Probability

Probability is the mathematical measure of how likely an outcome is, expressed on a scale from 0, meaning impossible, to 1, meaning certain, or equivalently as a percentage from 0% to 100%. In gambling it is the quantity that defines a fair price, and the ability to estimate it accurately is what separates value betting from guesswork. It connects directly to Implied Probability, the chance baked into a given set of odds. The link between probability and fair odds is exact. A genuine 25% chance corresponds to fair decimal odds of 1 divided by 0.25, which is 4.00; a 50% chance is 2.00; a 20% chance is 5.00. If a bookmaker offers more than the fair price, say 4.50 on a true 25% event, the bet carries positive expected value; offer less, say 3.50, and the value is negative even though the event itself is unchanged. Expected value makes this concrete. Backing a true 25% outcome at 4.50 with a 10 stake wins 35 (a 35 profit on the 10) one time in four and loses 10 three times in four: 0.25 x 35 minus 0.75 x 10 equals 8.75 minus 7.50, a positive 1.25 per bet on average. The same bet at 3.50 returns 0.25 x 25 minus 0.75 x 10, which is negative, so the price decides the verdict. The common error is the gambler's fallacy: believing that independent events such as roulette spins or dice rolls are 'due' to correct a recent imbalance. They are not; each trial carries the same probability regardless of history. Sound betting rests on estimating true probability and comparing it to the price, never on reading patterns into random sequences.