"true counted" unbalanced insurance count,
IRC(initial running count)=-4*(number of decks)
count tag for non-tens are +1
count tag for tens are -2
when 6 deck, total 312 cards.
C : number of cards dealt
N: number of non-ten cards dealt
T: number of ten cards dealt
number of cards in shoe = 312-C
number of decks in shoe = (312-C)/52
RC=-24+N-2T
N+T=C
probability of insurance win = P
after some calc,
TC=52*(-24+C-3T)/(312-C)
then (52+TC)/156=
by computation,
=(96-T)/(312-C)
this is equal to density of ten cards in shoe =P
Kelly optimal insurance bet = BR*(3P-1)/2=
by computation,
=BR*TC/104