double again blackjack

i sometimes play in a casino that has an extra double rule.
with your any first card, after doubling down, you may put one more your original bet you double again.
for example you have 8 vs 4 for a 100 dollars bet, you double, it comes a 2 now you put 100 dollars more and take a third card.
no more double after that.
what would be exact strategy for this casino.
i myself play basic strategy + double again soft 13 14 15 16 17 18 vs 4 5 6
double again 12 vs 7 and 8
double 7-8-9 vs 4-5-6
Can anybody calculate exact basic strategy, thanks.
(by the way, it is six decks, no hole card (you lose all your doubles, splits if dealer has bj), double after split ok, double any two card stay soft 17
early surrender against ten, no surrender against ace)
also another question, this casino has very bad penetration, like 50 percent other casinos without double again
have like 65-70 penetration. for a hi lo counter, which casino would be better in the long run.

Can you re-double for less?

Quote: neryervas

...for example you have 8 vs 4 for a 100 dollars bet, you double, it comes a 2 now you put 100 dollars more and take a third card....

In your example, do you mean you have two cards which total to 8 (such as 3,5) vs 4 for a 100 dollars bet, you double and get a 2 as your third card, and put 100 dollars more and take a fourth card? (Edit: I see from your strategy that you did mean this.)

I would double 8-11 vs 2-4, 6-11 vs 5, 4-11 vs 6, 9-11 vs 7-8, and 10-11 vs 9. And I would soft double 13-14 vs 2 and 13-18 vs 3-6.

I would do these second doubles: 10-11 vs 2-4, 8-11 vs 5, 7-11 vs 6, 11-13 vs 7, and 9-12 vs 8. And I would do these soft second doubles: 14-17 vs 2-3, and 14-18 vs 4-6.

no redouble for less, but you can double for less the first double and redouble less the exact amount.

for chesterdog: that is exactly what i mean, you have two cards and one unit bet. you double you get 3 cards and 2 units bet.
if you choose so you redouble you have 4 cards and 3 units bet.
thanks for info.