Probability and Poker (part 2)
Maybe I am not a genius to calculate the probability of every possible round; however, the math behind really excites me to look. Let’s talk about it today:
First thing first, the total combinations that you pick 2 different cards will be 51x52:2=1326 combinations. In those combinations: 936 are off-suit, 312 (13x12x4/2=312) are suited cards, and 13 are pocket pairs.
There are indeed some examples when we get closer to math: If you get a dominated pair of 2 and your opponent has a bigger pair, the chance of winning that game is only 18%. Maybe among the revealed 5 cards there are 3,4,5,6 but as I have said, the chance is pretty low. (I use Propokertool to find this out, you can also download it on the internet for more information).
I won’t dig deeper into bet rounds but rather tell you the interesting change of chance after the three cards are revealed. Assume that there are 4 players: imagine the first two come into the table, and they pick the card (the other two are assumed to disappear). So the 1rst player card is 2,2 and the second is QQ. As I’ve mentioned, the 2nd player’s chance to win is 81%. Now the other two appeared with 2,4 for the 3rd and K,9 for the 4th. The chance changed immediately with 10.62% for the first, 52.64% for the second, 11.47% for the 3rd, and 23.88% for the 4th.
Let’s see how this change after 3 cards are revealed.