PROBABILITY
A “probability “ is a number, between zero and one, which represents the relative frequency to of a particular outcome occurring as a cannot occur.
A probability of one means the outcome will occur with certainty.
A probability of 0.5 means was the event will occur one-half of the time. For example, shuffle a deck of cards and turnover the top card. That’s random event.
One of the possible outcomes is that the card is black, either a Spade or a Club.
The probability of this particular outcome is 0.5.
This means that one half of the time the card you draw will be one of the black suits.
A “probability distribution” is a list of all possible, mutually exclusive outcomes and their associated probabilities.
By “mutually exclusive” I mean that the outcomes don’t overlap in some way.
Each outcome is defined in such a manner as to be unique from other outcomes.
For example, still considering our event of shuffling the deck and turning over the top card, one probability distribution we could define would be:
OUTCOME PROBABILITY
BLACK CARD 0.5
RED CARDE 0.5
Law of Averages
The “law of averages” is a limit theorem that says the sample mean gets arbitrarily close to the actual term for average. “Actual mean gets larger.
“Mean is a technical average that’s implied by a probability distribution; “sample mean” is about actual observed results.
A sample mean is the mathematical average of some actual result.
For example, in poker our black-card red-card probability distribution, think about a black card as representing the value 1 (you win a dollar if the card turned up is black) and a red card is the value 0 (zero).
The mean of this distribution is 0.5.
On the average you win $50 for every turn of the card.
Half the time the card is black and you get $1, and half the time the card is red and you get nothing.
Mathematics of Poker / Other Books on Holdem / Poker and the Internet
