Let me preface by saying I'm not good at math. This question is purely from a mathematical standpoint. Thanks very much in advance!
Ok, so lets say I want to calculate the odds of a roulette wheel landing on red or black based on the last $10$ rolls. I realize that every roll is independent of each other and each roll has a $50\%$ chance of landing on red or black (assuming no $0$). But how could I calculate the probability of rolling a red or black on the $11$th roll if I know the previous $10$ rolls?
For example if the last 10 rolls had $5$ reds and $5$ blacks, I'd assume the $11$th roll would be a $50-50$ chance since there were an equal number of reds and blacks for the previous $10$ rolls (please correct me if this isn't correct). What if there were only $1$ red and $9$ blacks in the last $10$ rolls? How would I calculate the probability of getting a red or black on the $11$th roll? I'm assuming there's some kind of formula I could use to calculate this right?
Best Answer
Based on the rest of your question, respectfully I don't think you understand.
What this means is that the previous outcomes do not matter. At all. As in you could have a hundred reds in a row, and the probability of red on the next roll doesn't change.