As gambler's, most of us have an intuitive concept of what probability is all about.  If you flip a fair coin you might say it has a 50 - 50 chance of landing with the head side up.  Or you might say that it has a 1 in 2 chance of landing with the head side up.  Or you could say it has a 50% chance of landing with the head side up.  These are all descriptions of the same thing. 

The way that mathematicians describe probability is to find the thing you are measuring (heads) and divide it by the total possible outcomes (in this case two, heads or tails).  So we have one outcome (heads) out of two possible outcomes (heads or tails) or 1/2.  Decimal equivalents are commonly used, so this probability would be described as 0.5.  The sum of the probabilities for all of the individual outcomes of an event will always equal 1.  In our example the probability of heads is 0.5 and the probability of tails is 0.5.  Added together they equal 1. 

Looking at a single six-sided die, the probability of rolling any number on a given roll is 1/6 or 0.1667.  What if we wanted to know the probability of rolling a 1 or a 2 on any single roll?  Now we have 2 events out of 6 outcomes that we are measuring.  Making the probability 2/6 or 0.3333.  When looking at a combination of probabilities where any outcome is a measurable event, then the probabilities are added.  In this case we added the probability of rolling a 1 (1/6) with the probability of rolling a 2 (1/6).  This gave us 2/6 or 0.3333.

What if we flipped our coin and gave a roll of the die.  What is the probability of getting a head OR rolling a 1?  This is the same type of combination as above.  We add the probabilities of the individual events.  Our probability of heads is 0.5 and our probability of rolling a 1 is 0.1667.  Added together the probability of rolling a 1 or flipping heads is 0.6667.

What about the probability of flipping heads AND rolling a 1?  How would you calculate that combination?  If we look at all of the possible outcomes we get: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5 and T6.  There are 12 possible outcomes and only 1 satisfies our criteria of Heads and 1.  Therefore the probability is 1/12 or  0.0833.  Mathematically we can calculate this by multiplying the probabilities.  0.5 for heads times 0.1667 for rolling a 1 gives us a probability of 0.5 X 0.1667 = 0.0833 for getting heads AND 1.

This can also be illustrated using two consecutive rolls of the die.  What is the probability of rolling a 1 both times?  The answer is found by multiplying the probabilities of the individual events.  1/6 X 1/6 = 1/36, or 0.0277.

What of the probability of rolling the die two times and having the sum of the two rolls be 3?  This could be accomplished two ways.  We could roll a 2 and then a 1, or we could roll a 1 and then a 2.  As there are 36 possible outcomes from two die rolls, we have a 2/36 (0.5555) chance of the sum being 3.  Mathematically we would say that on the first roll we could get a 1 or a 2, so a 1/3 probability.  On the second roll, however, only 1 outcome will satisfy the criteria; dependent on the outcome of the first roll.  So the probability of the second roll is 1/6.  1/3 X 1/6 = 1/18 (0.5555).

Discussions involving probability will occur frequently throughout this website, so it will be best if you get a thorough understanding of it now.  If you have some questions, please post them in the sports betting forum.