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To help you calculate poker probabilities we will give you an
example on how to calculate the odds of getting a desired card.
This is how you calculate poker odds:
The easy example – a pair
You start with a pair of jacks – not bad! The flop – i.e.
the first three cards on the table – does not include a
jack.
Lesson 1: what the probability of a jack in “the Turn”?
Calculating fast you have seen 5 cards
which means that 47 cards are still undisclosed. There are
two more jacks in the game. The odds of getting a jack in the
turn is 2/47 or 0.0426 i.e. close to 4.3 %.
Lesson 2: no jack in the Turn – how about in “the
River”?
There are still 2 jacks in the game,
but one undisclosed card less, meaning that you have not seen
46 cards. The odds are 2/46 i.e. 0.0434 – still only close
to 4.3 %. Your chances of getting a jack have thus not improved
considerably …
Lesson 3: “I can't settle with just one more jack – I
want both!”
To
find the answer you need to multiply the probability of each
outcome. The probability of 1 jack in ”the Turn” was
0.0426 (4.3 %). In “the River” the odds are 1/46,
because now there is only one jack left that you haven’t
seen. The probability is around 0.0217
or 2.2 %. To get the correct answer you need to multiply the
two probabilities 0.0426 x 0.0217,
which adds up to 0.0009! The odds of
that happening are conclusively tiny.
Lesson 4: what’s the chance of even getting the
two jacks preflop?
You get one card followed by another.
What’s the likelihood of the other card matching the first?
There are three cards matching yours in the pile and 51 undisclosed
cards left altogether. 3/51 is 0.059 or 5.9 %. What are the odds
of the next card being a jack? There are 13 different kinds of
cards. 0.049/13 is approx. 0.0046 or less than 0.5%.
Lesson 5: What’s the likelihood of getting a jack in “the
Flop”?
Now you have to think reverse. Calculate
the chance of getting a jack in every card turned. With the first
card the odds are 48/50 (48 cards are not a jack and there are
50 cards left), with the second the odds are 47/49, with the
third 46/48. Summing up that’s 0.96 & 0.959 & 0.958.
Multiply these and you get 0.882 or rather an 88.2% chance of
not getting a jack in “the Flop”. Reverse the numbers
and you get 0.118 or rather an 11.8 % likelihood of a jack being
turned.
Chart of poker probabilities:
A major part of poker is evaluating the
odds of getting a good hand.
When you decide whether you want to bet and how much, it is
thus important to understands the odds/probabilities of getting
a desired poker hand.
What are the odds of achieving a given poker hand with 5 cards.
Below you find all the answers to your poker odds questions.
|
Poker
Hand |
#
Ways to construct the hand |
Chance
of that hand in 5 cards |
|
Royal
Flush |
4 |
1
in 649.740 |
|
Straight
Flush |
36 |
1
in 72.193 |
|
4
of a kind |
624 |
1
in 4.165 |
|
Full house |
3.744 |
1
in 694 |
|
Flush |
5.108 |
1
in 508 |
|
Straight |
10.200 |
1
in 254 |
|
3
of a kind |
54.912 |
1
in 47 |
|
2
pair |
123.552 |
1
in 21 |
|
1
pair |
1.098.240 |
1
in 2,36 |
|
No pair |
1.302.540 |
1
in 1,99 |
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