Probability and Statistics - Introduction

Even though poker is a game of deception and intuition, math has a very important role in Texas Holdem, since there are cards that are common to everyone’s hands.
In many situations you almost certainly know your opponent’s hand, and you need to check if you should fold or call his bet.
This decision is made by calculating the pot odds, as you will see in the next article.

First, here are some numbers and percentages:

Chances of your two pocket cards
* The chances of getting a pocket pair are… 5.8% or one out of every 17 hands
* The chances of getting a pair of AA are… o.45% or one out of every 222 hands
* The chances of getting two suited cards are… 24% or one out of every 4 hands
* The chances of getting any AK suited are… 0.3% or one out of every 333 hands

Chances on the flop
* The chances of getting a pair are 29% or one out of 3.5 hands
* The chances of getting two pairs are 2% or one out of 50 hands
* The chances of getting trips are 1.35% or one out of 74 hands
* The chances of getting a set when you have a pair are 10.8% or one out of 9 hands
* The chances of getting a set or better when you have a pocket pair are 11.8% or one out of 8 hands
* The chances of getting a flush when you’re suited are 0.84% or one out of 119 hands
* The chances of getting a flush draw when you’re suited are 10.9% or one out of 9 hands

Chances on the turn
* The chances of getting a straight when you have an open ended straight draw are 17% or one out of 6 hands
* The chances of getting a flush when you have a flush draw are 19% or one out of 5 hands
* The chances of getting a full house when you have two pairs are 9% or one out of 11 hands
* The chances of getting a full house if you have a set are 15% or one out of 6.6 hands

Chances on the river
* The chances of getting a straight when you have open ended straight draw are 17% or one out of 6 hands
* The chances of getting a flush when you have a flush draw are 20% or one out of 5 hands
* The chances of getting a full house or better if you have a set are 23% or one out of 4 hands