In roulette circles, there is a difference between the theoretical expectation of an event, a.k.a. the frequency of that event, versus the probability of that event occurring. We begin our discussion with an example of red or black numbers in roulette.
For the time being, we will ignore the green zero or 00 (American Roulette). The expectation in this scenario is that a red number should appear approximately 50% of the time. If there are two colours – red and black – the chance of red or black occurring in 10 spins is five times, and vice versa. But we expect with 100% certainty that either red or black will occur.
We calculate this expectation for two spins as follows: 1/2+1/2 or 100%. If we add those fractions together, we always get 100% or 1. Because we expect these colours to occur at least half the time on any given spin, that’s the expectation based on a perfect distribution of outcomes.
The probability of landing a red or black number in two spins differs. It is calculated as follows:1-(1/2 X 1/2) = 0.75. That means there is a 75% probability of landing a red or black number in two spins.
In summary, the expectation of an event occurring is typically higher than the probability of that event occurring. So, for example, we expect 100% of the time that if there are two roulette wheel spins, red or black should come up within those two spins.
The probability of such an event is equal to the probability of each outcome on each spin multiplied by one another, subtracted from 100%.
The expectation serves as a valuable guide for developing roulette strategies. The probability is beneficial insofar as it determines how a bankroll is determined. The expectation is a long-term theoretical proposition in a perfect world. It describes what should ideally happen.
Probability describes the certainty of a specific event occurring. The expectation is higher than the probability. These are not the same concepts, although they are frequently used interchangeably.
