Whenever you start talking systems like Singer's it is time to stop
talking complex math & follow the above. Even in Roulette, where the
martingale got its start, the same applies. If red has not come in 10
spins the odds are still 20-18 (2 zero wheel) against it this time.
Raising your bet to recover those 10 losses might now require an amount
exceeding the max bet allowed so you are out of luck. If you lose 10
hands of VP in a row the same rule applies. Going up in denom to
recover is foolish to the extreme.
BJ is 1 game where the rule does not apply as your chances of winning
rise & fall with the number of tens & aces remaining. That is why the
system of counting is the 1 system that works. That is also whycasinos
panic & toss innocent people.