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What Does It Take To Win (Mathematically Speaking?)

Topic closed. 134 replies. Last post 6 years ago by Stack47.

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Kentucky
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Posted: February 1, 2011, 11:53 am - IP Logged

"The attacks on the 1975 study as out of date don't even confirm that the article was read, since it was merely a reference that was mentioned in the paragraph I included as an excerpt."

The article mentions people overestimating probabilities and the 1975 study is about people overestimating the value of self picked lotto tickets. Only the findings of 1975 study are shown in the article and no mention is made of how the participants choose their self picks. If 75% of the draining history included one number from the previous drawing, it's obvious why self picks that included a number from a previous drawing would be given greater value by participants. I doubt the study was made to prove the subjects would use other mathematical probabilities and/or statistics.

What other conclusions should we expect from a study designed to prove "illusions of control"?

Thanks again for providing us with something we already know and some rather boring and useless information in a topic titled "What does it take to win?, Jimmy!!!

Leave it to Jimmy to go way off topic in his introductory post.


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    Posted: February 1, 2011, 1:53 pm - IP Logged

    It appears the excerpt in my opening post was not the best choice as it quickly prompted 5 people here to fixate on one reference and launch their typical attacks on me consisting of inane remarks which accomplish no more than distract anyone who might have a sincere interest in the psychological aspects of probability as it relates to lotteries.  If you click on the link below and actually READ the research article, you will find that the negative remarks made above are, in fact, trivial, and inane.

    So, let's try again!

    (I respectfully request that if you do not have a constructive contribution to make to this discussion that you please refrain from commenting.)

    --Jimmy4164

    --------------------------------------------------------------------

    Before proceeding with a breakdown of the odds in one of the popular Lotto games, here is something to think about:

    http://www.ecologyandsociety.org/vol2/iss1/art2/

    "Why are single-event probabilities hard for people to process?

    In cognitive science, two schools of thought have developed to explain people's difficulties with single-event probabilities. The first school, based on the approach of Tversky and Kahneman (1974), assumes that each type of error in probabilistic reasoning represents an inherent limitation of human cognitive abilities. The human brain is seen as incapable of the complexities of accurate judgment about uncertainty. Instead, the mind depends on arbitrary heuristics or rules of thumb, producing flawed judgments and decisions. In the words of Stephen J. Gould (1992: 469), 'Tversky and Kahneman argue, correctly, I think, that our minds are not built (for whatever reason) to work by the rules of probability.' Although the cognitive errors resulting from these heuristics occur reliably in a variety of settings, most of this research has required subjects to reason about problems involving decimal estimates of single-event probabilities. The researchers suggest empirical methods that seem to counteract the errors in some situations, but they do not fit the cognitive inadequacies into any broad predictive or explanatory model.

    The second school, based on the approach of Gigerenzer and Hoffrage (1995) and Cosmides and Tooby (1996) proposes the following arguments, based on evolutionary assumptions:

    1) The mind includes structures that evolved to help preliterate people reason adaptively about situations commonly encountered across human evolutionary history, including making judgments under uncertainty.

    2) Natural selection is unlikely to have produced a grossly inadequate mechanism for this purpose.

    3) Cognitive structures designed to reason about probabilities will include both input mechanisms, which pick up information about stochastic events in the environment, and well-defined algorithms for processing that information.

    Given these assumptions, humans in experimental situations can be expected to reason well about uncertainties only if two requirements are met: (1) input must be in a format 'expected' by the human data-gathering mechanism (similarly, a calculator 'expects' inputs in decimal, not binary, numbers); and (2) the problem must be structured to activate the information-processing algorithm that solves the particular problem, usually from probability theory, intended by the experimenter (a calculator will not provide a square root if the 'log' button is pressed.)

    Gigerenzer and his colleagues argue that cognitive illusions are artifacts of presentation format. People make mistakes, not because their reasoning ability is flawed, but because traditional experiments fail to provide the right conditions for the mind to reason correctly. They may present information in an inappropriate format (namely, decimal probabilities), or they may activate an algorithm in the mind that is not designed to process probabilistic information in the way that the experimenter expects. I will discuss issues of input format and algorithms in detail."

    http://www.ecologyandsociety.org/vol2/iss1/art2/


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      Kentucky
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      Posted: February 2, 2011, 12:05 am - IP Logged

      Usually when someone hijacks a thread they do it by going off topic but this is a first; the author of the thread goes off topic in his very first post and is still off topic on page two.

      To get back on topic, there is a mathematical way to win pick-5s, lotto games, and even Mega Millions every drawing, but as Pumpi would say "theoretically speaking of course". Most pick-5 games use 39 numbers and there is a nice 2 if 5 of 39 number wheel with 25 combinations right here on LP. Since every number is used the focus has to be on the order the numbers are entered into the wheel. The same is true about any wheel using all the numbers in any lotto type game.

      I don't have the mathematical formula, but it does answer the question purposed in this thread.


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        Posted: February 3, 2011, 2:00 am - IP Logged

        It appears the excerpt in my opening post was not the best choice as it quickly prompted 5 people here to fixate on one reference and launch their typical attacks on me consisting of inane remarks which accomplish no more than distract anyone who might have a sincere interest in the psychological aspects of probability as it relates to lotteries.  If you click on the link below and actually READ the research article, you will find that the negative remarks made above are, in fact, trivial, and inane.

        So, let's try again!

        (I respectfully request that if you do not have a constructive contribution to make to this discussion that you please refrain from commenting.)

        --Jimmy4164

        --------------------------------------------------------------------

        Before proceeding with a breakdown of the odds in one of the popular Lotto games, here is something to think about:

        http://www.ecologyandsociety.org/vol2/iss1/art2/

        "Why are single-event probabilities hard for people to process?

        In cognitive science, two schools of thought have developed to explain people's difficulties with single-event probabilities. The first school, based on the approach of Tversky and Kahneman (1974), assumes that each type of error in probabilistic reasoning represents an inherent limitation of human cognitive abilities. The human brain is seen as incapable of the complexities of accurate judgment about uncertainty. Instead, the mind depends on arbitrary heuristics or rules of thumb, producing flawed judgments and decisions. In the words of Stephen J. Gould (1992: 469), 'Tversky and Kahneman argue, correctly, I think, that our minds are not built (for whatever reason) to work by the rules of probability.' Although the cognitive errors resulting from these heuristics occur reliably in a variety of settings, most of this research has required subjects to reason about problems involving decimal estimates of single-event probabilities. The researchers suggest empirical methods that seem to counteract the errors in some situations, but they do not fit the cognitive inadequacies into any broad predictive or explanatory model.

        The second school, based on the approach of Gigerenzer and Hoffrage (1995) and Cosmides and Tooby (1996) proposes the following arguments, based on evolutionary assumptions:

        1) The mind includes structures that evolved to help preliterate people reason adaptively about situations commonly encountered across human evolutionary history, including making judgments under uncertainty.

        2) Natural selection is unlikely to have produced a grossly inadequate mechanism for this purpose.

        3) Cognitive structures designed to reason about probabilities will include both input mechanisms, which pick up information about stochastic events in the environment, and well-defined algorithms for processing that information.

        Given these assumptions, humans in experimental situations can be expected to reason well about uncertainties only if two requirements are met: (1) input must be in a format 'expected' by the human data-gathering mechanism (similarly, a calculator 'expects' inputs in decimal, not binary, numbers); and (2) the problem must be structured to activate the information-processing algorithm that solves the particular problem, usually from probability theory, intended by the experimenter (a calculator will not provide a square root if the 'log' button is pressed.)

        Gigerenzer and his colleagues argue that cognitive illusions are artifacts of presentation format. People make mistakes, not because their reasoning ability is flawed, but because traditional experiments fail to provide the right conditions for the mind to reason correctly. They may present information in an inappropriate format (namely, decimal probabilities), or they may activate an algorithm in the mind that is not designed to process probabilistic information in the way that the experimenter expects. I will discuss issues of input format and algorithms in detail."

        http://www.ecologyandsociety.org/vol2/iss1/art2/


        Maybe the abstract to the study will ring some bells!

        (If you see something here in the abstract or above in the excerpt that strikes you as even remotely connected to the kinds of thought processes you engage in to design or critique a number selection system, it might be a starting point for a question.  I would hope it at least prompts you to click on the link above and READ more of the study.)

        ABSTRACT

        Ecologists working in conservation and resource management are discovering the importance of using Bayesian analytic methods to deal explicitly with uncertainty in data analyses and decision making. However, Bayesian procedures require, as inputs and outputs, an idea that is problematic for the human brain: the probability of a hypothesis ("single-event probability"). I describe several cognitive concepts closely related to single-event probabilities, and discuss how their interchangeability in the human mind results in "cognitive illusions," apparent deficits in reasoning about uncertainty. Each cognitive illusion implies specific possible pitfalls for the use of single-event probabilities in ecology and resource management. I then discuss recent research in cognitive psychology showing that simple tactics of communication, suggested by an evolutionary perspective on human cognition, help people to process uncertain information more effectively as they read and talk about probabilities. In addition, I suggest that carefully considered standards for methodology and conventions for presentation may also make Bayesian analyses easier to understand.

        KEY WORDS: cognitive psychology; judgment under uncertainty; cognitive illusion; Bayesian statistical analysis; Bayesian decision analysis; probability; frequency; expert elicitation of probabilities.

          RL-RANDOMLOGIC's avatar - usafce

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          Posted: February 3, 2011, 2:26 pm - IP Logged

          Maybe the abstract to the study will ring some bells!

          (If you see something here in the abstract or above in the excerpt that strikes you as even remotely connected to the kinds of thought processes you engage in to design or critique a number selection system, it might be a starting point for a question.  I would hope it at least prompts you to click on the link above and READ more of the study.)

          ABSTRACT

          Ecologists working in conservation and resource management are discovering the importance of using Bayesian analytic methods to deal explicitly with uncertainty in data analyses and decision making. However, Bayesian procedures require, as inputs and outputs, an idea that is problematic for the human brain: the probability of a hypothesis ("single-event probability"). I describe several cognitive concepts closely related to single-event probabilities, and discuss how their interchangeability in the human mind results in "cognitive illusions," apparent deficits in reasoning about uncertainty. Each cognitive illusion implies specific possible pitfalls for the use of single-event probabilities in ecology and resource management. I then discuss recent research in cognitive psychology showing that simple tactics of communication, suggested by an evolutionary perspective on human cognition, help people to process uncertain information more effectively as they read and talk about probabilities. In addition, I suggest that carefully considered standards for methodology and conventions for presentation may also make Bayesian analyses easier to understand.

          KEY WORDS: cognitive psychology; judgment under uncertainty; cognitive illusion; Bayesian statistical analysis; Bayesian decision analysis; probability; frequency; expert elicitation of probabilities.

          jimmy

          Black Jack vs lottery

          Card counters and lottery self pics.  When a player starts playing BJ he first lays down his bet before

          the first card is drawn from the deck.  He may however watch the game for a while before deciding to

          enter the game waiting for the most oppertune time to begin play.  He may calculate the odds for the

          remaining cards left in the deck.  The lottery player watches the game and then decides to give it a 

          try by picking his numbers based on information gotten watching the game for awhile.  Both of the

          players enter the game not knowing what will be drawn next.  After the BJ player places his bet he

          then receives two cards one face down and one face up.  All the player are able to see the face up

          cards for each player.  Once the game has started and the cards dealt then the game becomes more

          a game of skill for some players.  The point I make is that both lottery and BJ players enter the game

          with the same mindset of winning and enter the game blind so to speak.  Neither knows with any

          certainty what will happen next.  Of course after the game starts the BJ player has other options 

          based on the cards he was dealt vs the lottery player who has none.   Now take a scratchers ticket

          which requires the player to uncover many unknown areas that may or may not reveal a prize. 

          The  scratchers ticket is a winner or loser even before it is scratched.  The self pick has a chance of

          winning based on the odds for the game and the BJ hand is determined on many things such as how

          many people are playing.  When all three entered the game they placed the bet or wager having no

          idea beyond the odds for the game what the outcome would be.   Black jack is considered a game of

          skill but at what point does it become skill and not chance.  A unskilled player could effect the outcome

          of the most skilled player.  Would this not boil down to all games being chance regardless of which

          one played.  Counting cards could give an advantage but with so many variables it seems that the results

          could be considered random at best.  It seems that because so few people ever win a jackpot of any

          size verses the dollars spent which is purely a matter of odds,  that many jump on the bandwagon of

          criticism feeling safe and secure instead of attempting something in which they might fail and this post

          might be a way to feel better about their lack or fear of trying.  Predicting someone will lose is easy. 

           

          RL


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            Posted: February 3, 2011, 3:32 pm - IP Logged

            jimmy

            Black Jack vs lottery

            Card counters and lottery self pics.  When a player starts playing BJ he first lays down his bet before

            the first card is drawn from the deck.  He may however watch the game for a while before deciding to

            enter the game waiting for the most oppertune time to begin play.  He may calculate the odds for the

            remaining cards left in the deck.  The lottery player watches the game and then decides to give it a 

            try by picking his numbers based on information gotten watching the game for awhile.  Both of the

            players enter the game not knowing what will be drawn next.  After the BJ player places his bet he

            then receives two cards one face down and one face up.  All the player are able to see the face up

            cards for each player.  Once the game has started and the cards dealt then the game becomes more

            a game of skill for some players.  The point I make is that both lottery and BJ players enter the game

            with the same mindset of winning and enter the game blind so to speak.  Neither knows with any

            certainty what will happen next.  Of course after the game starts the BJ player has other options 

            based on the cards he was dealt vs the lottery player who has none.   Now take a scratchers ticket

            which requires the player to uncover many unknown areas that may or may not reveal a prize. 

            The  scratchers ticket is a winner or loser even before it is scratched.  The self pick has a chance of

            winning based on the odds for the game and the BJ hand is determined on many things such as how

            many people are playing.  When all three entered the game they placed the bet or wager having no

            idea beyond the odds for the game what the outcome would be.   Black jack is considered a game of

            skill but at what point does it become skill and not chance.  A unskilled player could effect the outcome

            of the most skilled player.  Would this not boil down to all games being chance regardless of which

            one played.  Counting cards could give an advantage but with so many variables it seems that the results

            could be considered random at best.  It seems that because so few people ever win a jackpot of any

            size verses the dollars spent which is purely a matter of odds,  that many jump on the bandwagon of

            criticism feeling safe and secure instead of attempting something in which they might fail and this post

            might be a way to feel better about their lack or fear of trying.  Predicting someone will lose is easy. 

             

            RL

            Most people here are aware that counting cards in Blackjack is a skill that can be learned.  Metaphorically speaking, they should also know that Lottery players must deal with a newly shuffled deck after each hand.  Your evasive discussion of Blackjack is what in Western PA we call, "A Lot of Baloney!"

            Do you have any thoughts on the study quoted above?  The ABSTRACT touches very closely on where your thinking is going awry.  I hope you will read it again.

            We can get to the question of "What Does it Take to Win" soon enough.

              RL-RANDOMLOGIC's avatar - usafce

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              Posted: February 3, 2011, 9:22 pm - IP Logged

              Most people here are aware that counting cards in Blackjack is a skill that can be learned.  Metaphorically speaking, they should also know that Lottery players must deal with a newly shuffled deck after each hand.  Your evasive discussion of Blackjack is what in Western PA we call, "A Lot of Baloney!"

              Do you have any thoughts on the study quoted above?  The ABSTRACT touches very closely on where your thinking is going awry.  I hope you will read it again.

              We can get to the question of "What Does it Take to Win" soon enough.

              Jimmy

              Why don't you quit being so nice and instead of posting links for us to read just come out

              and tell us how our ignorance and severe lack of math skills is placing us in jepordy of

              of not being able to make sound decisions that will change our lifes. The reply above to my

              post is considered in MO. to be a copout.  I would very much like you to show me in correct

              form how to calculate the odds for a five hand game with all the possible outcomes based

              on all the different plays that each of the other four players could make.  Show me the MATH.

              It's funny to me how people value their own views as being the only correct way to go. 

              RL


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                Posted: February 3, 2011, 10:20 pm - IP Logged

                Jimmy

                Why don't you quit being so nice and instead of posting links for us to read just come out

                and tell us how our ignorance and severe lack of math skills is placing us in jepordy of

                of not being able to make sound decisions that will change our lifes. The reply above to my

                post is considered in MO. to be a copout.  I would very much like you to show me in correct

                form how to calculate the odds for a five hand game with all the possible outcomes based

                on all the different plays that each of the other four players could make.  Show me the MATH.

                It's funny to me how people value their own views as being the only correct way to go. 

                RL

                RL-RANDOM-LOGIC,

                I initiated this topic to discuss Probability in relation to the lottery.  I chose to start by encouraging people to read a research report that deals directly with the problems most people have digesting probability theory.  I don't expect everyone to completely understand everything discussed in the report; I'm still studying it myself.  If others are willing to READ it, perhaps we can collectively understand it better.  But this is not your cup of tea apparently.  You are now demanding that I produce a mathematical proof of some aspect of the game of Blackjack.  This reminds me of the last time we reached an impasse like this.  At that time, you requested I take a test in Fortran because I mentioned I had formerly written Fortran programs to perform tasks that I felt were more challenging than those you claimed were not possible.  Namely, write a simulation to prove or disprove your Digit System.  So now, it appears we've come full circle.

                I intend on continuing with this topic as it was initiated, your desires notwithstanding.  If you would like to discuss the mathematics of Blackjack, you are free to start your own Topic.

                --Jimmy4164

                  RL-RANDOMLOGIC's avatar - usafce

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                  Posted: February 4, 2011, 2:25 am - IP Logged

                  RL-RANDOM-LOGIC,

                  I initiated this topic to discuss Probability in relation to the lottery.  I chose to start by encouraging people to read a research report that deals directly with the problems most people have digesting probability theory.  I don't expect everyone to completely understand everything discussed in the report; I'm still studying it myself.  If others are willing to READ it, perhaps we can collectively understand it better.  But this is not your cup of tea apparently.  You are now demanding that I produce a mathematical proof of some aspect of the game of Blackjack.  This reminds me of the last time we reached an impasse like this.  At that time, you requested I take a test in Fortran because I mentioned I had formerly written Fortran programs to perform tasks that I felt were more challenging than those you claimed were not possible.  Namely, write a simulation to prove or disprove your Digit System.  So now, it appears we've come full circle.

                  I intend on continuing with this topic as it was initiated, your desires notwithstanding.  If you would like to discuss the mathematics of Blackjack, you are free to start your own Topic.

                  --Jimmy4164

                  Jimmy

                  I read the Embracing Uncertainty: The Interface of Bayesian Statistics andCognitive Psychology.

                  The reply I posted really had nothing to do with blackjack.  The post was on topic and gave three

                  different games of chance for which both Bayesian Statistics andCognitive Psychology could be

                  applied.  The math was just to show that many unknowns exist in a multi player game which go

                  mostly unmentioned.   When using Bayes as a method to calculate the probability these variables

                  are needed.   I will now refrain from making any more post here


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                    Posted: February 10, 2011, 6:59 pm - IP Logged

                    Jimmy

                    I read the Embracing Uncertainty: The Interface of Bayesian Statistics andCognitive Psychology.

                    The reply I posted really had nothing to do with blackjack.  The post was on topic and gave three

                    different games of chance for which both Bayesian Statistics andCognitive Psychology could be

                    applied.  The math was just to show that many unknowns exist in a multi player game which go

                    mostly unmentioned.   When using Bayes as a method to calculate the probability these variables

                    are needed.   I will now refrain from making any more post here

                    RL-RANDOMLOGIC said,"The reply I posted really had nothing to do with blackjack."

                    He sure fooled me, starting with the Title - Blackjack vs Lottery!

                    Counting cards in Blackjack is a skill based on observing the cards drawn which are NOT RETURNED to the decks until the NEXT SHUFFLE.

                    In the Lottery, all the balls selected are returned to the machine AFTER EACH DRAW to await the NEXT DRAW.

                    This is an EXTREMELY LARGE difference between the 2 games!

                    --Jimmy4164

                      RL-RANDOMLOGIC's avatar - usafce

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                      Posted: February 10, 2011, 11:33 pm - IP Logged

                      RL-RANDOMLOGIC said,"The reply I posted really had nothing to do with blackjack."

                      He sure fooled me, starting with the Title - Blackjack vs Lottery!

                      Counting cards in Blackjack is a skill based on observing the cards drawn which are NOT RETURNED to the decks until the NEXT SHUFFLE.

                      In the Lottery, all the balls selected are returned to the machine AFTER EACH DRAW to await the NEXT DRAW.

                      This is an EXTREMELY LARGE difference between the 2 games!

                      --Jimmy4164

                      jimmy

                      Only if you ignore the psychology behind why one would consider BJ a acceptable game of chance

                      with such a large total of possible outcomes.  Anyone who gambles against odds greater then 

                      50/50 should expect to lose more then they win.   Enough said.

                        time*treat's avatar - radar

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                        Posted: February 11, 2011, 8:53 am - IP Logged

                        In the era of computer controlled drawings, sometimes things happen more often than pure "math" would predict. Some people take advantage of this. Their payouts indicate they did better making those self-selections than others who did not follow suit.

                        California: http://www.lotterypost.com/news/112810

                        Kansas: http://www.lotterypost.com/news/125196

                        Tennessee: http://www.lotterypost.com/news/173231

                        In neo-conned Amerika, bank robs you.
                        Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.


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                          Posted: February 11, 2011, 3:31 pm - IP Logged

                          In the era of computer controlled drawings, sometimes things happen more often than pure "math" would predict. Some people take advantage of this. Their payouts indicate they did better making those self-selections than others who did not follow suit.

                          California: http://www.lotterypost.com/news/112810

                          Kansas: http://www.lotterypost.com/news/125196

                          Tennessee: http://www.lotterypost.com/news/173231

                          Also check my comment here:

                          http://www.lotterypost.com/news/227521

                          It is not only possible, but highly likely, that people will "beat the odds" in the SHORT run.  You need to understand the concept of Standard Deviation in Stochastic Processes to know why this is true.  The important question you need to ask is, "How LONG is SHORT in my particular game?"  Because when your SHORT time comes to an end, unless you know it has, and you run with the money, you will very likely give back all your winnings in the LONG run!  (Unless you hit the Jackpot, of course!)


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                            Posted: February 11, 2011, 3:37 pm - IP Logged

                            P.S.  For the reasons shown in your 3 links,

                            I don't play games with computerized Draws.

                            I feel much more secure with the Ball machines!

                            I say this from the point of view of a Computer Programmer.

                              CajunWin4's avatar - Lottery-061.jpg
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                              Posted: February 27, 2011, 4:00 pm - IP Logged

                              The only random act is the very first draw .......