The system Bruce Irwin explains and recommends, is the Labouchere betting system (also known as the Cancellation system).
However, at the end of his book he gives a warning, which makes this system worthless! He says:
"I have found that rather than stick to one color all the time, if you find you are loosing more than winning switch back with the wheel or table for a few spins, or switch against the wheel or table until you pitch it up again. I have found that a lot of people get attached to red or black, odd or even, and if at first they have a good winning streak, they will continue to play the same way all the time. Remember this, because black or red, odd or even, has been lucky a few times, this does not necessarily mean that it will always be lucky. To break that habit before it becomes difficult, learn to switch rather than play all the time on one color or odd and even."
Switch colors! But when? That's precisely what nobody can tell.
If one knows when to SWITCH colors, it will not be necessary to use a betting system at all.