No Bust Strategy
I did an analysis of this game back in 2000, for two slightly different variations. The basic strategy house edge for the two games where 1.23% and 1.99%, so you're bucking a pretty hefty edge to start with.
I can't recall the exact rules without doing some research, but I recall that these "no-bust" games allow a push if the dealer busts with a higher total than the player busts. Blackjack pays even money. There are jokers that make any hand twenty-one, and Joker,Joker pays 2:1.
Though the specific rules obviously matter, here's a summary of the best strategy for the first game I analyzed. The main differences between this and regular blackjack strategy are hitting 12s and 13s,
and splitting 9s vs 7.
Surrender:
Surrender hard 13 to 17 vs Ace.
Surrender hard 16 vs Ten.
Hard Totals:
Double 9 vs 4,5,6.
Double 10 vs 2-8.
Double 11 vs 2-9.
Stand on hard 17 or higher, except hit 17 vs Ace if you can't surrender it.
Stand on hard 15,16 vs 2-6.
Stand on hard 14 vs 3-6.
Hit 13 or less.
Soft Totals:
Double A,3 vs 6.
Double A,4 & A,5 vs 5,6.
Double A,6 vs 4,5,6.
Double A,7 vs 3,4,5,6.
Stand with soft 18 (except doubles above) vs 2-8, hit vs 9,T,A.
Hit soft 17 or less.
Pairs:
Split (A,A) except vs Ace (Split vs 2-T)
Split (2,2) & (3,3) vs 2-8.
Split (4,4) vs 5,6.
Don't split (5,5) or (T,T).
Split (6,6) vs 3-6.
Split (7,7) vs 2-7. (Surrender (7,7) vs Ace).
Split (8,8) & (9,9) vs 2-9. (Surrender (8,8) vs Ten or Ace)
If these games are still widely played in California, update me with the latest rules, and I'll consider adding them to the Basic Strategy Engine.