Consider a fair roulette game with 18 red numbers, 18 black numbers and 1 green zero.
At each round, the probability of winning by betting on red or black is 18/37, which is 48.6%.
If we play a lot of rounds and count how many sequences of N consecutive colors are drawn, we'll see that there are fewer sequences as N grows.
By this logic, the chance of drawing 10 consecutive reds are lower than drawing 9. But this conflicts with the 48.6% odd.
What am I missing? Why is it not better to bet on black after seen 10 reds?
