Poker Odds
Playing the game of Poker has become in many ways a mathematical science,
with television broadcasts providing instant probability analyses for
players' different card combinations. Unfortunately, this information
is not available to the players at Poker games, whether they are physical
ones or games played at online Poker rooms.
Players learning to play Poker should have a basic idea of how likely
it is to get high-ranking hands, and what the odds are to make their hand
during games.
Dealt Hands
First, what are the chances of being dealt five cards from a fresh, shuffled
deck in a physical Poker game and getting the following possible hands?
| |
Percentage |
Odds |
| Royal flush |
0.0002 % |
1 in 649,740.00 |
| Straight flush |
0.0012 % |
1 in 72,193.33 |
| Four of a kind |
0.0240 % |
1 in 4,165.00 |
| Full house |
0.1441 % |
1 in 694.16 |
| Flush |
0.1967 % |
1 in 508.80 |
| Straight |
0.3532 % |
1 in 254.80 |
| Three of a kind |
2.1128 % |
1 in 47.32 |
| Two pair |
4.7539 % |
1 in 21.03 |
| One pair |
42.2569 % |
1 in 2.36 |
| Nothing |
50.1570 % |
1 in 1.99 |
Making a Texas Hold'em Hand
In the game of Texas Hold'em, when players are initially dealt two facedown
cards, what are the chances of making a hand, before and after the Flop?
Let's take a look at the Texas Hol em odds:
| Texas Hol em odds before the Flop... |
Percentage |
Odds Against It |
| You will hold a Pair |
5.88 % |
16 to 1 |
| You will hold suited cards |
23.53 % |
3.25 to 1 |
| You will hold 2 Kings or 2 Aces |
0.90 % |
110 to 1 |
| You will hold Ace-King |
1.21 % |
81.9 to 1 |
| You will hold at least 1 Ace |
14.93 % |
5.70 to 1 |
| Texas Hol em odds if you hold... |
Percentage |
Odds Against It |
A Pair, probability that at least one more of that
kind will Flop
|
11.76 % |
7.51 to 1 |
If you hold no Pair, probability that you will pair
at least one of your cards on the Flop
|
32.43 % |
2.08 to 1 |
If you hold two suited cards, probability that two
or more of that suit will Flop
|
11.79 % |
7.48 to 1 |
| Texas Hol em odds if after the Flop you have... |
Percentage |
Odds Against It |
| Four parts of a Flush, probability that you will make it |
34.97 % |
1.86 to 1 |
| Four parts of a Flush, probability that you will make it |
8.42 % |
10.9 to 1 |
| Four parts of an Open-end Straight Flush, probability that you will
make at least a Straight |
54.12 % |
0.85 to 1 |
| Two-Pair, probability that you will make a Full House or better |
16.74 % |
4.97 to 1 |
| Three-of-a-kind, probability that you will make a Full House or
better |
33.40 % |
1.99 to 1 |
| Pair, probability that at least one more of that kind will turn
up (on the last two cards) |
8.42 % |
10.9 to 1 |
| Texas Hol em odds if you begin... |
Percentage |
Odds Against It |
Suited and stay through seven cards, three more
(But not four or five more!) of your suit will turn up
|
5.77 % |
16.3 to 1 |
Paired and stay through seven cards, at least
one more of your kind will turn up
|
19.18 % |
4.21 to 1 |
A Quick Lesson in Calculating Odds
When playing Texas Hold'em, players frequently need to quickly calculate
the probability that their missing card will turn up either in the Turn
or the River.
The term outs refers to the number of cards in the deck
that will improve your hand (and includes the unseen cards held by other
players).
An easy example of how to calculate your odds:
You start with a pair of Jacks, but the Flop doesn't contain another
Jack. What is the probability that a third Jack will turn up on the Turn?
To figure this out, determine the number of outs and divide it by the
number of cards left in the deck.
Holding two Jacks, there are two remaining Jacks - or outs.
For the Turn, the odds of seeing that third Jack are therefore two divided
by 47 (you've already seen 5 out of the 52 - your pocket and the 3 cards
of the Flop).
The probability of getting that third Jack at the Turn are 2/47 = 0.426,
or close to 4.3%.
If that third Jack didn't show up on the Turn, what is the probability
of it showing up on the River?
For the River, the odds of seeing that third Jack are therefore two divided
by 46 (you've already seen 6 out of the 52 - your pocket, the 3 Flop cards,
and the Turn).
The probability of getting that third Jack at the River are therefore
2/46 = 0.434, or still close to 4.3%.
Combining these two calculations, we can conclude that the probability
of getting that third Jack at either the Turn or the River is 8.42%, or
10.9 to 1 against making Three of a Kind.
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