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Pot Odds Texas Hold'Em

Texas Hold'Em Odds and Probabilities


Hold'em Starting Hands - Probability of being dealt:
Odds
%
Pocket Aces
220:1
0.45
Any Pocket Pair
16:1
5.9
Ace - King suited
330:1
0.3
Ace - King offsuit
110:1
0.9
Ace - King suited OR unsuited
82:1
1.2
Any two suited cards
3.3:1
24.0
Pocker Aces OR Pocket Kings
110:1
0.9
Pocket Aces, Pocket Kings OR Ace-King
46:1
2.1
Any Pocket Pair OR two cards ten or higher
4.5:1
18.0
Any Pocket Pair of Sevens OR higher
5.4:1
16.0
Taking a pocket pair to the river, to make a set or better
4.2:1
19.0
Taking two suited cards to the River to make a Flush
15:1
6.4
Making a Flush by the River with two unsuited cards
53:1
1.8
Probability of making on the FLOP in Hold'Em:
Odds
%
With any Pocket Pair to make a Set
8.3:1
10.8
With any Pocket Pair to make a Full House
136:1
0.74
With any Pocket Pair to make Four of A Kind (Quads)
407:1
0.25
A Flush from two suited cards
118:1
0.84
Four cards to a Flush from TWO suited cards
8.1:1
10.9
Three cards to a Flush from TWO suited cards
1.4:1
41.6
Four cards to a Flush from ONE suited cards
88:1
1.1
Three cards to a Flush from ONE suited card
6.8:1
12.8

Probability of cards hitting the FLOP in Hold'Em:
Odds
%
Three of a Kind 424:1 0.24
a Pair 5:1 17.0
Three suited cards 18:1 5.2
Two suited cards 0.8 55.0
No suited cards (rainbow flop) 1.5:1 40.0
Three cards to a Straight 28:1 3.5
Two cards to a Straight 1.5:1 40.0
No Straight cards 0.8:1 56.0

Probability of hitting from FLOP to the TURN in Hold'Em:
Odds
%
A Full House or Better on a set from the next card
5.7:1
15.0
A Full House or Better from two pair from the next card
11:1
9.0
A Flush from a 4 to a Flush from the next card
4.2:1
19.0
A Straight from an Open Ended Straight Draw from the next card
4.9:1
17.0
A Straight from a Gutshot Straight Draw from the next card
11:1
9.0
A Pair from 2 Non Pair
6.8:1
13.0
A Second Pair and an opponent holding the same pair but out kicking you
15:1
6.0
Probability of hitting from the FLOP to the RIVER in Hold'Em:
Odds
%
A Full House or Better
2:1
33.0
A Full House or Better from two pair
5:1
17.0
A Flush from a 4 to a Flush
1.9:1
35.0
A Flush from a 3 to a Flush
23:1
4.2
A Straight from an Open Ended Straight Draw
2.2:1
32.0
A Straight from a Gutshot Straight Draw
5.1:1
17.0
A Pair from 2 Non Pair
3.2:1
24.0
A Second Pair w/kicker and an opponent holding the same pair but out kicking you
7:1
13.0

Probability of making from the TURN to the RIVER in Hold'Em:
Odds
%
A Full House or Better from a set
3.6:1
22.0
A Full House from two pair
11:1
9.0
A Flush from a 4 to a Flush
4.1:1
20.0
A Straight from an Open Ended Straight Draw
4.8:1
17.0
A Straight from a Gutshot Straight Draw
11:1
9.0
A Pair from 2 Non Pair
6.7:1
13.0
A Second Pair w/kicker and an opponent holding the same pair but out kicking you
14:1
7.0


On Strategy: Pot Odds Made Easy

Because some players have difficulty with the concept of pot odds and others stumble over the practical task of calculating them in the heat of battle, it’s time to demystify and sweep out whatever confusion still surrounds this subject while simplifying the arithmetic for readers.  In fact, no arithmetic is needed at all.  Instead, a handy chart is included that ought to prove helpful to new and experienced players alike.

Figuring pot odds is a necessary part of any poker player’s game.  Without it, we don’t have any way of knowing whether the odds against making our hand are offset by this fundamental relationship: How much will it cost to keep playing this hand and how much money am I likely to win if I catch the card I need? By understanding the relationship between the odds against making our hand and the money we figure to win if we get lucky, we can play skillful high percentage poker instead of treating the game like some form of gambling.

These calculations involve comparing the total number of unknown cards with the number of cards that will complete your hand ¾ the “outs” ¾ then doing a bit of division.

For example, whenever you hold four cards to a nut flush on the turn in a Texas Hold’em game, there are 46 unknown cards, (52 minus your two pocket cards and four on the board).  Of those 46 cards, 37 cards won’t help you, but those other nine cards are the same suit as your flush draw and any one of them will give you the nut flush.

The odds are 37-to-9, or 4.1-to-1, against making your draw.  Percentage poker players will call a bet in this situation only if the pot is four times the size of the bet.  In a $20-$40 game, the pot would need to contain at least $160 ¾ or else you’d have to be able to count on winning at least a total of $160 from future calls (this is called “implied odds,” and is a guestimate of sorts) ¾ to satisfy this requirement.

If you’re the kind of player who’s fond of inside straights and other long shot draws, consider this: You have only four outs on the turn.  That’s not much when you consider that 42 of the remaining cards won’t help you at all, and chances of completing your hand are less than nine percent.  If you’d prefer expressing that figure in odds, here’s the bad news.  The odds against completing your inside straight draw are 10.5-to-1, and you’d need a pot that’s more than ten times the cost of your call in order to make it worthwhile. 

If you had two pair and knew for a fact that your opponent had a flush, you’d be in the same kettle of fish, since only one of four cards will elevate two pair to a full house.  When can you play hands like this?  On two occasions.  The first occurs when you hit the multistate powerball lottery, win 90 million dollars or so, and $20-$40 hold’em now becomes the equivalent of playing for matchsticks. The other occasion is in a game with complete maniacs whose collective motto is: “All bets called, all the time.”  You would need to win more than 10 times the amount of your call to justify this kind of draw.  But if you figure to win a $450 pot by calling a $40 bet with an inside straight draw, go ahead. Go for it. 

A chart is provided that makes it easy to learn the odds against all the common draws you’re likely to come up against in a hold’em game.  If you memorize it, you won’t have to waste even a fraction of a second doing arithmetic at the poker table.  Personally, I find it tough concentrating on the cards in play and my opponents while trying to do calcs at the poker table.  Fortunately, there are simplified methods that allow you to approximate the percentage of time you’ll make your hand.

An easy method involves multiplying your outs by two, then adding two to that sum.  The result is a rough percentage of the chance that you’ll make your hand.  Suppose you have a flush draw on the turn.  You have nine outs.  Nine times 2 equal 18, and 18 plus 2 equals 20.  That’s pretty close to the 19.6 percent chance you’d come up with if you worked out the answer mathematically. 

If you have only four outs, our quick proximate measure (four outs x two, plus two = ten) is very close to the actual figure of 10.5.  If you have 15 outs, our quick measure yields a figure of 32, while the mathematically precise figure is 32.6 percent. 

The strategic implications of this are simple: If you have a ten percent chance of winning, the cost of your call should not be more than ten percent of the pot’s total.  With a thirty-two percent chance, you can call a bet up to one-third the size of the pot.

While the “Outs times 2 plus 2” method is an easy calculation to make at the poker table, it’s even easier to commit the chart to memory.  That way you never have to figure a thing.  Just tap into your memory banks and pull out the correct figure.  And anytime you find yourself fighting a tinge of self-doubt, you can always double check yourself using the “Outs times 2 plus 2” approximation.

If you want to estimate your chances on the flop without the need for much arithmetic, try this: If you have between one and eight outs, quadruple them.  Eight outs multiplied by four yields 32, while the precise answer is 31.5 percent.  With four outs, the quadrupling method yields 16 percent, while the accurate answer is 16.5 percent. 

With nine outs ¾ a common situation, because it represents the number of outs to a four-flush ¾ quadruple the number of outs and subtract one.  You’ll be spot-on when you do, since the arithmetical answer is 35 percent.  You can use this method up to 12 outs, though with 12 outs our shortcut method yields 47 percent, while the precise answer is only 45 percent. 

For 13 through 16 outs, quadruple the number of outs, subtract four, and your results won’t be anymore than two percent off dead center.  And remember, anytime you find yourself with 14 outs or more, you are an odds-on favorite to make your hand and pot odds of any size become worthwhile.

This chart shows odds against making your hand with two cards to come (flop to river), as well as with one card (turn to river) remaining.

Odds and Outs

 

 

Flop to River

Turn to River

Outs

Draw

Percent

Odds

Percent

Odds

20

 

67.5

0.48-to-1

43.5

1.30-to-1

19

 

65.0

0.54-to-1

41.3

1.42-to-1

18

 

62.4

0.60-to-1

39.1

1.56-to-1

17

 

59.8

0.67-to-1

37.0

1.71-to-1

16

 

57.0

0.75-to-1

34.8

1.88-to-1

15

Straight +  Flush

54.1

0.85-to-1

32.6

2.07-to-1

14

 

51.2

0.95-to-1

30.4

2.29-to-1

13

 

48.1

1.08-to-1

28.3

2.54-to-1

12

 

45.0

1.22-to-1

26.1

2.83-to-1

11

 

41.7

1.40-to-1

23.9

3.18-to-1

10

 

38.4

1.60-to-1

21.7

3.60-to-1

9

Flush

35.0

1.86-to-1

19.6

4.11-to-1

8

Straight

31.5

2.17-to-1

17.4

4.75-to-1

7

 

27.8

2.60-to-1

15.2

5.57-to-1

6

 

24.1

3.15-to-1

13.0

6.67-to-1

5

 

20.3

3.93-to-1

10.9

8.20-to-1

4

Two Pair

16.5

5.06-to-1

8.7

10.50-to-1

3

 

12.5

7.00-to-1

6.5

14.33-to-1

2

 

8.4

10.90-to-1

4.3

22.00-to-1

1

 

4.3

22.26-to-1

2.2

45.00-to-1


Other Probabilities

Wired Pair: flops a set 11.8 percent of the time

 

A-K: flops at least one ace or king 32.4 percent

 

Two Suited Cards: Makes a flush 6.5 percent

 

Two Suited Cards: Flops a flush 0.8 percent

 

Two Suited Cards: Flops four flush 10.9 percent

 

Two Unmatched Cards: Flops 2 split pair 2.2 percent

 

Hanging on to unprofitable draws for whatever reason ¾ and many players persist in drawing to long shots even when they really do know better ¾ can be a major leak in one’s game.  For many it’s the sole reason they are lifelong losing players instead of lifelong winners.

There’s no real excuse for that kind of play. Even if you are not mathematically inclined (and if you’re in this category, you’re in the majority. Most people I know loath doing calculations while playing poker) you now have two surefire ways to get the answers without having to do anything more difficult than multiplying by two or four, or memorizing a simple chart.  Now all you have to do is count the size of the pot, or even approximate it, compare one to the other, and make your decision.  It’s that easy.  Really.


 
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