Bet what? #3

[Bill Yung]

This is a proof that any strategy is better than no strategy. No game is random.

Assume that every conceivable game is not random, and therefore that a strategy can be devised for each. Even if the assumption is wrong, then nothing is lost because any counter-example game to the assumption would be random or break-even regardless any strategy already devised for it.

Eg, suppose someone randomly picks two unequal real numbers from 1 to 10 and then reveals one of the numbers, either the higher one or the lower one. Bet what, that the other number is higher or lower than the one revealed?

A real number in base n=10 is any number of the form 123.456789... which comprises the digits 0 to n-1=9.

[slingshot]

I would drink, for the first time in my life, until I got stoned, and my circumference doubled, and then ask for more Π. Then, whatever number my face flopped on, bet on that one until the tangent in my diameter changed. But that's just me.

[Bill Yung]

I would drink, for the first time in my life, until I got stoned, and my circumference doubled, and then ask for more Π. Then, whatever number my face flopped on, bet on that one until the tangent in my diameter changed. But that's just me.

If anything, not crazy enough.

[Bill Yung]

How about this guy?

First, you can "beat random"; then, you can't.

[Bill Yung]

First, you can "beat random"; then, you can't.

No, that doesn't make sense.

The first variant game of this sort, proposed by the video, was defeated, however meekly, by splitting the random game into two sub-random games or selections which yielded a non-random game over the same natural numbers or aleph-null cardinality in general. Not quite what Parrondo had in mind, yet good to go as far as it goes. This variant allows for the removal of the possibility of advantage by deliberate superimposition of the two randomly selected numbers, thus making it impossible for either number to be lower or higher. The second variant orients the methods of selection as directly between end-points, ie, as a matter of probability when the "real numbers" are taken, simplistically, as centerable. (Jiggling the method of selecting the reference number as the center or off-center while employing the same strategy of predicting the lower or higher number from the one revealed or mixing up the strategy, respectively, is demonstrable proof that there really is no better set of strategies here.) Random numbers revealed randomly allow a 0.25 probability-advantage; non-randomly reveal for 0 probability-advantage. The non-randomly revealed numbers game, when both are to one side of the oriented center, and the center-most is revealed, can itself be resplit into two sub-games which in turn yield a non-random game over the same natural numbers, or aleph-null cardinality in general, as with the initial variant of randomness. Don't try this one at home. Better to look for psychological tells with the non-random reveals.

The main problem in applying such strategies, for either variant here, to games of losing and winning is that these involve worse-or-lower and better-or-higher types of prediction. Losing and winning aren't comparative, and can't be thus predicted. This problem arises only when we predict either a not-so-bad loss or a not-so-good win, and it's unclear where these cross over the center.

One must look at how the first variant morphs into the second, and versa, to bring each variant's positive or negative aspects to the other, and dig further to combine the good aspects, to gain a more appreciable advantage with respect to also the games of losing and winning. Perhaps, select the numbers involved from the real numbers in a way which maps the real numbers onto an interval with decreasing likelihood of very large numbers. A better mathematical understanding of the types of numbers involved is helpful. At any rate, I'm not going (all the way) there today. It's great when a question can be posted, and left to simmer while other, more-pressing stuff may be fleshed out. Seeing how Fibonacci has something to do with the Platonic solids is simple; seeing how the solids have something to do with the conic sections, and, more importantly, how the conic sections have something to do with numbers/dimensions, particularly the complex numbers, was more-pressing stuff. (Shuffling back and forth between the physical and the mental.)

The only game which can't somehow be split off and reworked is randomness, itself. But the divine or absolute doesn't exist to us, so we may as well conclude that there are no random games.

[Bill Yung]

Almost forgot to add this. The general approach to beating randomness begins with the various ways that losses and wins even out in a random-walk type game of a single dimension. Such random walks always even out, with probability 1. Therefore, simply wait out a turn, and guess the opposite of the losing event on the next turn(s) until things even out. The walk necessarily evens out, so one more win than loss when it does. The time or length of the sequence of outcomes to even out linearly dilutes the profit of the one more win, but is based on more-complicated math. I used to post up Adobe Reader links to this sort of textbook stuff, but let those documents fall to the wayside at the lack of interest early on. These sorts of probability and statistics, and game theory studies are a boon to number theory in that with different possible logical and non-logical strategies, and nuances of, come seemingly endless flavors of the ordinal numbers. Teases them out. The upshot is that if you want to make the math go one way, you can; if you want it to go the other way, you can do that to.

There's also a quantum mechanical sense to this stuff, analogous to very tiny particles smeared out in probability to appear bigger in some way. Reminds me of also the Wizard's view of the two dice problem. He paraded only the general, averaged-out perspective, and marginalize the specific. Earlier on, he reversed his own reasoning with his explanation of the two envelopes problem, in which he eschewed working with the averaged-out amount. I don't know, the guy who didn't answer a single question over there on his own, aside from some simple odds stuff found on most gambling forums in one form or another. What you get from not putting in the effort for yourself. World-class dunce. A hair or two of money in being a good-little dunce.