PRE-FLOP
The probability of being dealt:
Pocket aces - 220/1
0.45%
Either pocket aces or pocket kings - 110/1
or
0.9%
Any pocket pair - 16/1
5.9%
AK suited - 331/1
0.3%
AK offsuit - 110/1
0.9%
AK suited or offsuit - 82/1
or
1.2%
Any two suited cards - 3.3/1
24%
Either pocket aces, pocket kings or AK 46/1
or or
2.1%
QUESTION: What is the probability that I will get pocket pairs on 4 out of 4 hands?
ANSWER: The odds against getting a pocket pair are 16-1, meaning that there is a one in 17 chance. 17^4 = 83,521. So, the odds that your next four hands will contain pocket pairs is 83,520 to 1.
QUESTION: What is the probability of getting pocket pairs 4 hands in a row when i play 200 hands?
ANSWER: The odds against getting a pocket pair are 16-1, meaning that there is a one in 17 chance. 17^4 = 83,521. So, the odds that your next four hands will contain pocket pairs is 83,520 to 1.
The probability that during a given sequence of 200 hands you will see four consecutive pocket pairs is approximately 1 in 83,521/197 = about 1 in 424. Note that 197 is used (not 200) because the beginning of the sequence of four hands can't start after the 197th hand.
The exact probability of seeing at least one group of four consecutive pocket pairs in 200 hands is
1-(83,520/83,521)^197.
