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The Rules of Multiplication in Betting

This article focuses on the two rules of multiplication in betting, the general rule of multiplication and the special rule of multiplication. Smart bettors must know how to differentiate between independent and dependent variables and how to calculate the joint probability of an event.

The special rule of multiplication

The formula for the special rule of multiplication is P(A and B) = P(A) P(B) . To better understand it, we must look at dependent and independent events separately.

Independent events

This rule requires that two events, A and B are independent, meaning that the occurrence of one of them does not influence the probability of the other. In order to find the probability for an independent event to take place, a bettor must multiply the probabilities. For example, when flipping a fair coin twice, there is a 50% chance for each outcome and a previous result does not alter the next outcome.
If we are trying to find out the probability for two heads in a row, we must use a certain denotation, P (A and B), where A and B are the events and P the probability. The formula then becomes Probability of (Heads on the first flip and Heads on the second flip). When we multiply the probabilities we get P= chance of heads flip 1 x chance of heads flip 2 = 0.5%x0.5% = 0.25. So the probability of two heads in a row is 25%. Regardless how many events you have, you can use the same multiplication rule if they are independent.

Dependent events

If we are talking about dependent events, then the occurrence of one event influences the probability of the other event. Let’s assume that you have 25 bets that match your bet analysis criteria after you have used a bet screening software that has a 80% success rate and a 5%+ finding value. You select one bet that has a 5/25 = 1/5 = 20% chance it won’t pass, so it doesn’t match the criteria. The next potential bet now has a 4/24 = 1/6 = 16.67% probability of failing as well, but the next potential value bet has a 5/6 or 83,33% chance of being authentic.

The general rule of multiplication

If you’re trying to find the joint probability that 2 events will occur one after the other, you must use the general rule of multiplication. The formula is P (A and B) = P (A) x P (B|A) or P (A and B) = P (B) x P (A|B) where P (B|A) and P (A|B) are the conditional probabilities. The first formula then becomes the probability of A and B happening = the probability of A occurring x the probability of B occurring given that A happened. In the second formula, the B event happened. If we use the same example with the 25 bets, A will be the probability of the first bet will not pass: (P (A) = 5/25) and B that the second bet will not pass either (P (B) = 4/24). B is 4/24 because we have eliminated A and now we have only 24 bets. The formula would look like this: P (A and B) = P (A) x P (B|A) = 5/25 x 4/24 = 200/600 = 0.0333. This means that the two bets have a 3.33%. probability of being no good. If you use the formula for three events, you have P (A and B and C) = P (A) x P (B|A) x P (C|A and B). For the example above it will be 5/25 x 4/24 x 3/23 = 60/13800 = 0.0043 (0.43%).

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