The game of five card draw is largely thought of as the most basic of the variants. While it has not always been the most popular game, it is so classically common that when most people refer to poker they mean this variant. Here are some more specific probability calculations for use in five card draw:
Know the odds of being dealt a given starting hand.
Know the odds of improving your hand.
These calculations are only the tip of the iceberg. With a decent knowledge of mathematics, a poker player can computer the probability of any given draw or improvement. Also, with vastly more complex equations it is possible to determine the odds of such things as whether or not a particular opponent has a better hand then you based on the number of cards he drew.
The reason it is important to learn these mathematical principles is to take some of the random chance out of the game and replace it with the skill of calculating and betting based on the odds.