Yes this definitely makes sense. I guess maybe what im getting mixed up is related to you even saying it hitting 9 times being an unlikely scenario meaning its really not supposed to hit 9 times in a row thus showing it being less likely to hit the same side over and over no? Definitely a mind bender although i do get its just 50/50 each flipI think (some) people are confusing the a priori expectation with the actual outcome.
Let's you and I play a game. You will flip a (fair) coin exactly 10 times and I win if it lands on heads all 10 times.
A priori (a statistics term meaning before the event or game has started) my chance (ie probability) of winning is exceedingly small. The exact probability can be calculated using the Binomial distribution (@RainmanTrail Help????).
After the first 9 trials the result has been all heads (itself a very unlikely outcome but here we are). My chance of winning the whole game is now 50% (i.e. the 10th and final coin flip is a 50/50 chance). However unlikely I am to be in this scenario to begin with, the next coin flip is independent of what preceded it. This holds true (obviously) for rolling a die (1/6), black or red in Roulette (making these tracking systems somewhat curious), or hitting my two outer on the river (~5%).
Would you have predicted I would have won before we started? Probably not. Would you bet with me for the final flip? Probably.