My position, to avoid ML and etc. deciding to attack their versions:
Given any size shoe, rounds taken from any depth, excluding hands that involve the cut card or reshuffling, are going to average the same expectation using basic strategy.
A round dealt one deck in, and a round dealt one deck from the back, are going to have the same expectations on average. Counting the cards, up to the round one deck in, and extracting the true count, will result in exactly the same correlation to results, for both the deep and shallow rounds, they are part of the same remainder.
The tendency for any true count is to overestimate the player expectation at both extremes, high and low of the true count distribution. The average expectations, when grouped with each actually seen true count, are going to show that the middle range of true counts underestimates player edges and overestimates the more extreme.
Actually seen true counts are discrete; they obey this rule: For N=all integers including zero, a true count at a given number of cards left can only have these values: N*52/(#of cards left unseen).
Analysis of simulations often has ignored this despite warnings from myself, T-Hopper, and Gwynn and Seri. When you round observed true counts in reporting a sim, deep into the pack the average true count for a range has crept upward; so the edge reported deeper is actually for higher true counts.
Now if you count the cards that are between the true count for the start of the shallow example round above, and the start of the deepr round, the edge for those rounds has never changed. The true count has gotten higher in amplitude and more of its distribution is in the ranges where the count's prediction of edge is distorted. A new averageing of observed edge versus TC thus results in more bow effect; it grows deeper with more cards being counted before a round. But the edge per round is exactly the same.
Now we come to the lies told by the clone opposition to truth:
The rounding error is the only effect that raises the edge for all true counts. Schlesinger on rge21.com, "clearly the edge for every true count is shown to rise." Contrary to this is Griffin's clear description of the bow effect where, in later editions of TOB, he clearly says that what is gained at middle range counts is lost at more extreme counts.
Parker here and on rge21.com, "Clarke and Frank would make a great team;-)." The rounding error is real; no one here can really tell if Frank is for real with his claims of the "FLAW." You only have to followup on the hints in the email I got, that I quoted below in another post, and go back to the orginal pages of Blackjack Forum, that did NOT, make it into Blackjack Attack, from Gwynn and Seri on this. G&S clearly made sure that every time they reported on observed true counts in a simulation report that they included mention of how each reported true count was grouped. Some of the reprinted simulation reports in BJA are altered from that format. It also coincides with the decision of Gwynn and Seri to step asside; making the role of these two investigators to go with other collaborators and not to participate with Schlesinger very interesting.
Parker here claiming that he never received or busted any post which was in favor of my views of the FA. You have message #14245 from the Sissyphus Project and the post here from alienated/Ted to directly refute this. I recieved over 100 emails expressing support, where about 30 reported that they attempted to post support on rge21.com and were post busted by Parker. Ted/alienated's posted comments here are being very kind to Parker in that his posted messages on the CCC indicate that he might have actually posted afterall, by hesitating on the post button, even though now he says his intention was to bailout. IMHO he is simply being a gentleman and taking every possible step to give Parker the benefit of a doubt.
I have interpreted T-Hopper's discovery that Playing Efficiency can be far more important than expected as evidence that the general effect of playing index gains is to straighten out the bow effect. Your playing gains, as is postulated by clone but still strong thinker never the less, ETF, limit how the player's edge tops off in high counts and drops in lower counts. This breaks the balancing act that creates the bow effect in the first place. It also creates more extra gains than can be explained by the playing index gains alone. I explain them as the playing gains stopping the normal bow effect related drop-off.
Unfortunately T-Hopper is not available to comment. In financial straights he signed to play with DD's team. His agreement to play with that team was altered after the fact to limit him to simple spotter and player wages for one year, where he was not to be allowed to reinvest and parley his share in any new bankrolls. Like all of us T-Hopper has used several AKAs and not all of those AKAs have been totally free of criminal history. Be careful from who you get new ID materials. T-Hopper also objected to the frequency of travel that DD imposed. T-Hopper had to of necessity not report all of his AKAs for player card rebate purposes. DD has made several claims that one of his players ripped off his team and one of his players had violated an agreement with wage only players to give the team player's card moneys, and have player card comps deducted.
The potential is obvious. Free T-Hopper!
Finally there is the ML claim that because the mean decks for true counts of zero are the same as more complete packs (ie an single deck at TC=0 at one deck left, a double deck at TC=0 with 2 decks left etc.) that this still means the strong version of the FA claims is true despite the rounding error etc. As an exercise for the public to confirm the figures I will give, just look at how often a deck dpeletes to a condition where the denominations are exact 1/13 (non tens) and 4/13 (tens) configuraton. Less than 3% of the time a one deck game will come to this at any point 3/4, 1/2, 1/4 etc. Less than .06% will a double deck come to this. In shoe games it is a miniscule probability for the mean to be absolute. All other TC=0 decks have the distributions that I have outlined above. There simply is no strong version of the Floating Edge to hide how the clones have mixed in the bow effect with this rounding error. The only such FA component is a very very weak tendency I posted on in my Quantum post below.
The dangers of this new FA myth created by the clones should be obvious. Instead of following T-Hopper's lead and re-considering the i18 and going for more playing gains, one is encouraged to use new betting ramps for deeper dealt games. IMHO this is not only going to cause a bit of over betting, but it is going to make worse the normal tendency for all of us to have our higher bets out deeper into a game. For nothing whatsoever you are being encouraged to put yourself subject to more heat.
Those are the facts. Now bring on the insane excuses and non-rebutal rebutals. I am just plain the hell correct on all of the above and that is that!
