Just about everyone on this board is aware of the D'Alembert, which starts at 1 unit and increases by 1 after a loss and decreases by 1 after a win.  The theory is that if you lose at 1, lose at 2, win at 3 and then win at 2, you will have won 1 unit for each win that you have had (the 3 won offsets the 2 lost and the 2 won offsets the 1 lost).  Anyone who has taken it for a spin knows that the streaky nature of roulette can turn against us quickly, with a series of losses taking our drawdown to steep levels quickly.  However, we know that a balanced number of wins and losses gives us a bunch of +1 wins equal to the total number of our wins for the session, with the wins at high points to offset the lower losses.

It is great that the +9 offsets the -8 and the +8 offsets the -7.  What is even better is when a +9 offsets the -8 and +9 also offsets the -7.  If a win on a D'Alembert is always at a recent high-water mark, so is a streak of wins back to back.

What I am doing with this progression is moving up on a loss like the typical D'Alembert.  If I get a win, rather than dropping a unit down, I repeat my bet.  If I lose, it is a wash and I repeat again at the same level.  However, if I get a string of wins, I let them continue winning at this high level for as long as the wins come.  I stop betting only after my first loss.  For instance, if I am at level 9 and I hit a string of 5 wins and then a loss, I have effectively won 9 units a net of 4 times.  This is +9 against -8, -7, -6, and -5, meaning that I have netted +1, +2, +3, and +4, or a total of +10 instead of the usual +4.  At this point, I will reduce my betting level by the net wins (4), meaning in the example I would begin betting again at level 5.  If I lose again, I move up to 6.  If I win at 5, I repeat again as before and look for another profitable streak.

Variation:

What you will notice is that a series of chops is nothing more than a wash in this method.  In the typical D'Alembert, each chop is a +1 unit for your bankroll, such as +9 -8 +9 -8 +9 -8.  The same can be accomplished with this method by decreasing after the first win and then holding at the next level down for the remainder of the streak.

Bringing this over from the other board upon request:

This is based on the series of discussion concerning the minimum of 4 repeats over the course of a 37-spin cycle and how to play that information.  It is based on the expectation based on the above statistic that one of the dozens will have at least 2 repeats over the course of the 37 spins.

Bet selection is as follows:

Track all spins until you have your first repeat.  This could happen on the 2nd spin or on the 20th.  Just keep tracking all results until then.  Upon the first repeat, whichever dozen the repeat occurred in becomes active.  You can't possibly get your second repeat in a dozen until your first has already shown, and now it has.  Every number that has appeared in that activated dozen now becomes a potential second repeater for that dozen.  This could be as few as a single number, it could be as many as 8 or 9.  You will bet every number with the money scheme as described below.

If a second (or even the third) dozen show a repeat, then all numbers in those dozens also become active as potential repeats without diminishing the possibility in the original dozen.

When you get a hit, you will delete all the spins up to and including whichever spin was the earlier of your two repeaters in a dozen.  If on spin 7 you get a 11, spin 9 a 6, spin 13 a 6 (activating this dozen and the numbers 6 and 11) and on spin you get your win with an 11, you would erase all spins up to spin 7.  If you won with another 6, you would delete up to spin 9, making 11 no longer an active number.

After a win, you need to reevaluate what numbers disappeared, as the missing numbers may inactivate one or more dozens or numbers to be bet.

Money management is as follows:

You will bet 24 units on every spin, evenly divided between the total number of spots covered and rounded down.  If you only have a single number to cover, you will bet 24 units on that number until other numbers become active.  If you have 5 numbers, you would bet 4 units on each (24/5=4.8, rounded down to 4).  The maximum number of spaces covered is 12 (2 units apiece).  Beyond 12, I choose to stop betting and the table get this little burst of random out of its system.  Any more than 12 spaces would require a single unit bet according to my rules and would not pay out at least 24 units (another spin for later), so I don't chase it.  There is no progression - 24 units (or less when rounding down) on every spin, win or lose.  My suggested session bankroll is 1008 units (42 * 24) to get through some nasty stretches.

When you hit a single number with 24 units, you win 840 units.  A hit with 2 units on 12 spaces nets 48 units up. 

There will be some staggering wins (I won a 840 and a 420 within 7 spins of starting a session the other day) and some incredible drawdowns, although I have not busted a session yet.  This is not a method for the faint of heart - you need money and risk tolerance/discipline.  This is actually not the sort of method I would play myself, but for that sort of gambler, it has a LOT of potential.