Changing B.S.
mickpk,
OK... now that we have more information, I would like to point out that you should modify your B.S. for this game to account for the way they handle splits and double downs.
For example, say you've won your two previous decisions and on a $1 bet you receive 9-9 vs. 6. If you win this hand, you'll be "On Fire" and thus be able to bet $100 with a 1.87% edge: in other words, if you win this hand, your next hand is worth $1.87.
Now B.S. says to split 9-9 vs. 6. In fact, you can see this for yourself if you look at Norm's data and select the "Advantages for Each Dealt Hand" table. There, you'll see that with 9-9 vs. 6 your advantage for standing is +29.66% (of $1), or +$0.2966, while for splitting your advantage is +22.49% (of $2), or +$0.4498. Since EV(split)>EV(stand), B.S. says to Split and win an extra $0.1532.
However, in your particular case, if you split I believe you have to win BOTH hands to continue your streak (by the way, if you win one and lose the other, does that count as a push overall, or does the streak reset to zero? What if you win and push? Push and push? Lots of questions, and the answers will dictate your optimal strategy). Since splitting is worth only $0.1532 more than standing, probably your best bet would be to stand on this hand, so that on the next hand you'll be able to win $1.87.
In other words, you need to develop a new B.S. for the $1 hands: the $1-B.S.
Typically, B.S. is determined by finding the E.V.-maximizing play (thus, splitting 9's vs. a 6). What you need is a Win-maximizing B.S. (or perhaps a Lose-minimizing B.S.), where your definition of "Win" is whatever the casino requires to perpetuate your streak. To get the information on your winning percentage for each hand, I'd suggest you invest in a softcover copy of Don Schlesinger's Blackjack Attack 3, which includes tables with the requisite data.
As a first approximation, though, I'd suggest that your $1-B.S. would probably include the following revisions (assuming that on Splits you most win BOTH to continue):
1. Do NOT DD on 11 vs. 7-X (you may want another hit).
2. Do NOT DD on 10 vs. 7-9 (you may want another hit).
3. Do NOT DD on 9 (you may want another hit).
4. Do NOT DD on any soft hand (you may want another hit).
5. NEVER split A's (since I assume you get only one more card on each Ace).
6. NEVER split 9's.
7. Do NOT split 8's vs. 9, X, A: just hit and pray.
8. The "baby splits" (2-2, 3-3, etc.) will also need to be calculated carefully.
These are off the top of my head... you should do the calculations yourself to confirm them.
Note that these modifications apply only to the $1 hands.
However, even for the $100 hands you have an incentive not to lose, since a non-losing hand will allow another hand with an E.V. of +$1.87. Thus, on a close B.S. play (for example, doubling A-2 vs. 5), you may find that the "future E.V." makes hitting the overall E.V.-maximizing play.
Hope this helps!
Dog Hand