You said that if a win then stay on the same level yet in your " analysis" you increased the bet. why ?
Oops! It was my mistake because you never stay on the same level,the simpler way to consider "Maxim Principle" is like "D'Alembert" BUT
instead of 1 unit up when you lose and 1 down when you win,raises by 1 unit after each bet regardless if lost or won till you are 1 unit.
Also when the next bet exceeds the amount needed in order to be 1 unit in overall,reduces the last bet accordingly in order to win just 1 unit.
There is also a variation of "D'Alembert" which called "half peak",this name is no coincidence because every D'Alembert progression needs approximately the half of the progression in order to recoup.
For example: -1 -2 -3 -4 -5 6 5 4 1 instead of -1 -2 -3 -4 -5 6 5 4 3 2 1
I consider "Maxim Principle" slightly better than "half peak", if you encounter series of 1 loss and 1 win alternating one after the other,both of them win 1 unit every second result,but "Maxim Principle" achieves this by steadily increasing bets,while D'Alembert remains on the same bet levels going one step forth and one step back.
The true difference between them can be realized when a session with many lost bets occur,the Maxim Principle could recoup easier under such occasions,while the D'Alembert the deeper it falls,the harder becomes to get out.