I have been accurate but only hinting at what is wrong with ML's proof.
What is really wrong is actually simple. Every time a round is played that subset, of the total reaminders of the original pack, has a definite mean basic strategy expectation, which is the same as the mean of the subsets of each round that will be played from that point.
So you have E(R) for the edge of the total remainder subset, and E(r) for the subsets for each round.
You apply what ML called Theorem II to the edges E(r) and not the edges E(R) as he did.
In no case is there a reversion to the means that excedes the tendency of deeper penetration to result in a trend where the edges increase.
But the true count attempt to measure E(R) is subject to the accumulated divergence from prior means, growing the same way that the true count grows, division by the decreasing number of decks left. Hence the bending of the bow effect increases with penetration.
What I termed Theorem III is the consequence of Theorems I and II applied to different sized groups of E(r).
