Without the green and assuming a fair wheel, the chance of red or black on any given spin is 50/50, irrespective of whatever sequence of results preceded the current spin.
Each spin is an entirely random and independent event, the previous spins of the wheel 'don't exist' in terms of exerting any influence whatsoever over the current spin, or changing the probability of any given result.
Try this as a thought experiment, you have just seen a roulette wheel spin ten blacks in a row when someone walks in off the street into the casino, so he has no idea what the last ten spins were.
He bets on black, you bet on red, do you have a better chance of winning with your bet on red than he does with his bet on black?
This is an age old mathematical problem that has never really been explained. In games of chance, people often forget the time aspect as well as the 'in the moment' odds which you correctly state are 50%. The odds of spinning black 10 consecutive times are 1024/1. The odds against 11 times are 2048-1. So the perspective of the guy walking in from the street is a simple 50-50 as you say. The guy in the casino's perspective is that for black to come, it's going to stretch an already unlikely sequence to a very unlikely and far rarer event so he is essentially correct to back red.
This was researched once, a game show where the winner had 2 picks from 3 boxes to get the main prize. As you know, chronologically (irrespective of whether you name the boxes A-B-C or 1-2-3) there is a 67% chance the contestant will have the car keys in the first two boxes he picks in time. The research demonstrated that if the these were laid out in a line, and the main contestant had picked the left box first (going in logical reading sequence L-R) and it was empty, then a new person was sent in with the two boxes remaining (with the perception of a 50-50 chance obviously) and was told to pick the middle box or the left one of the remaining two in other words, he would 'win' 67% of the time, thus defying the apparent 50-50 odds.
A good example is the fiendish DOND game show. You can check this out yourself. There is a 22/1 chance at the start of the contestant picking the premium £250,000 box. Every show. In the instances where the £250,000 box was still present when players were down to the final two boxes, purely mathematically the perspective of the onlooker is that there is a 50-50 chance of the contestant having it on the table. Then consider this was unlikely at the start. The banker offers a swap to the player. Over time, the correct thing to do would be swap, but of course from the player's perspective having had it and then given it away would be unbearable afterwards so they tended (when brave enough) to open their own box. Let's just say this went badly over the series for the reasons above.
It's very tempting for people like you did in your post to see odds and individual events/choices in purely binary black-and-white mathematics. Alas, although not always quantifiable and explainable, sequences and time DO affect these seemingly simple calculations. There was a Canadian mathematician who observed this sequence factor in new national lotteries. After the first 20-30 draws he would identify numbers which hadn't come out at all, or only once or twice and suggested these would be more likely in the coming weeks (despite, again, the seemingly unconnected and random nature of each individual draw) and was right, every time. I even saw this on the UK lotto when it started in 1994, I got a few tenners after the start when I noticed a few of the '8' numbers like 18, 38 etc. were hitherto very scarce. So I backed those until they balanced out and did better than I would expect randomly.
The reason apparently is that due to the huge permutations and combinations with drawing 6+ numbers from 49, the odds against certain numbers having a huge differential in frequency after a certain amount draws gets progressively higher and hugely unlikely! Yet these draws are seemingly independent, unconnected to us. He did explain that his observations were less and less relevant as the lottery 'matured' and had run for so many years.