In roulette, each spin of the wheel is an independent event, meaning the outcome of one spin does not affect the outcome of the next spin. Imagine we're betting on red. The probability of the ball landing on red in a single spin is approximately 18/38 (or 47.37%) in American roulette and 18/37 (or 48.65%) in European roulette, assuming there are 18 red pockets out of 38 (or 37) total pockets.
Now, let's say we've witnessed three consecutive red outcomes. The probability of the next spin also resulting in red remains the same, around 18/38 or 18/37. However, the probability of observing four consecutive red outcomes (a streak of length four) is the probability of one red spin raised to the power of four. In other words, it's (18/38)^4 or (18/37)^4.
As the streak lengthens, this probability decreases rapidly. For example, if we've observed ten consecutive red outcomes, the probability of the next spin being red is still around 18/38 or 18/37, but the probability of seeing eleven consecutive red outcomes is significantly lower: (18/38)^11 or (18/37)^11.
This diminishing probability with increasing streak length is what's meant by "the probability of its continuation diminishes exponentially." It's like a snowball effect where each additional consecutive outcome becomes increasingly unlikely.