Blackjack Therapy by Clarke Cant
Chapter 10, Why I believe in Anarchy, Chaos, and human progress.
Part one, why real Gods don’t give a damn about your little 16 versus 10 problem.
Consider if you will all of the attitudes people have, not against gamblers who lose, but gamblers who win. One exwife was a strict southern baptist (who I still wonder why I married), who would rant and rave about how terrible the casinos were, and would claim to approve of me beating them, but harped against me for disrespecting God for doing so, and seemed more upset I beat-em than she claimed to be over the way they beat others.
The roots of this go back to ideas of predestination and God knowing all and how gambling was letting God decide where the money should go (even today it is alleged that the LDS church –the Mormons—are opposed to gambling not on strictly moral grounds but that their priesthood system still uses “the office of the urim and thurim,” to find out God’s will, and that gambling is opposed more, in colloquial terms, to prevent bad ripples in the force…). Anything else using gambling methods was to mock God. It was Cardano that pointed out that where the ball on the roulette wheel fell was decided more by the opportunities for it to fall that any selection by God.
God deciding EVERYTHING made a big comeback in the time of the protestant reformation when Calvin came along. Freewill was just a dellusion of sinners trying to deny the grace of God…..to more or less decide arbitrarily who goes to hell, even if you accepted him. A more live and let live view of God slowly developed over time.
Then came quantum mechanics with all of its strange twists of logic and common sense—but the math cameup right and the equations predicted the outcomes of experiments well. The universe wasn’t built like a perfect watch like Newton thought afterall. Randomness and not being able to really findout where an electron was, developed in the full rules by Feynman eventually, came about by looking and relooking at the fact that the frequency of a photon was always in proportion to its energy. It turned out that the orbits of the electron were determined to stay only because the inability to find its precise location behaved like a wave, and the wave had to have a pattern that didn’t put more than one set, of all things PROBABILITY numbers on finding the little sucker. It was shear dern randomness that kept the universe going in the little things and there weren’t any clockwork laws.
After Planc got it, Einstein wrote a paper on how the best explanation was that light was only emitted in discrete packets he called quanta. After starting the field he decided he didn’t like it and went into relativity. DeBroglie figured out that the old e=mc^2 stuff if applied to an electron’s mass and orbital momentum energy, meant that it might have a wavelength by applying the Planc stuff to the total energy state. The orbit would get screwed-up if this wavelength didn’t form a standing wave. Shrondenger and Heinsenberg argued politics and physics for 15 years before they decided to leave it at Shrondenger’s Wave Equation that every real particle had to have a stable energy state and a stable energy state required that every possible pathway through time and space had to have integer DeBroglie wavelengths over that interval.
Dirac made things complicated by adding relativity to quantum mechanics, discovering things like anti-matter and making it necessary for Richard Feynman to have to discover new principles in statistics to explain virtual particles and having to make equations work forward and backwards because of that darn Dirac.
Relativity began with a Scot named Maxwell, who developed the first equations to explain electromagnetism. It was all thought at the time that he used tensor (exact differential) equations to save on paper and ink costs. Another bad explanation of Maxwell was that his electromagnetism required something called the aether for electromagnetic waves to vibrate in. An american, Michelson ruined that idea by showing no results for trying to detect the aether by examining the interference patterns in a huge concrete table floating on mercury with mirrors along 2 perpendicular paths (he must have also been trying to pickup cable for free too?).
An Irishman named Fitz-Gerald simply decided that aether must have somehow had properties where it got dented by differences in motion, so he wrote an equation to correct assumptions and went back to the nearest Dublin pub to chase women and raise hell but smart hell so as to be tolerated. Einstein was of a similar bent (he liked to please the women so much they sometimes said “ouch Albert.” His first wife divorced him for “physical incompatability” while his second wife insisted on spending their honeymoon in a pushchair around the gardens of their hotel. Albert, after his first trip to the USA developed a fasination for chearleaders and American Football, and even talked DePathe films into doing a few films about it, which were bizzare, due to being filmed in Germany. He died a New York Giants fan, with several Princeton cheerleaders giving birth to smart children with bad hair.) but had an excuse for being lazy about math that came from reading Ernst Mach.
Mach stated that there could be no such thing as any previledged observers in Physics and that all math did for physics was insist there was. Einstein used this excuse to write about the stuff with the mirrors, by saying maybe the aether wasn’t dented, but maybe the way you can measure things is. By denting time and space any observer is just as good as any other if the laws of physics really are fair and for everyone (good hair or bad). A Polish guy named Minkowsky really upset Einstein when he proved that while each observer would have different views of events they were viewing, compared to other observers, their measurements were linked by an equation that was more or less the 4 dimensional hypotenuse of their measurements. The problem for Einstein was that there was a link but no way to show how their observations would change if they tried to visit each other. Special Relativity told you how they were linked if they were already on the way toward each other, but it had problems with how they accelerated to get going.
Einstein kept trying to do the math but all he got was tired….and writing up Newton’s law of gravitation in tensor form…and kept hating it. At one point 1912, he decided, what the hell I’ll publish anyway and everyone said so what. At this point a young lad named Swartzchild (actually blond and German) told Albert that there was a type of math that made it possible to use the same equations to describe acceleration the same way for both linear acceleration and spinning a weight about the room on a string, since you really wanted to preserve that Mach stuff, but you would have to learn more math. It was Reinman spherical geometery, where every line had to be set on an n-dimensional spherical surface, and the diameter of the surface was given by a differential equation that was most easily solved by putting it in a matrix form called a Ricci tensor.
Now Einstein knew about that e=mc^2 (he developed it as an approximation for the apparent rise in mass for objects going near the speed of light, and others, like those irritating quantum guys were using it saying, “if it’s good for the delta, it’s good for the whole damn mass”) but also saw that if accelerations were equal in their local effects and the result of increased speed is apparent increased mass, who is to say that the bending of space is not equivalent if viewed as a consequence of acceleration, or as a consequence of the mass increase, and that if we believe those quantum guys, maybe all gravity is, is the bending of space, by mass in general, forcing a change in Minkowsky invarient solutions where bent space-time means that as you expand the time interval you contract the space interval.
That is what special and general relativity are. Invariance is just invariance the way a problem solves and doesn’t mean you are spinning your wheels the way those CS machine guys thought.
But Dirac added relativity to quantum mechanics…..but let’s just see what happens when you add quantum mechanics to general relativity that way another skirt chaser, this one in a wheelchair, Stephen Hawking did (yey Steve; way to go. Losing a divorce suit badly by having all your conquests brag about you despite MS in court—what a guy.).
Hawking simply was willing to admit both Relativity and Quantum mechanics were true, in his famous paper (written for the Gravity Research Foundation prize competition) called, Blackholes are Fuzzy but have no hair. The strange probability things quantum stuff does created a loop-hole in the solutions for General Relativity, where something Swartzchild used to chide Einstein about, blackholes (before getting killed in WWI), turned out to be not totally black; they actually would fade out over time. The solution had to acknowledge the time effects caused by a black hole, meant that this fade-away, now called Hawking radiation, had to be spread over the lifetime of the blackhole. Hawking was a little scarred of that result and tried to gloss it over by stating that there was no information content in this artifact and the radiation would not be detectable until the background radiation from the big bang faded enough to allow real observations of Hawking radiation to be made.
Hawking goofed.
Two more papers, in 1989, entered into the same competition (it is a tradition to give such papers goofy names and use weird aliases) were, Einstein is Smiling; Feynman is laughing, by Charles Kelley (name allegedly drawn from a Minneapolis Phonebook – the paper was entered on a postcard with, “guess what this is a stolen identity,” written on it), and, All Interactions are Virtually Relative, by Odo Kubiyashy (mailed from a Star Trek convention in Lakeland Florida.) established this goof. My original source on these papers was the shopper paper for the Dinkeytown neighborhood of Minneapolis Minnesota that a nurse had with her, while I was being prepped for a Positron Emission Tomogrphy scan, at Hennepin County Medical Center. A poor guy got a call from the Gravity Research Foundation asking if he were Dr. Kelley. It was so funny I had to research it further…
The “postcard paper” just stated that background radiation doesn’t really rule out detection of Hawking radiation that has information about the future size and lifecycle of a blackhole and that this timelooping must result in a new parallel universe, and that the process must include all blackholes, even those that arise out of vacuum fluctuations, and where the entropy flow is not visible (entropy increasing from a future to past flow of information, decreasing in the root universe etc…beyond the scope of this book) due to cosmic censorship imposed by blackhole thermodynamics. The Kobiyashy paper said that all interactions that appear to be only virtual particle interactions, to observers far from a blackhole, will appear to be real particles and excede background radiation near a blackhole, providing a window for the time reversed information to flow from the ultimate fate of a blackhole, or at least the version in the observer’s universe. This proved that universes have to be branching off at all times: The Kelley-Kobiyashy conjecture. It is the accepted explanation of the arrow of time problem (why does time always seem to flow in the direction of increased entropy?) too.
Well parallel universes do damage to the idea of the Christian God who is so loving and powerful and already has everything worked out such that you either go to heaven if you accept his solutions which are perfect, or go to hell if you don’t. Such an all knowing God can only be all knowing of one of those parallel universes (not?). A real God (worthy of the capital G) is probably one who creates by allowing interesting Chaotic things to happen, and doesn’t really need to run your life or have already laid out what is going to happen when you hit your 16. Good Luck and Embrace the Chances that creates.
We really prove that bankroll equation: why infinite ruin is really lower than finite boundary ruin (and doesn’t require any new ruin formula either ).
The really total correct way to figure out ruin chances would be to use Feyman’s methods and totally exhaust all of the possible bankroll outcomes and solve them as a sum over histories. The bell curve is an infinite approximation of what an interim solution to the limits of a probable histogram would be. The formula given here is almost the same as taking infinite solutions for ruin, and solving the bankroll requirements over what Brett Harris calls his similar h0 (the long run index) as being the required bankroll to survive enough hands at a given probability to break into the long run.
That is used to approximate the optimal bet to bank ratios.
But ruin over a finite number of trials IS ALWAYS twice the Classic element of ruin, calculated over an infinite number of hands and infinite spread of outcomes. Having double ruin over a finite domain, DOES NOT change the fact that the bet to bank ratio is optimized. Otherwise the classic coin flip examples would not show optimal growth even with (diminishing) barrier ruin.
Finite ranges have to have discrete win/loss states. In the Classic formulas, expected value always exists, independent of wins or losses and is just offset by fluctuations. In the Classic formulas expected value is there just hidden at some times, while in real world, with finite states with discrete win/loss states, EXPECTED VALUE adds to our bankrolls ONLY AS COUNTABLE MONEY after a win. With a win equated to ½ probability, ruin increases by 2 to 1 within any finite range, even while expected value still rises as given in the Classic Formulas. Once outside of the initial long run number of trials, expected value more approaches the Classic approximation where expected value is not discrete. The length of the long run index, in sd terms, equates to long run element of ruin, as given Classically, even while, in the initial range, the short term element of ruin is double etc.
Having established the term discrete state expected value we must still broaden our estimates for optimal bet to bank ratios. Blackjack falls into the discrete win state only about 47.5% of the time, and not 50%. The number of discrete win states is decreased, and the impact of losses is increased. The ratio of sd/ev that has been used by Brett Harris and Patrick Sileo to develop their similar bankroll formulas is not optimum, in my opinion. To reflect the discrete state reduction in ev you must multiply by (.475/.525)^2 or use the approximate ratio 1.2sd/ev and expand from there, WHICH IS EXACTLY MY BANKROLL FORMULA AND HAS BEEN SINCE 1982! Chapter 4 was my understanding in 1982. Chapter 4A was to good deeper into why you can have extra ruin and not have it effect your bankroll. The conjecture I give here is that all initial finite ranges tend to have twice the short term ruin as their long term ruin, without effecting estimates of optimal bankroll required, with the other half of this being the well known decrease in edge, as measured by total bets over the history of your bankroll, that Stanford Wong wrote about in his paper, What Proportional Betting Does to Your Win Rate. The same way the Wong result does not effect the growth of your bankroll, just the total money return over history, this effect ends too, with growth of about 2.5 to 3 times of your bankroll. The 1.2 adjustment is based on the newest claims made concerning the possible behavior of normal curves when examined by Chaos Theories. Generally those claims are that the effects of discrete wins and loses are such that normal curve estimates have to be further broadened by the square of the actual loss/win probability, in addition to the standard measure of standard deviation per hand, in approximately the same range of initial outcomes as the range where the Wong effect, in terms of bankroll growth, is overcome—even while it remains for the history of how much money was bet etc. While there is almost as much evidence that this becomes as unnecessary as other attempts to account for this initially higher ruin, practical unit size rounding for the chips used in most casinos appears to extend such effects. Neither the initially higher ruin, when you first play, or the edge over history, ever mean that you need more money for an optimal bankroll. (On further analysis double discrete ruin appears to be permanent even at infinity as your bankroll goal. Even then bankroll requirements are not doubled.)