Yes. All exposed cards and every seen card has been counted at their proper weight for perfect insurance. It doesn't matter if they are in your hand, in the discard tray or on the table.
The counts that have neutral cards and miscounted cards can be made more accurate with adjustments to improperly weighted cards by tag. Once adjusted situations are no longer part of the general situation the general index changes because those situations that were adjusted are no longer part of what is left. That changes the average of the set of situations in the general set. If you weighted all the situations in Caraculo's post by frequency and averaged them their indices will add to the general index.
In my opinion the better way is to tag tens as +2 and non-tens as -1. Then by knowing the number of tens/non-tens remaining to be dealt, the running count can be computed without regard for number of decks.
Examples:
36 non-tens(-1), 16 tens(+2) ---- running count = 36*(-1) + 16*2 = -4 (happens to be starting composition of a single deck)
72 non-tens(-1), 32 tens(+2) ---- running count = 72*(-1) + 32*2 = -8 (happens to be starting composition of a double deck)
8 non-tens(-1), 5 tens(+2) ---- running count = 8*(-1) + 5*2 = +2 (no matter how many decks at the start of a full shoe)
Mathematically when a negative card is removed, minus a minus results in a positive so running count increases. When a positive card is removed, minus a plus results in a negative so running count decreases. In tagging non-tens as +1 and tens as -2, removal is the only consideration. Tagging like this is relative to what has been removed whereas reversing the sign of the tags is relative to what remains to be dealt and includes a way of computing a starting point.
Either method works but I prefer the first way.
k_c
I understand your point of view, but to me, this is a straight counting concept. The cards fall, and you count them as you seem them. If you WANT to take insurance, non-tens are plus, tens are minus. You reach 4 x the number of starting decks and you insure; you're not yet there, you don't. Simplest possible way, no?
Don
Just about the same thing - start out count at -4 * (number of decks) and insure when (running) count is above 0. (Count at 0 is zero EV.) As you say when a non-ten falls running count increases by 1. (Removing a minus card adds to running count.) When a ten falls running count decreases by 2 (Removing a positive card running count decreases.) It's just about how the sign of the tags is defined.
k_c
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