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The mechanism of the random walk is very different from selecting various pre-shuffled decks of cards. The decks are not transformed from one to the next to the next.However the end result is the same. The order in which the deck is drawn is mutually independent of the order of the cards within the deck.(answering this question does not mean that I volunteer to peer review this--I would advise not putting to much effort into this line of questioning until you have spent some time learning more about probability calculations. They're tricky at first, but there are only so many types of scenarios that commonly arise that once you have learned a few of the tricks, it's not so bad)

I believe that if science can not replace ? with a true value, then this alone proves I am correct

Neither science nor maths can do this.It does not prove you are correct as unfortunately your maths does not make sense.The reasons have been explored in the other thread and I don't think you are going to find anyone willing to spend the time on this thread.I echo what ChiralSPO said, do learn basic probability, also the maths of fractions and decimals.Please don't waste more of your time and energy on this, there are better things to do with your life.

I'm saying you are not correct with your maths, it doesnt prove anything.

probability is a measurement

Can this have effect on probabilities and outcome over time?

History therefore changes probability as it does the outcome.

Quote from: Thebox on 11/08/2015 13:06:52probability is a measurementWrong. Probability is an a priori estimate. Measurement is an a posteriori statement of fact.QuoteCan this have effect on probabilities and outcome over time? No. QuoteHistory therefore changes probability as it does the outcome. no. History (i.e. measurement) allows us to refine our estimate of probability. We can start by assuming the dice are not loaded, but if we get a significant excess of 6s we might suspect that the dice are not entirely symmetrical. The national lottery ball story is a simple example of a problem that turns up in many mass-production industries. How do you ensure a consistently even distribution of, say, pigments in car paint? Easy enough if you only have one pigment, but if you add something like metalflake you need to be sure that the mixing process doesn't allow clumping. My favourite example is Ambriosa Rice Pudding. This used to (maybe still does) come in ordinary and deluxe varieties. The difference is that deluxe contains exactly four sultanas per can: any more and it turns a yukky brown color on heating, and any less produces complaints that it doesn't taste as good as it used to. Simply stirring an appropriate number of sultanas into a ton of rice pudding doesn't produce an adequately homogeneous mixture. The machinery actually inserted four in each can, and even that isn't sufficiently consistent: each can was then x-rayed to count the sultanas! Back to poker. Hand-shuffling isn't entirely random. Cards are "clumped" by the players trying to assemble the best possible hand by discard and purchase. A simple shuffle at the end of a round redistributes clumps of cards, so pairs and even threes may be more frequent than random in the next deal. If the dealer deals "threes and twos" the hands gradually strengthen as the evening wears on. A riffle shuffle splits pairs, but still retains more order than a random distribution. Online poker, as described here by Mr B, should be entirely random at each deal since there is no "history" in the new pack, and each deal is therefore truly independent.

Is probability just a manifestation of the human mind trying to make some sense of ordered chaos. By ordered meaning apparent chaos being produced by historical inputs. To demonstrate this consider that a deck of cards cannot be shuffled by hand or by a machine into a completely random order. Such that the chance of turning over an ace at the top of the pile is not 4/52 as the non random shuffling has placed the ace at the top of the pile resulting in the probability being 1.The national lottery is not random as the balls are put in in order. The time of the button press is more or less the same to start the picking process. This produces a assumed random result but in fact it isn't. The recent move to 59 balls was a result of people seeing patterns in the result and writing programs to predict the outcome. A low set with balls all under 15 come out frequently. The select 6 balls from 15 dramically increases the chance of winning. People have realised this. History therefore changes probability as it does the outcome.

everyone keeps quoting back x and ignoring y.

Quoteeveryone keeps quoting back x and ignoring y. That is because each online hand is entirely independent of all previous hands, unlike real cards. Your "y" is by defintion irrelevant in online poker, but very relevant in the real game. Playing with real cards, you are much more likely to be dealt three aces at the end of the evening than at the beginning. But so is everyone else!

Just read what I wrote. Every deal in online poker is entirely random and independent of all other deals. Every successive 3/2 deal in real poker is subtly dependent on the previous round. They are different because they are different!

Quote from: alancalverd on 20/12/2015 23:11:18Just read what I wrote. Every deal in online poker is entirely random and independent of all other deals. Every successive 3/2 deal in real poker is subtly dependent on the previous round. They are different because they are different!So to confirm, you are saying, that using a single deck, your chance of an ace is 4/52, if you receive an ace, the chance the next shuffle of receiving an ace, is (4/52)^2.On-line, my chance remains 4/52, a greater chance of receiving another ace?

No, the chance is always 4/52. There is a 4/52 chance of drawing an ace from one shuffled deck. If you draw one card from each of two shuffled decks, there is a (4/52)^{2} chance of drawing two aces. But if you draw from one deck and get an ace, the chance of drawing an ace from the next deck is still 4/52. (together this makes (4/52)^{2}...)Seriously, just read an introductory book on statistics. I learned this stuff in grade school, so there should be many different introductory level textbooks available that don't require a lot of background knowledge.Something like this might be a good place to start: https://www.mathsisfun.com/data/probability-tree-diagrams.html