Nice post Danny.
I have just 2 comments:
. . .what is the math behind this? . . .
Probability. By computing the probability of winning the various hands and applying that probability to the payoff involved in a win, you can determine the house edge.
I think most strategy charts for blackjack are created using simulation, rather than analytically computing the probabilities. Play each situation enough times with randomly shuffled cards and find out what actions work best on average.
While this is correct strategy when the dealer stands on 17, at bitzino the dealer hits on 17 so the proper strategy at bitzino is to double in this situation.
You mean "soft 17" here I think. i.e. if the dealer has 7/17 (like A6, or A24). If the dealer has a hard 17 (89, say) he always stands, under all sets of rules.