Point 1:
The disagreement was not on whether the TC is a constant or not, of course the TC would be constant for both cases, however the disagreement was on the divisor for the true count. BA is advocating that for 8 deck show if TC was 4 after 2 decks, i missed 2 decks, came back the TC would be 4 (so far so good), to get the RC multiply by TC by the divisor (4), this is where we disagree the divisor should be 6 and not 4, because the TC divisor should include ALL nonseen cards, NOT the remaining cards.
Point 2:
The purpose of the sims was to show that all the INFORMATION we have when we are counting cards is contained in the running count and the number of unseen cards. All 3 sims yield the same SCORE (within the sim standard error, the second decimal will not match for 500 million hands) which shows what i have mentioned several times: missing cards during a shoe has the effect of reducing the effective shoe penetration, for instance turning a 91% game into a mediocre 50% penetration game.
Point 3:
The TC theorem has nothing to do with the sim results. The sim results are so because the information you have with card counting is contained in the running count and the number of unseen cards (TC divisor) The TC is the same because your RC and DIVISOR DON'T CHANGE when you miss cards during a shoe and come back to the show to play, not because of the true count theorem.
Again again, the TC theorem states that the cards played during a round must be SEEN and COUNTED, if they are not you can't use the TC theorem.