Introduction

Probability and statistics are at the heart of Poker. Poker is one of the games that is more dependent on chance ("luck of the draw") than on skill. The skill in Poker usually revolves around the Bet and Bluff, not what is dealt. Variations of Poker sometimes try to add skill back into the game. Techniques used range from dropping and redealing cards (for example, 5-Card Draw) to using a set of common cards that all players share (Texas Hold 'em), and having players match three cards of their five with the two on the table.

Thus I thought it would be interesting to create a table of the probabilities. Let me introduce some of the "magic" numbers that are common when dealing with a playing card deck:

There are 4 suits in a deck.
There are 13 cards in a suit.
There are a total of 52 cards in a deck.
A deck usually has 2 jokers, raising the total to 54 when playing with jokers.
Games generally deal 5 or 7 cards. (I'll focus on five for now.)
The total number of 5-card hands that can be dealt from a deck of 52 cards is 2598960 and is referred to as 52 C 5. (n C r represents the number of possible combinations of r items out of n items. nCr from the Math | Probability menu in the graphing calculator performs this.)

You find that these numbers are used a lot, usually in the denominator of the ratios.

An interesting sidenote I read mentioned that the hands are basically arranged by probability, while the way to determine the difference between two of the same is hand is generally arbitrary and sometimes counter to probability.

I've tried doing the math myself (so there may be mistakes), and I've tried to show my work. Click the headings to show the text.