1. Uniform Probability Distribution
When a wheel is divided into N equal slices, each option A has an identical probability of being selected on any given spin. Mathematically, this is modeled as a Discrete Uniform Distribution:
For example, on a 5-slice wheel, the theoretical probability of landing on any single slice is exactly P(A) = 1/5 = 0.20 or 20%.
2. Weighted Wheel Mathematics
When slices have custom weights assigned to them, the probability of selecting option $i$ with positive weight $w_i$ is proportional to its weight relative to the sum of all weights:
If Option A has weight 3, Option B has weight 2, and Option C has weight 5, the total weight sum is $3 + 2 + 5 = 10$. The probability of Option A winning is $3 / 10 = 30\%$.
3. The 1654 Pascal-Fermat Correspondence
Modern probability theory was formally founded in 1654 through a series of letters exchanged between French mathematicians Blaise Pascal and Pierre de Fermat. They solved the famous "Problem of Points" (how to divide stakes fairly in an interrupted game of chance), establishing the principles of expected value:
This foundation allows us to quantify long-term statistical expected outcomes for games, raffles, and random choices.
4. Law of Large Numbers (LLN)
The Law of Large Numbers states that as the number of independent spins $N$ increases, the observed empirical frequency of an option converges toward its theoretical probability $P(A)$. While 10 spins may produce minor variance, 1,000 spins will closely mirror theoretical probabilities.