"Note here that the size of the bankroll does not matter."
-That applies only to example case 1. When players live longer than
one round the bankroll does matter.
"You can't designate that everyone will die."
-All players do have finite lifetime. This is a relevant point that
shouldn't be ingored in BJ calculations. This "lifetime" of course
has a biological upper limit, but may also be more finite for many
other reasons. (One nasty example reason being casino backoff.)