## Method to Derive Perfect Insurance (any counting system)

This method shows how to get perfect insurance from any counting system. It requires maintaining 2 simultaneous running counts. I'm not sure I could now do this in a real game but I can see that I may with practice. When I played I found that I could keep a side count of aces for 2 decks but gave up on this for 6 decks.

The method involves defining an insurance reference count that is relative to whatever your count is. When your count's running count equals the insurance ref running count then insurance is an even bet. When your count's RC is greater than insurance ref RC then insurance is +EV.

The signs of the tags I use are such that when a negatively tagged card is removed RC becomes more positive and vice versa for a positively tagged card. Reversing the tag signs would make no difference as long as application is consistent.

Insurance ref count tags are obtained by subtracting insurance count tags from your chosen count's tags.

Count              Tags (A-T)                        Initial running count
Insurance count    {-1,-1,-1,-1,-1,-1,-1,-1,-1,2}    -4 * decks

HiLo               {1,-1,-1,-1,-1,-1,0,0,0,1}        0 * decks
HiLo Insurance ref {2,0,0,0,0,0,1,1,1,-1}            +4 * decks

KO                 {1,-1,-1,-1,-1,-1,-1,0,0,1}       -4 * decks
KO Insurance ref   {2,0,0,0,0,0,0,1,1,-1}            0 * decks

Below is example of 18 specific cards drawn from 2 decks. It shows RC pairs (HiLo RC, HiLo ins ref RC) and
(KO RC, KO ins ref RC) following each of the 18 drawn cards. **Specific example is player hand of T-6 versus A following first 15 cards drawn.
Positive insurance EV is indicated when count RC (1st number of pair) > ins ref RC (2nd number of pair) for both HiLo and KO examples.
Any other count would show same result. Method works for any number of cards drawn.

Cards drawn: T,6,5,9,8,A,T,7,2,8,3,A,9,5,3

HiLo     KO         Ins EV
IRC  0,8      -8,0       neg
T    -1,9     -9,1       neg
6    0,9      -8,1       neg
5    1,9      -7,1       neg
9    1,8      -7,0       neg
8    1,7      -7,-1      neg
A    0,5      -8,-3      neg
T    -1,6     -9,-2      neg
7    -1,5     -8,-2      neg
2    0,5      -7,-2      neg
8    0,4      -7,-3      neg
3    1,4      -6,-3      neg
A    0,2      -7,-5      neg
9    0,1      -7,-6      neg
5    1,1      -6,-6      0
3    2,1      -5,-6      pos

T    1,2      -6,-5      neg
6    2,2      -5,-5      0
A    1,0      -6,-7      pos**