OK, let’s get probability and odds squared away first. Essentially they are expressing the same thing but doing them in a slightly different manner. Odds are expressed as a relationship between an event occurring or not and probabilities are expressed as a ratio of possible events to total events. Probabilities by definition are therefore between 0 and 1 inclusively. They are commonly expressed as a fraction, decimal or percentage.

In other words if we look at an event that can occur.

The odds of it occurring are expressed as the relation of the chance for it occurring to the chances against it occurring.

Odds = (Chances for):(Chances against)

The probability of it occurring is expressed as the ratio of the chances of it occurring to the total chances that can occur (the sum of those for and against).

Probability = (Chances for)/(Total Chances) where Total Chances equals the sum of Chances for and Chances against.

For example, getting a winning bet on the Iron Cross.

The odds are 30:6 or 30 to 6 which could be reduced to 5:1 or 5 to 1.

The probability of winning a bet with the Iron Cross would be 30/36, 5/6, .833 or 83%.

There is no conjecture or guessing in calculating the probability. It has the same degree of accuracy as the odds.

The odds of throwing a head with a single flip of a coin is 1:1 or 1 to 1. The probability of a head is 1/2, .5 or 50%. The odds and probability are both taking the same data into consideration. They are both looking at the possibility of 1 event occurring out of 2 possible outcomes.

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