United States Member #124498 March 14, 2012 7023 Posts Offline

Posted: February 7, 2013, 12:22 pm - IP Logged

Quote: Originally posted by SergeM on February 7, 2013

There is no good random generated by computers following articles on Internet. If true would be the random from random.org, then I would want to play big cash money against it. Maybe there are a few patents that generate better random results, but then again, what is random? It surely doesn't have to follow any mathematical rule. That is what it is.

Main Entry:1ran£dom Pronunciation:*ran-d*m Function:noun Etymology:Middle English, succession, surge, from Anglo-French randun, from Old French randir to run, of Germanic origin; akin to Old High German rinnan to run — more at RUN Date:1561

: a haphazard course –at random : without definite aim, direction, rule, or method *subjects chosen at random*

Main Entry:random walk Function:noun Date:1905

: a process (as Brownian motion or genetic drift) consisting of a sequence of steps (as movements or changes in gene frequency) each of whose characteristics (as magnitude and direction) is determined by chance

United States Member #93949 July 10, 2010 2180 Posts Offline

Posted: February 8, 2013, 12:21 am - IP Logged

Quote: Originally posted by dr san on February 7, 2013

Random sampling

Referring to a simple Lottery "1 of 5".Suppose the numbers 1, 2, 3, 4, 5, dropped to 20 circulations with frequencies of 2, 2, 4, 8, 4.To create a table that presents the data in a usable form.

_ N _ _ F _ _ RF _ _ _ CRF

1 2 0.10 0.10

2 2 0.10 0.20

3 0.20 0.40 4

0.80 0.40 8 4

4 5 1.00 0.20

How can you choose the numbers to select the number of probability is directly proportional to its frequency of occurrence in history (or, equivalent, is equal to its relative frequency)?A very simple way would be to take your tiles set of 10 ornaments China, with pen on one of them to call a number one, the other two, two, three, four, and two 5:0 pm 4.Then put them in a jar, shake well, and blindly remove nodules.Probability, which would you choose 4 number dominoes is 0.40, the probability that you select a number of dominoes is 0.10, and so on.All nodes of the fingers of choice (the next election the junta extracted must be returned to the Bank, and that the unrest) is random with probability of the frequency selected on the number fell in previous editions.This-the random selection, but weighted random (probability-weight), with "hot" items weighing more than the weight of "cold" numbers.Otherwise you could do the same random sample, using uniform random numbers, and the following distribution function.Our distribution function:

_N_ _CRF_

1 0.10

2 0.20

3 0.40

4 0.80

5 1.00

Use RAND () to select one of two-digit uniform random number.Assume that this is-the number 0.34.Look at the column of CRF.The number fell between 0.34 and 0.40 0.20, choose the number 3 (You randomly selects 3 in distributors).Use RAND () to select another random number.Suppose that this time you have 0.69.From 0.69-between 0.40 and 0.80, select the number 4.And so on.What is happening here?It is very simple.Since the RAND () produces a uniform random number, then the probability that the number of falls-equal to 0.20 -0.40 0.20 (less 0.20 0.40), then there is the relative frequency of fall-3 emission (see the table at the top of this page.)Thus, the choice to interpret 0.34, a number between 0.20 and 0.40, which is similar to a random selection of numbers 3.Likewise, our random number is between 0.40 and 0.80 0.69, is interpreted as a randomly selected number 4:.The relative frequency corresponding to 4, 0.40, is the same as the probability that we could choose a uniform random number between 0.40 and 0.80 This random selection process can be automated (no conscience), using the following simple rules.Rule.Use RAND () to select a random number ravnomernoraspredelennoe, call it r. If R falls between two values of a column, the FRC, choice of column N is a number that corresponds to the higher of the two values of which obtained r. If R is not equal to one of the values in the column, column choice no CRF corresponding number.Illustration with the rule.If R = 0.53, picked 4 because 0.53-lies between 0.40 and 0.80, and 4 correspond to 0.80.If R = 0.31, choose 3 because it is between 0.20 0.31 and 0.40, and 3 corresponds to 0.40.If R = 0.20, choose 2.If R = 0.80, select 4.Lottery conducted by the Government as Lotto Texas use mechanisms of mixing and playing balls, trying to ensure that they totally random occurrence.By "completely random" I mean simply that each ball in a game full of balls, can be selected with equal probability in any quantity.This is a sample function of a uniform distribution.If, in fact, the machine reaches the perfect objective randomization, the RAND function (50) to the Texas Lotto or RAND (40) for the Plus Lotto-how a good a way as any to select the numbers for your tickets.

Your weighting scheme using RAND() should provide you with sets more or less congruous with those in your input. Unfortunately, I suspect your reason for wanting to do this is firmly rooted in a belief in the Gambler's Fallacy. Unless the objects being selected are clearly not equal in weight, shape, or size, the value of your output will be of lttle or no value.

That is a very interesting article. (Trying To Be Random in Selecting Numbers for Lotto - Boland) It could be subtitled, "Where Psychology Meets Mathematics!"

I wasn't able to access Speckman's article, "Lottery Loophole Explained." Do you know what the loophole was, and how long after 1986 it took them to close it?

Here are a couple quotes from Boland's article that others here might enjoy:

"For Lotto 6/42, P(MG = 1) = 0.56 is the probability of a selection containing two consecutive numbers. Students usually find it very surprising and nonintuitive that it is more likely than not that a random selection will contain two consecutive numbers. Before giving students the probability of two consecutive numbers appearing in Lotto, it is a worthwhile exercise to test their intuition by asking them for estimates of it!" (Read the article if this intrigues you!)

"5. Conclusions

"21 The whole concept of randomness is a delicate one, and one about which considerable research has been done, particularly in the field of psychology. Reichenbach (1949) claimed that humans are unable to produce a random sequence of responses, even when explicitly asked to do so, and considerable research since then (including our work) generally supports this. Many teachers/lecturers have told us of classroom activities they use to get students thinking about randomness, and Green (1997) gives an interesting account of an experiment on recognizing randomness.

"22 How well can individuals perform when they attempt to be random generators for a game like Lotto? Some interesting insights into human intuition about randomness may be obtained by asking a class of students to participate in an exercise that tries to answer this question. We asked each of the students in a large class to act once as a random generator for the winning numbers in our Irish National Lottery - Lotto 6/42 game. The results were then analysed and compared with actual recent winning selections in our Lotto game, as well as with another set simulated by computer. Using boxplots, histograms, QQ-plots, and some basic measures of spread in a sample, one is able to generate interesting classroom discussions about biases that individuals seem to possess. We observed (perhaps not surprisingly) that there seems to be a propensity for individuals to select numbers in increasing order. We also observed that individuals tend to select numbers which on the average are smaller (by at least two) than would be expected from a truly random generator. Of course, in other countries or states where a different form of Lotto is played, the results will probably differ. When it comes to the spread in a selection, we observed that individuals tend to make selections that are reasonably spread out as measured by sample variance, but not in other ways (for example, as measured by the so-called minimum gap in a selection). In particular, we observed a clear reluctance of individuals (compared to a truly random generator) to make selections containing consecutive numbers."

--Jimmy4164

P.S. Remember: Você não pode tirar sangue de um nabo!

Economy class Belgium Member #123705 February 27, 2012 3093 Posts Offline

Posted: February 8, 2013, 12:38 pm - IP Logged

Even knowing the probability you will have hard to guess right based on that.

Let's say that you have a pick 5 game with 56 numbers. You think, hope, guess, dreamt, ... that there will be exactly 2 consecutive numbers drawn. 5-2=3 not consecutive numbers, but that is still unsure, you can have 5 consecutive numbers or just none.

Again, 2 consecutive numbers of 56 numbers, 55 tickets to get 2/5 right!

United States Member #93949 July 10, 2010 2180 Posts Offline

Posted: February 8, 2013, 1:40 pm - IP Logged

It is actually worse than that, SergeM.

Don't forget that the probability of 2 consecutives is quite a ways from 1.0, so your 55 tickets don't even guarantee that!

By the way, I agree with your signature line! And if any of the cigarette corporation officials who suppressed laboratory evidence of the hazards of smoking as far back as the 1930s are still alive, they should be prosecuted, and hopefully, jailed!

Economy class Belgium Member #123705 February 27, 2012 3093 Posts Offline

Posted: February 8, 2013, 2:07 pm - IP Logged

You can prosecute and jail people working in the tobacco industry today. Same for resellers and mean smokers. People with master degrees are working in the tobacco industry, they should be lynched.

bgonÃ§alves Brasil Member #92566 June 9, 2010 1629 Posts Offline

Posted: February 8, 2013, 2:14 pm - IP Logged

Hello, this condition of sergem followed can also put vertically

Example =

01 02 03 04 05

06 07 08 09 10

11 12 ...

Depending on how it assembles an array, but this example = 01.06.Are consecutive numbers

Another example = 05.10, are numbers in a row vertically, there are also the delta value for the pair worth = two and three example = 01.03 = value delta 2 and delta value 04 01.04

So in addition to the sequel in horizonta, = we have in vertical sequences 01.02 (as array) 01.06 and caom delta value 2.3,

New Jersey United States Member #99034 October 18, 2010 1439 Posts Offline

Posted: February 8, 2013, 2:21 pm - IP Logged

Quote: Originally posted by jimmy4164 on January 31, 2013

Coin Toss,

Incredible! Isn't it?

I got lucky last night after only letting it run a couple of hours and hit a 5+0. Set to Powerplay, the $2M hit still only pushed the ROI to about $0.90. Without the Powerplay, it was significantly less. Which brings me to my reason for this thread:

Obviousely, if you hit a 5+0 or 5+1 within your lifetime you're going to be ahead of the game, but is the higher ROI with Powerplay (without a Jackpot) worth the tradeoff of having less chances at the big ones? I'm thinking it's a personal decision based on your beliefs. If you really believe you can engineer a big hit, you'll probably opt out of the Powerplay, otherwise, you'll opt in to take advatage of the [approx] 60% increase in ROI for all hits of 4+1 and below.

What do you think?

--Jimmy4164

I disagree. Your ROI may be higher, but your overall expense per ticket is also greater. If it's .30 and .50 return on the dollar, but you can spend $2 or$3 dollars respectively, the overall cost is larger playing the Powerplay option. And if you play when there are large jackpots only, the EV actually probably get's larger without the powerplay option. I didn't actually do the math to find out - I'm kinda just guessing because I don't wanna do the work right now (and b/c I don't really like to play Powerball anyway.)

http://en.wikipedia.org/wiki/Empirical_probability "Empirical probability, also known as relative frequency, or experimental probability, is the ratio of the number favorable outcomes to the total number of trials, not in a sample space but in an actual sequence of experiments. In a more general sense, empirical probability estimates probabilities from experience and observation. The phrase a posteriori probability has also been used an alternative to empirical probability or relative frequency."

Bayesian probability: http://en.wikipedia.org/wiki/Bayesian_probability "According to the Bayesian probability calculus, the probability of a hypothesis given the data (the posterior) is proportional to the product of the likelihood times the prior probability (often just called the prior). The likelihood brings in the effect of the data, while the prior specifies the belief in the hypothesis before the data was observed."

http://en.wikipedia.org/wiki/Propensity_probability "Theorists who adopt this interpretation think of probability as a physical propensity, or disposition, or tendency of a given type of physical situation to yield an outcome of a certain kind, or to yield a long run relative frequency of such an outcome."

http://en.wikipedia.org/wiki/Kolmogorov_complexity "In algorithmic information theory (a subfield of computer science), the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity) of an object such as a piece of text is a measure of the computational resources needed to specify the object."

http://en.wikipedia.org/wiki/Pseudorandomness "A pseudo random process is a process that appears random but is not. Pseudo random sequences typically exhibit statistical randomness while being generated by an entirely deterministic causal process."

http://en.wikipedia.org/wiki/Statistical_randomness "A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal die roll, or the digits of Pi exhibit statistical randomness. Statistical randomness does not necessarily imply "true" randomness, i.e., objective unpredictability."

http://en.wikipedia.org/wiki/Ramsey_theory "Ramsey theory, named after Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear. Problems in Ramsey theory typically ask a question of the form: how many elements of some structure must there be to guarantee that a particular property will hold?"

This document is very interesting, because it refers to intuitive opinion of children: "Children’s understanding of randomness as a model" http://www.bsrlm.org.uk/IPs/ip28-3/BSRLM-IP-28-3-09.pdf Definitely worth reading!

"PEOPLE’S INTUITIONS ABOUT RANDOMNESS AND PROBABILITY" http://tinyurl.com/mvz8m5 "A recent empirical study indicates that students in introductory statistics class are generally confused about the different notions of probability (Albert, 2003). Clearly, continuing to teach only the frequentist conception cannot reduce the confusion. This implies to students either that there is only one “correct” conception of probability or that the frequentist and Bayesian conceptions are competitive, which should not be the case (Vranas, 2001). Moreover, an exclusive focus on frequentist notions may conflict with the students’ intuitions and representations about probability (see e.g., Hawkins and Kapadia, 1984). In any case, as emphasized by Konold (1991, p. 144), “the teacher cannot, by decree, enforce a normative view.”

http://en.wikipedia.org/wiki/Calculus_of_predispositions "According to Aron Katsenelinboigen, calculus of predispositions is another method of computing probability. Both methods may lead to the same results and, thus, can be interchangeable. However, it is not always possible to interchange them since computing via frequencies requires availability of statistics, possibility to gather the data as well as having the knowledge of the extent to which one can interlink the system’s constituent elements. Also, no statistics can be obtained on unique events and, naturally, in such cases the calculus of predispositions becomes the only option."

http://en.wikipedia.org/wiki/Outlier "In statistics, an outlier is an observation that is numerically distant from the rest of the data. They can occur by chance in any distribution, but they are often indicative either of measurement error or that the population has a heavy-tailed distribution. In the former case one wishes to discard them or use statistics that are robust to outliers, while in the latter case they indicate that the distribution has high kurtosis and that one should be very cautious in using tool or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two distinct sub-populations, or may indicate "correct trial" versus "measurement error"; this is modeled by a mixture model."

http://en.wikipedia.org/wiki/Imprecise_probability "The notion of Imprecise probability is used as a generic term to cover all mathematical models which measure chance or uncertainty without sharp numerical probabilities. It includes both qualitative (comparative probability, partial preference orderings,...) and quantitative modes (interval probabilities, possibility theory, belief functions, upper and lower previsions, upper and lower probabilities, ...). Imprecise probability models are needed in inference problems where the relevant information is scarce, vague or conflicting, and in decision problems where preferences may also be incomplete. Imprecise Probability Theory aims not to replace, but to complement and enlarge the classical notion of Bayesian probability, approach to probability theory, by providing it with tools to work with weaker information states."

http://en.wikipedia.org/wiki/Combinadic "In mathematics, a combinadic is an ordered integer partition, or composition. Combinadics provide a lexicographical index for combinations. Applications for combinadics include software testing, sampling, quality control, and the analysis of gambling games."

http://en.wikipedia.org/wiki/Factoradic "In combinatorics, factoradic is a specially constructed number system. Factoradics provide a lexicographical index for permutations"

Terence Tao: "Structure and randomness in combinatorics" (http://arxiv.org/abs/0707.4269) "Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has proven profitable to decompose such objects into a structured component, a pseudo-random component, and a small component (i.e. an error term); in many cases it is the structured component which then dominates." _________________

United States Member #93949 July 10, 2010 2180 Posts Offline

Posted: February 9, 2013, 3:13 am - IP Logged

Quote: Originally posted by Boney526 on February 8, 2013

I disagree. Your ROI may be higher, but your overall expense per ticket is also greater. If it's .30 and .50 return on the dollar, but you can spend $2 or$3 dollars respectively, the overall cost is larger playing the Powerplay option. And if you play when there are large jackpots only, the EV actually probably get's larger without the powerplay option. I didn't actually do the math to find out - I'm kinda just guessing because I don't wanna do the work right now (and b/c I don't really like to play Powerball anyway.)

Boney526,

Please double check my calculations. If they're correct, it seems to me that the $3 Powerplay is a better bet than the $2 ticket, especially if you ignore the 5+0 and 5+1 Jackpots. It's still not much consolation though. I wonder how many people would play Roulette if the payouts there were structured in proportion to these?

As usual, choosing a payout value for the 5+1 is problematic. If they really do pay back 0.50, an adjustment would need to be made there. It's surprising that the commission would allow for such a significant difference between the 2 options, about 10.6 cents, not including a 5+1 hit.

While running the Powerball Simulator, notice how the 2 highlighted numbers below dominate as long as you don't get a 5+0 or 5+1 hit.

$2 Powerball $3 Powerplay Hit Odds Payout ROI* Payout ROI*

New Jersey United States Member #99034 October 18, 2010 1439 Posts Offline

Posted: February 10, 2013, 11:19 pm - IP Logged

The ROIs might be close (if you include the top two prizes, which I'd argue you should,) but you are increasing the total expense. If you don't count those - then Powerplay is a better bet, but both are terrible without the top two prizes inclusion (and are pretty terrible, anyway.)

And as the jackpot grows, I'd imagine the ROI of not taking powerplay to exceed the ROI of taking it, although, with a starting jackpot taking Powerplay is better from an ROI standpoint.

If I was forced to play with or without, I still pick without.

United States Member #93949 July 10, 2010 2180 Posts Offline

Posted: February 11, 2013, 2:41 am - IP Logged

Quote: Originally posted by Boney526 on February 10, 2013

The ROIs might be close (if you include the top two prizes, which I'd argue you should,) but you are increasing the total expense. If you don't count those - then Powerplay is a better bet, but both are terrible without the top two prizes inclusion (and are pretty terrible, anyway.)

And as the jackpot grows, I'd imagine the ROI of not taking powerplay to exceed the ROI of taking it, although, with a starting jackpot taking Powerplay is better from an ROI standpoint.

If I was forced to play with or without, I still pick without.

It looks like the "break even" point is a Jackpot of $112M.

The total ROI, NOT including the 5+1 Jackpot, for

PB vs PP is .181 vs .287. (See above)

So, excluding the 5+1 Jackpot, the ROI for Powerplay is significantly better, nearly 60% better.

Increasing the Jackpot to $112M changes the

PB (Jackpot Only) ROI to .320 and the

PP (Jackpot Only) ROI to .213 .

.181 + .320 = .501 (PB)

.287 + .213 = .500 (PP)

.500 is the amount most lotteries claim they give back, so I think this is a reasonable conclusion. As the Jackpot increases above $112M, PB will outperform PP, in total, as you indicated.

Admittedly, neither is a good bet when compared to 93% and better returns possible at casinos, but I'm surprised you would pass up the 60% advantage of the Powerplay 2nd tier and lower to get those extra shots at the [very remote] Jackpot.