Hey Ethan,
No problem, I'm interested to see how it works myself.
If you start with 20/20/20/20 and you win Game 1, then as you say, you would be at 20/20 for the next series. It basically just means that you're that much closer to clearing that line. Your next bet would still be 20+20=40. So let's say you're at 20/20 and you won the next game you bet then you would have cleared that line (gotten rid of all the numbers on that line). I am increasing the bet every time I clear the line. So I would start the next line as
25/25/25/25. Now my first bet is $50 instead of $40. The next time I cleared a line I would be at 30/30/30/30. Let me know if any of that doesn't make sense.
I'll use an example to explain the difference between this and the chase you describe. Let's say for simplicity that every bet we make is +100, so if we bet $20 we would get back $40 on a win (our original $20 plus the $20 we won). So let's look at a situation using a normal chase in which things didn't go so well.
Let's say we're chasing a 3-game series and we lost all 3 games (starting with a $20 and assuming $20=1 Unit). So we would have bet:
$20 on the first game
$40 on the second game (to win the $20 we already bet plus 1 Unit)
$80 on the third game (to win the $60 we already bet plus 1 Unit)
So far we've spent $140 and at the start of the next series we have a serious decision. Do we simply take the $140 as a loss, or do we keep chasing in order to try to make it back. Depending on your bankroll continuing to chase could get pretty expensive.
We could spend $160 on Game #1 of the next series and possibly $320 and $640 on the next two game. However, let's say we lose Game 1 of the next series, but then win Game 2, so we're up $20. However, the scary part is that before the win in Game 2 we were down $300.
Now let's take a look at what would happen using Labouchere:
Let's use a 10/10/10/10 line so that our first bet is the same as the other example, $20.
$20 on the first game (line is now 10/10/10/10/20)
$30 on the second game (line is now 10/10/10/10/20/30)
$40 on the third game (line is now 10/10/10/10/20/30/40)
$50 on the first game of series 2 (line is now 10/10/10/10/20/30/40/50)
The first thing we notice is that we only spent $140 on the four losses, compared to the $300 in the first example. So we're not risking nearly as much. Our next bet would be $60, if it won as it did in the first example, we would now be down $80.
But wait, the key is that since our line has been keeping track of our losses, we will eventually win back everything we lost on the first series without risking nearly as much.
Let's say we go on a hot streak and win our next 3 game 1's. In our first example we would be up the original $20 we won, plus $60 from these 3 wins for a total of $80.
In our Labouchere example our line is currently 10/10/10/20/30/40.
Our next 3 wins would get us $50, $40 and $30, so our current profit would be -80+50+40+30=$40.
And now that we've cleared the line we can move up to the next level of 15/15/15/15.
So even though we didn't make quite as much as we did in the straight chase, we didn't risk nearly as much. I have done a couple of straight chase systems and quite frankly, there were times when it scared the crap out of me. Using the Labouchere system the chase is far more conservative and hoping it will be less stressful. Plus, once you clear a line, you can move the bet up to make more money and hopefully you have the bankroll to cover it from your previous wins (since you had to win to clear a line).
So to summarize, even though I'm new to the system, I think the benefits will be that we won't risk nearly as much as a straight chase, and are still guaranteed to win our losses back. Plus it sets up a system in which you know you're safe to increase your bets because you have just won money on your last line.
Hope this helps, let me know if you have any questions and obviously others are welcome to add comments since I'm very new to this system.