Refining the Insurance Count
The Insurance Count accurately measures the density of ten value cards (Ten, Jack, Queen, King) remaining to be dealt. This is its strength since the presence of a relatively large proportion of tens generally translates into increased expected value for a blackjack player. Its weakness is that it treats all non-tens as equal. In particular the ranks of ace, 8, and 9 are misrepresented by tagging them as -1 along with ranks 2, 3, 4, 5, 6, and 7. Removing one ace from a full shoe results in a decrease in overall EV. This decrease is closest to the decrease associated with the removal of 1 ten value card. However, when employing the Insurance Count removing one ace INCREASES the count by 1 while removing a ten DECREASES the count by 2. This suggests that the Insurance Count undervalues the ace by 3 for overall EV. Similarly we find that the 8 is undervalued by 1 and that the 9 is undervalued by 2 when comparing the removal of those ranks to the removal of a ten. Since the Insurance Count accurately measures the density of tens, in order to refine it to more accurately be able to predict the overall EV of a given shoe composition we need to find a way to incorporate this additional information into the Insurance Count. We need to keep the accurate measure of tens density while at the same time approximate the relative value of the variation of the non-ten ranks of ace through 9. We'll do this by creating a secondary non-tens count which can be combined with the Insurance Count (aka tens count) to improve the ability to predict overall EV better than the tens count alone. Below are 3 slightly differing approaches to this problem. The first leads to an improved version of the KO Count, the second to an improved version of the HiLo Count, and the third to the Wong Halves Count (with doubled tags.) The Tens (Insurance) Count is refined by creating a secondary count where the tag of a ten value card = 0 and the other ranks are tagged closer to their value relative to the value of a ten value card.
Improved KO: Tag rank order {2,3,4,5,6,7,8,9,T,A}
Tens (Insurance) Count: {-1,-1,-1,-1,-1,-1 -1,-1,2,-1} initial running count = -4 per deck
Secondary Count: {-1,-1,-1,-1,-1,-1,1,2,0,3} initial running count = 0 per deck
Improved Count = Tens Count + Secondary Count: {-2,-2,-2,-2,-2,-2,0,1,2,2} initial running count = -4 per deck
Note: 7 is grouped with 2,3,4,5,6
Improved HiLo: Tag rank order {2,3,4,5,6,7,8,9,T,A}
Tens (Insurance) Count: {-1,-1,-1,-1,-1,-1 -1,-1,2,-1} initial running count = -4 per deck
Secondary Count: {-1,-1,-1,-1,-1,0,1,2,0,3} initial running count = +4 per deck
Improved Count = Tens Count + Secondary Count: {-2,-2,-2,-2,-2,-1,0,1,2,2} initial running count = 0 per deck
Note: 7 considered to be correctly valued in the Tens Count
Wong Halves (doubled): Tag rank order {2,3,4,5,6,7,8,9,T,A}
Tens (Insurance) Count: {-1,-1,-1,-1,-1,-1 -1,-1,2,-1} initial running count = -4 per deck
Secondary Count: {0,-1,-1,-2,-1,0,1,2,0,3} initial running count = +4 per deck
Improved Count = Tens Count + Secondary Count: {-1,-2,-2,-3,-2,-1,0,1,2,2} initial running count = 0 per deck
Note: 2,7 considered to be correctly valued in the Tens Count, 5 considered more negative than Tens Count
Conclusion
The Tens (Insurance) Count can be used as a basis for more refined counts.