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Poker probabilities
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Now we will take a quick look at
mathematical probabilities for the different "winning" hands. It is
essential probability calculations that are good to be familiar with.
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What
are my chances?
To calculate your chance you need to know the number of outs (cards
that makes your hand better). There are 52 cards in the deck. When the
cards have been dealt there are 50 unknown cards left. After the flop
you're down to 47 unknown cards, after the turn 46. In the table below
you can find the probability of hitting one of the cards you're looking
for.
| Outs |
On The Turn |
On The River |
| |
(numbers are in %) |
| 1 |
2,13 |
2,17 |
| 2 |
4,26 |
4,35 |
| 3 |
6,38 |
6,52 |
| 4 |
8,51 |
8,70 |
| 5 |
10,64 |
10,87 |
| 6 |
12,77 |
13,04 |
| 7 |
14,89 |
15,22 |
| 8 |
17,02 |
17,39 |
| 9 |
19,15 |
19,57 |
| 10 |
21,28 |
21,74 |
Make a printout of this table at take a look at it as often as
possible. Notice how the probability is close to a multiple of 2, so
you could use this a quick way to asses your chances of hitting your
missing card.
A
little on how to asses probabilities in poker
Let us assume that you have a pair of jacks in your hand - not a bad
hand. The flop shows no additional jacks - what is the probability of
hitting another jack?
Lesson 1:
What are the chances of hitting a jack on the turn?
You quickly realize that you know 5 cards and therefore have 47 unknown
cards. There are two jacks in the deck that you haven't seen so the
probability of hitting a jack is 2/47, or 0,0426 which is roughly 4,3
percent.
Lesson 2:
You did not catch a jack on the turn - what are my chances on the river?
There are still 2 jacks in the game, but a card less. You know 6 of the
cards and there are 46 unknown cards left. Therefore the probability of
hitting a jack is 2/46 or 0,0434, which also roughly is 4,3 percent.
Your chance of hitting another jack is not improved much!
Lesson 3:
"I don't want only one more jack, I want both of them!!"
What is the probability to achieve this? To find the answer we must
multiply the probability for each card. The probability of getting a
jack on the turn is 0,0426. The probability of getting another jack on
the river is 1/46, because there is only one jack left. That is around
0,0217 or roughly 2,2 percent. To get the correct probability we
multiply the two probabilities, 0,0426 X 0,0217 is roughly 0,0009 or
0,09 percent! Chances are you won't get that last jack anyway - so
perhaps you shouldn't put your money on it!?!
Lesson 4:
What are the chances of getting a pair of jacks on the hand anyway?
You are dealt one card and then another, what is the probability of the
second card matching the first card? There will be 3 cards like the one
you got left and there are 51 unknown cards left. This gives us a
probability of 3/51 or 0,059 which is roughly 5,9 percent. What are the
chances of the cards being jacks? The deck consists of 13 different
values. This gives us 0,049/13 which is 0,0045 or roughly 0,5 percent.
Lesson 5:
What
are the chances of hitting a jack on the flop?
Now you've got to think reversed. Figure out what the chance of not
hitting a jack for each card that is turned. The chance of the first
card not being a jack is 48/50 (48 cards is not a jack and there are 50
unknown cards left), second card is 47/49 and third card is 46/48.
Multiplied this gives us 0,882 or an 88,2 percent chance of NOT hitting
a jack on the flop. The probability to get a jack on the flop therefore
is 1,0-0,882=0,118 or 11,8 percent.
Where
can I get more information?
You should be well equipped to start playing Texas Hold'em Poker by
now. Keep in mind that experience is at least as important as the tools
presented to you through this Texas
Hold´em guide.
Good luck at the tables!
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