2,33$ = roughly 2.5 : 1.

If you've ever watched televised poker you probably remember that it's common to use % value when determining the chance of winning a poker hand. That's why it's really handy to be able to convert the ratio (used to represent Pot Odds) into % (used to represent equity which is basically a share of the pot that belongs to us at certain point in a hand based on our chance of winning that hand).
Here's an easy way to do that:

Let's say our opponent is betting 2$ into 6$ pot so our pot odds equal 4:1. To convert the ratio into % add both sides of the ratio (4 + 1) and use that number as a divisor for the right part of the ratio (1 / 5 = 20%).

In the example above you need to win 20% of the time to break even when your opponent is giving your 4:1 pot odds. How often do you need to win to make the call in other popular situations? Here are some examples for you to memorize:

  • 1:1 = 50%
  • 2:1 = 33%
  • 3:1 = 25%
  • 4:1 = 20%

Rule of 2 and 4


Now that you know what pot odds and odds are you can learn the quick way of calculating the percentage chance of your hand improving. It's called the rule of 2 and 4 and it's very simple:

With one more card to come (on the flop waiting for the turn or on the turn waiting for the river) multiply your outs by 2 to calculate the % chance of your hand improving. With two more cards to come (opponent all-in on the flop or any other situation when you have to call just one bet to see both turn and river) multiply your outs by 4 to calculate the % chance of your hand improving.

Example: You're holding T8 on a J24 board, you have 9 outs to hit your flush. Villain goes all in on the flop. Your % chance of improving to a flush equals 4 * 9 = 36%. Let's consider the same situation but this time flop went check/check, the turn is an Ace of clubs and your opponent is betting. Your % chance of improving in that situation would be 2 * 9 = 18%.

Rule of 2 and 4 is fairly accurate when it comes to no-limit hold'em. If you have 9 or fewer outs you should never be off by more than 2% in your calculations when using this rule and it's very rare to flop more than 9 outs in no-limit hold'em. That being said you probably don't want to make those calculations every single time and it's a very good idea to memorize some common situations that can occur at the tables.

Hand vs. Hand All-in Pre-flop


Hand Calculator Poker


Example

Odds

%Odds/Equity

Pocket Pair vs. Smaller Pocket Pair

AA vs. TT

4 : 1

80%

Pocket Pair vs. Two High Cards

88 vs. AQ

1.2 : 1

55%

Pocket Pair vs. Two Low Cards

QQ vs. 67

4.9 : 1

83%

Pocket Pair vs. High Card and Low Card

JJ vs. A9

2.3 : 1

70%

Two High Cards vs. Two Low Cards

AJ vs. 78

1.9 : 1

65%

High Card and Low Card vs. Unpaired Hand

AT vs. KQ

1.2 : 1

55%

Odds of Improving Post-flop



Example

Outs

Flop%/Odds

Turn%/Odds

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Gutshot Straight Draw

JT on Q83

4

16.5%/5.1 : 1

8.7%/10.5 : 1

Two High Cards

AK on 962

6

24%/3.1 : 1

13%/6.7 : 1

Open-Ended Straight Draw

89 on A76

8

31.5%/2.2 : 1

17.4%/4.7 : 1

Flush Draw

AhQh on Jh5h8c

9

35%/1.9 : 1

19.6%/4.1 : 1

Flush Draw + High Card

As2s on 8sQs4d

12

45%/1.2 : 1

26.1%/2.8 : 1

Open-Ended Straight Flush Draw

Td9d on Jd8dKh

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15

54.1%/0.85 : 1

32.6%/2.1 : 1


Poker Odds Calculator

So far you've learned about outs, odds, calculating the chance of improving your hand on the fly, and figuring out if it's profitable to make a call based on the pot size and bet size of your opponent. That's enough to get you started, but it probably doesn't answer every question you might have.

Maybe you want to figure out what's the equity of your set vs. two opponents holding a flush draw and straight draw? Maybe you want to know if your hand has any chance of winning in a 5-way family pot. Fortunately, we got you covered! You can answer those and many other questions using the Odds Calculator provided below:

If the Odds Calculator is not displaying, please check your browser settings and enable scripts.

Here's a quick guide on how to use the odds calculator:

  • In the top right, you can choose your preferred game (you can even calculate the equity of winning a hand in games like Omaha Hi/Lo or Razz).
  • Choose the number of players in the pot.
  • Click on player's hole cards and assign them using the list provided at the bottom of the calculator.
  • You can add cards to the board in the same way.
  • Click 'Get Odds' et voila!

Now you can calculate the odds of winning any poker hand. With such a powerful tool at your disposal, you'll improve as a poker player in no-time!

Other Top Recommended Content

If you enjoyed reading this article, check out our other top recommended articles on poker mathematics!
  • Poker Maths - Combinations
  • Odds & Outs
Or why not try out some poker mathematics related coaching videos?

Which Poker Hand Wins Calculator


  • Odds & Outs
  • Bitesize Poker Concept - Implied Odds

Calculator

The table below shows the odds of each hand winning in typical all-in match ups in Texas Holdem. The percentage chance of winning assumes that both players are all-in and that all 5 community cards will be dealt to determine a winner. The table also assumes that there are no other players in the hand, although the results should be very similar.

All-in hands probability odds chart.

Typical Match UpHand 1Hand 2
Under Pair vs. OvercardsT T57%43%A K
Overpair vs. PairK K80%20%9 9
2 Overcards vs. 2 UndercardsA Q63%37%5 7
Dominated HandA J79%21%J T
Very Dominated HandQ Q89%11%Q J
Overcard vs. Dominated KickerA 929%71%9 9
Pair vs. 1 Overcard8 869%31%A 5
1 Overcard vs. 2 Middle CardsJ 457%43%6 8

How to use the all in match-ups odds chart.

The table can be used to estimate your chances of winning in common all-in situations, however, the table does not highlight the exact probabilities for the certain match-ups in general.

For example: in the pair v overcards match-up, 2 2 would be a 53% favourite against A K instead of being a slightly stronger favourite like T T with a 57% chance of winning. The is due to other factors such as the increased probability that two overpairs will appear on the board creating a higher two-pair with a better kicker for the player holding A K.

Poker Hand Vs Hand Odds Calculator

All in match up odds evaluation.

As you can see from the table, some of the match-ups are closer than you might expect them to be. For example, if you have another player dominated with a hand like A J against J T, your opponent will win the pot 1 time in 4. Therefore you should be careful not to become overly excited when cards like these are turned over in an all-in situation, because your opponent is not always as far behind as you think.

Another interesting all-in match up is the very common AK versus an under pair. The table shows that although the odds are fairly even, the under-pair will usually have the slight advantage.

Poker Hands Order Chart

This means that it is always better to be pushing all-in rather than calling an all-in with AK if necessary, because to call with AK against an under pair is a losing play in the long run. By pushing all-in with AK you give your opponent the opportunity to fold for fear of an overpair, which will improve your expectation in the long run.

Go back to the poker odds charts.

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