I'm baaaaaaaaaack....
"Can we show mathematically that some sort of Martingale fares better than their AP art they boast of?" - No, but we can show mathematically that a Martingale has a long-term negative expectation, while advantage play has a long-term positive expectation. It doesn't get simpler than that.
Long term negative expecation if ONLY martingale is used. My new system is a 'generalization' of the current count along with martingale. So , a bit of a combination of the 2.
Lets face it, even if you're a perfect card counter at times it's a complete waste & your winnings could be minimal at best. meanwhile, you caused yourself an extreme migraine in the process.
Combining 2 important
safeguards along with martingale could be your saving grace.
#1 try your best at getting a reserved table. (it's the easiest way to count and/or generalize)
#2 KNOW when to use your reshuffle...You usually only get 1 per day anyway. (most casinos) If you are seeing high cards galore and you just lost 5 hands in a row...don't worry about the money you just lost...RESHUFFLE !
#3 Generalizing the count is much easier than counting. Much less straining and less noticeable as well by the pit bosses. You may be off by as much as + or - 3 or 4 when Generalizing... but that means nothing compared to how you COULD lose 5 hands in a row when the count is +10 in your favor.
I spread my martingale out, and have 2 instances in which I play the same bet amount if I lose. If I lose 8 hands in a row, i'm wiped out... But as long as you GENERALIZE correctly and ask for that RESHUFFLE when needed, you'll be alright. (most of the time) You will still lose 8 hands in a row occasionally regardless....but in the long haul you should be on top.
any douchebags that disagree with me are just hard-nosed , book readers , that don't believe in anything except what they've been taught in their reading literature. (and don't have a mind for themselves..or don't have the experience in terms of years of playing blackjack)
I've lost 15 hands or more in a row 5 times in the last week. Enough said.
once again, plain martingale on it's own will give you horrible streaks like these at times.