Look for the unexpected: The Mandelbrot set arrises out of
bounded outcomes and the reinteration of those boundaries proving to be complex. For Blackjack there are few such bounds.
But here are a few of them at random:
A good example would be if a prgressionist were to look at the True Count Theorem and decide that he can start his progression at the first time that the count is high enough to have an edge.
The TC will tend to remain the same, but the progressionist will be forgetting that the TCT exists only because the average path of the running count is a straight line toward zero at the end of the pack for balanced counts, as the mean of an unbounded random walk. This is because of the following paradox: it is the random walk itself that causes the average path to sum to the straight line.
The progressionist is looking at a totally unbounded condition, and treating it as a bounding condition. Because the random walk of the running count is indeterminant except for origin and destination-- it is a random walk--the only thing that can be plotted about it is the origin and destination. Thus the True Count Theorem does not provide any boundary condition.
The cut card effect though does provide a boundary condition where rounds that use more cards, result in higher counts for new hands, and less probability of those higher count hands because the rounds that lead to higher counts push you more toward the cut card preventing a new round. The effect is more pronounced the deeper the cut card goes, because the true counts are divided by the number of cards left, making for higher TCs being cut off the deeper the card goes.
Yet in simulation results accounting, the more rounds that come before a cut card are the rounds where less cards were used, and simulation accounting, as in the true count rounding I have mentioned, in conection with the alleged floating advantage, results in an anti-cutcard effect. You see more rounds where high cards have been dealt--a largely ignored problem.
The cut card effect is a boundary condition where its negative ev effect on preventing future high count hands is noted, but not its postive ev effect on observed hands.
Another boundary condition exists in several high roller, whale, situations, where credit is often extended to a gambler who has gone beyond his current ability to pay, simply for accounting purposes, so that the current amount he has lost can be shown on a casino companys balance sheet as a win that is likely to be paid-off, ie where the casino win is from a gambler that is now below his new credit limit, and thus can be considered a more valid receivable. A risky accounts recievable is actually morphed into a riskier one, but that riskier one does not have to be classified as risky and taken off the current income books.
These are just a few boundary conditions that can cause Chebayechev periodic behavior, and might also cause Mandelbrot type effects, but such boundary conditions often have totally unexpected results, such as a casino win often leading to having to take down accounts recievable unless new credit is issued, or the progressionist confusing a boundary condition with the total lack of the same.
