# Pocket Pair Odds Example

You start with a pair of Jacks in the pocket playing texas holdem. Not too shabby. The flop however, doesn't contain another Jack.

**Lesson 1:** *What's my chance
of getting a Jack on the turn? *

You need to figure out the number of outs and divide it by the
number of cards in the deck. There are 2 more Jacks in the 47 remaining cards
(since you've seen five already). The answer is 2/47, or .0426, close
to 4.3%.

**Lesson 2:** *No luck on the
turn, how 'bout the river?*

Still 2 Jacks left, but one less card in the deck bringing the grand
total to 46. What's 2/46? That's .0434, which is close to 4.3%.
Your chances didn't change much.

**Lesson 3:** *Screw getting just
one Jack! I want them both! What are my chances?!*

Since we're trying to figure out the chances of getting one on the turn
AND the river, not one on EITHER the turn or the river, we don't
have to reverse our thinking. Just multiply the probability of each
event happening. The chances of getting that first Jack on the turn was
.0426, remember? The chance of getting a second Jack on the river would
be 1/46, because there will only be one Jack left in the deck. That's
about .0217, or 2.2%. To get the answer, multiply them: .0426 X .0217
is about .0009! That is less than one-tenth of a percent. I wouldn't bank
on that one.

**Lesson 4:** *Hey, what were
my chances of getting a pair of Jacks anyway?*

To figure that out, think of it as getting dealt one card, then another.
What are your chances of the second card matching the first one? There
will be 3 cards left like the one you have. There are 51 cards left in
the deck. 3/51 is .059 or 5.9%. What's the chance that it'll be Jacks?
Well, there are 13 different cards. So, .059/13 is about .0045, a little less
than half a percent.

**Lesson 5:** *What were my chances
of getting a Jack on the flop?*

Now, you do have to "think in reverse" as in the previous example.
Figure out the chances of NOT getting a Jack on each successive card
flip. On the first card, you have a 48/50 chance (48 non-Jack cards left, 50
cards left in the deck), second card is 47/49, third card is 46/48.
Those come out to .96, .959, and .958. Multiply them and get .882, or
an 88.2% chance of NOT getting any Jacks on the flop. Subtract that from 1 to discover
what your chances really are and you get .118 or 11.8%. This will
be your chance to getting at least one Jack.

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