Excellent suggestion!
getting a good understanding about gambling in general, the concept of positive and negative expectation, etc, before even learning to count
I like to suggest The Mathematics of Games and Gambling by Edward Packel. It combines just the right amount of history, fun problems, and discipline. Important to know that brilliant mathematicians spent their lives and fortunes getting it wrong so we can get it right.
Another excellent intro is Oswald Jacoby on Gambling, written by one of the greatest (if not the greatest) card players, alive or dead.
If you really had to struggle through high school algebra, I'd suggest reading Lady Luck by Weaver, before tackling one of the above. A really breezy romp through the elements for everyman (but not enough preparation for serious gamblers).
All of these books have sections discussing the fallacy of betting systems (progressions). Perhaps the shortest proof on this is in Elementary Probability by none other than Ed Thorp, but I hesitate to recommend this, unless you're a math major.
Some of these may be out of print, but they are all attainable in this wonderful age of the internet.
I think even a skilled counter who knows 200 indeces is doomed to failure without a certain amount of understanding of some general principles. There are too many ways to go astray.
Wise words.
ETF