Very interesting gtatix,
So many times I've seen the same number come in after 1 or several spins.  With a 1 to 35 chip hit I can see this possibility.
One thing,
When do you get out.  If it lands 5, you take 5 and so on until 8 spins then ...get out and start again or not?
I see on one of the lines that 34 came in 3 out of 8 spins with 2 being consecutive.
Being a great lover of gambling...in fact my friends know me for betting on 2 old ladies crossing the road to see who wins.  I'd be interested in knowing a little more..think i will try this method out when I'm next throwing my cash at a croupier and exchanging for chips.
		
		
	 
Firstly, I devised this system entirely on my own.  I have NEVER made it public.  IT IS LIKELY NOT infallable.  It is as good to a working system as I have ever come close to seeing.
What I haven't done is choose a perfect money management methodology.  Why haven't I become rich doing this?  A couple of reasons.  One is that the closest casino to me is over 2 hours away.  To make it worth my while travelling, I would expect to make $500 in a trip - and I would need to do this 5 times a week to make a decent INCOME!  To make this happen, I suspect that I would need a $5000 bankroll.  These are the main reasons.  I am currently not sitting on this kind of money.  I have turned to FOREX because I think it can be "beaten" more easily than roulette.  I am working on it.  I could be wrong.  I would offer that given a $50,000 bankroll.  A gambler could become professional - making $1000 a day.  You would want to live close to a casino - or several for that matter.  You would wager in such a way that you could make this $1000 in approximately 8 to 15 sets.  You want to avoid the CHANCE of running into a streak of 40 misses (5 sets)  You would need to be "happy" losing a specific amount.  Perhaps 2 sets worth.  This is where the system is mildly flawed.  When do you get out - how much do you accept as a loss.  
THAT SAID:
To answer your question, you wait until 8 numbers are confirmed.  you write these 8 numbers exactly as they are shown on the print-out.  you include the repeats etc.
you bet for UP TO 8 spins on the 8 different previous numbers.  Making sure that all 8 numbers are different.  If the previous 8 have a repeat, go back to the ninth last number and use it.  If it is not different, go back to the 10th last number and use it etc.  I have had to - on occasion - go back to the 15 last number based on the fact that there were 3 within the eight the same plus a couple of the last numbers of the previous 8 the same as those or the other few.  This is where it can get a little confusing - but not mind boggling in any way.
Lets suppose you have : 0 2 17 22 3 5 33 0 12 3 33 27 21 2  as your most recent numbers.  you would choose - moving backwards - 2,21,27,33,3,12,0 AND 5 because of the repeated 33.  You would use these 8 numbers until you HIT or until there are 8 spins without a win.  If you win.  You wait for the "new" 8 numbers to run through.  Whether there are repeats or not you need not concern yourself immediately. You now place these 8 numbers under the previous 8.  suppose they are 36 14 8 27 27 27 0 19.  You would have won on the 4th spin for starters.  That is the first number 27.  After winning, you would have waited out the next 4 spins which gave you 27 again, 27 again then 0 then 19.  You have now sat through 
8 NEW spins.  You now pick your new 8 numbers.  The last 8 numbers spun were: 19 0 27 27 27 8 14 36.  You only have 6 different numbers here.  You NEED 8, so you go back further in the string which is now thus:
0 2 17 22 3 5 33 0 12 3 33 27 21 2 36 14 8 27 27 27 0 19.  This gives you - from most recent to oldest of the 8:  19 0 27 8 14 36 2 21 - These are technically the last 10 numbers in that you are skipping the 
repeated 27s for your choice of the most recent 8
 different numbers. 
You would keep this neat by having them organized on a score card like this:
--  --    0   2   17  22   3   5
33  0 12  3  33 27 21 2
36 14  8 27 27 27  0 19
You will always have 8 in a row - repeats or not.  You will simply count backwards from lower right back to get your new 8 numbers.  If you are number crunching - like I have done - you get to see this quite easily and quickly.  You will notice the great numbers of occurences where there are repeats within a few spins.  This is another thing I had noticed.  With extensive testing, it appears that the "8 for 8" is the best method.  I had also looked at "continuous 8"  meaning that each new number cancelled the FIRST or OLDEST of the 8 numbers and one would just bet constantly on the last most recent different 8 numbers each spin.  I even used BOTH to make an ultra safe wager but I won't even go there at this time - if ever.  This is the best I have managed.  I call it EIGHT FOR EIGHT.