I am interested in probabilities regarding roulette. I know only the most basic rules apply to this game and each number and spin of the wheel is independant. So I dont want to go into much detail cause my math skills are good, but my knowledge of the subject is limited.
I want to compare it to a coin toss scenario cause its easier for my little brain to understand. Assuming a fair coin. If tossed once has the same chance of landing heads(H) or tails(T) 50/50. Of course like roulette, each coin toss is indepandant of the next. I know this so there is no need to point it out.
However, stastically speaking, if we flip a coin an unlimited number of times, and somewhere in that number it decided to show 8 heads in a row (still assuming its fair), is there not now a much higher chance that the next one will be heads.
If not why, or if so why, either way how can I calculate the odds of this situation.
Before answering, consider one further point. If you as a mathematician, were forced to bet (life of death, literally no choice in the matter), given the conditions above, which side of the coin would you bet on, and why. Explain with maths if possible.
This is my edit: First thank you kindly for your answers. I have 3 so far, all of them doubt the fairness of the coin. Lets forget its a coin at all, I would even say put in a machine that is truly random, but then someone is going to tell me that it uses a formula and therefore cant be truly random, it is therefore psudo random.
So lets forget the coin and machine, and use a magical harry potter device with 2 sides that definitely always is truly random, no matter what.
Assume it is truly random and fair
Given an unlimited number of flips, this possibility will happen eventually. Imagine it did, and your life depended on the correct answer.
How would you bet and why.
One last edit (Independance):
Many people answering questioned the fairness of the coin. This as mentioned above is unquestionably that the coin must be considered fair.
One answer below by "tskuzzy", highlighted the key phrase "Independance". I never said anything about independance. In fact, I did make a point of saying an unlimited number of times and somewhere it decided to show 8 heads in a row.
Given the only thing in question is the independance of the throws, it is quite safe to say something like "well the last 8 times it came up heads, lets group it into a set of 10 throws which means it came up 8 out of 10 times heads, therefore twice only tails" Or even equally safe to group it such "The last 8 times it came up heads, lets group it into a set of 20 throws which means it came up 8 out of 20 times heads (assuming you know for sure this was the case. i.e. that no other heads were thrown prior to the 8 in a row)".
This brings probabability back into it. Which was the point of the question. Otherwise gambelers falacy theorm definitely applies. So does it still apply or not?