Robert Johnson
New member
- Joined
- Feb 17, 2020
- Messages
- 5
How to apply the empirical rule (68–95–99.7 rule) to the following scenario:
I have spent a significant amount of time trying to do the impossible (i.e., mathematically beat a game 'of chance' that has a negative expectation). Yes, I know, mathematicians for hundreds of years have failed at this (but that is only partially true). I can give examples, if need be, where games conventionally thought to be unbeatable have been beaten. My formulas do not involve the simplistic use of input/variable change the way, let’s say, card counting or other such formulas have been used to win at certain ‘games’ of chance. My dad taught me calculus by 7th grade and ‘card counting’, of all things, by 8th grade, so my love of math and ‘beating games of chance’ has been an ongoing love affair over my short life : - )
I have not as yet been able to program/code the formulas to test large data sets, as coding my formulas is proving to be challenging, so I have been performing longhand calculations (very time consuming and tedious). My starting points are: (a) I may only start with a small sum of money ($100 to $500 as an example, let's use $100 in this example) and (b) when wagering (on paper), I am never increasing the spread between bets (i.e., I am winning by flat betting (always using the same amount each time as the wager), but I have also created changes to my formulas that allow me to stagger my betting amounts (as with card counting) to 1.5x, 2x, 4x, (my cap is 4x the lowest bet amount). In all cases, whether via flat betting or using a small spread (1.5x to a max of 4x), I am able to consistently have a positive outcome (i.e., a profit/net gain), and always, over time, multiply my starting amount/sum/bankroll (albeit only on paper, as this is math/mathematical logic challenge for me).
Is my achievement random?
I have now multiplied my ‘random’ hypothetical starting sum (bankroll) 57x which means the odds of this occurring randomly are low: X/(X + (57X)) = 1 / (1 + 57) = 0.01724 (a 1.724%) chance my success is random (assuming I am using that correct algebra formula to calculate this ratio which indicates the probability of my achievement being a random event. I have been told that when I reach 1% or lower (which will take a fair amount of time testing data manually) this is considered by most mathematicians to be ‘near certainty’ that the result I am achieving is ‘not random’. I am current in some areas of math and not current in other areas (i.e., I still have yet to take the courses in statistics or teach myself) but I am wondering what variables to plug into the empirical rule to see if I am within 3 standard deviations.
I typically retain 18% of every dollar I win on paper… meaning I will win $100, then lose $82, then win $100 and lose $82, with the 'retained' amount of $18 accumulating over time as I get through larger and larger data sets. In other words, the $18 that my formulas allow me to attain (i.e., the sum of total $ retained (won)), have now accumulated to 57x my random starting sum (i.e., called bankroll by gamblers). E.g. I started with $100 and now have $5700. I am not a gambler, just trying to solve a long thought to be impossible math matter.
What numbers can I plug into 68–95–99.7 rule to ascertain my level of certainty that my formula is working?
Using this formula:
Pr(μ-2σ ≤ X ≤ μ + 2σ) ≈ 0.9545
or
Pr(μ-3σ ≤ X ≤ μ + 3σ) ≈ 0.9973
I know where Χ is “an observation from a normally distributed random variable”, but in my case/scenario what is “X”? The number of ‘Sums/Multiple of starting Bankroll” won? The amount ($) retained (i.e., the net) per $100 of gross winnings? I know it is likely none of these, but what value should I use for X?
μ is the mean of the distribution, and σ is its standard deviation, but in my scenario what numbers do I plug into μ and σ?
My goal is in asking this question is to have some method for determining when I am within three standard deviations, and therefore my result will be considered "significant” and able to qualify as a discovery.
Please do not ask me to share my formulas (in order to allow for peer review), as even my existing formulas, although still being tested/validated) have significant ‘real world’ value that I plan to apply ‘for public good’. I may be young, but as a kid growing up these days, I am not gullible just because I am young : -) [no insult intended]. The internet has made us aware and savvy in terms of gaining real world skills at a young age. Also, I have nearly lost the use of my writing arm because I have spent so many thousands of hours after school (sitting and not moving) and just writing, that I feel like my left arm is atrophying, so for that reason alone I would not share my formulas. I actually want to use what I have discovered to earn a PhD, but not till I have achieved the level of monetization I seek and only then in order to apply such monetization towards a special philanthropy project I have created for the public good. I understand that I will likely be required to share the formulas to attain my PhD, so I will only apply after I monetize my formulas and have my philanthropic efforts well underway.
I hope there are some math majors/professors/teachers/tutors on this forum who understand statistics as applied to games of chance (such as casino table games, which have a built in negative expectation (commonly referred to as the house edge)) who can help me learn what values to plug into X, μ and σ --- so I can apply the empirical rule/68–95–99.7 rule to learn when I have attained ‘near certainty’ and to determine whether my equations are yielding results that are ‘not random’. I know I still must accumulate more results over a larger data set, but how much larger a data set??... and how do I apply the empirical rule to determine whether my results are approaching 'near certainty'? And, how do I apply see if my results fall within the "three-sigma rule of thumb") or five as the case may be for this field of study.
I do have a feeling that for the results I am achieving to be considered "significant" I may have to apply the convention of a five-sigma effect (99.99994% confidence) before my results/formulas qualify as a discovery. At the very least, my existing results do currently have real world value, but once I learn how to code my formulas in order to be able to test data sets in the billions, I can then quickly ascertain where I sit in terms of whether I have achieved the five-sigma effect... (versus the tedious practicality of testing/calculating longhand). However, for now, just using the empirical rule, I cannot figure out what numbers to plug into the variables (X, μ and σ) in this scenario (as referenced above).
Thank you in advance for any assistance.
I have spent a significant amount of time trying to do the impossible (i.e., mathematically beat a game 'of chance' that has a negative expectation). Yes, I know, mathematicians for hundreds of years have failed at this (but that is only partially true). I can give examples, if need be, where games conventionally thought to be unbeatable have been beaten. My formulas do not involve the simplistic use of input/variable change the way, let’s say, card counting or other such formulas have been used to win at certain ‘games’ of chance. My dad taught me calculus by 7th grade and ‘card counting’, of all things, by 8th grade, so my love of math and ‘beating games of chance’ has been an ongoing love affair over my short life : - )
I have not as yet been able to program/code the formulas to test large data sets, as coding my formulas is proving to be challenging, so I have been performing longhand calculations (very time consuming and tedious). My starting points are: (a) I may only start with a small sum of money ($100 to $500 as an example, let's use $100 in this example) and (b) when wagering (on paper), I am never increasing the spread between bets (i.e., I am winning by flat betting (always using the same amount each time as the wager), but I have also created changes to my formulas that allow me to stagger my betting amounts (as with card counting) to 1.5x, 2x, 4x, (my cap is 4x the lowest bet amount). In all cases, whether via flat betting or using a small spread (1.5x to a max of 4x), I am able to consistently have a positive outcome (i.e., a profit/net gain), and always, over time, multiply my starting amount/sum/bankroll (albeit only on paper, as this is math/mathematical logic challenge for me).
Is my achievement random?
I have now multiplied my ‘random’ hypothetical starting sum (bankroll) 57x which means the odds of this occurring randomly are low: X/(X + (57X)) = 1 / (1 + 57) = 0.01724 (a 1.724%) chance my success is random (assuming I am using that correct algebra formula to calculate this ratio which indicates the probability of my achievement being a random event. I have been told that when I reach 1% or lower (which will take a fair amount of time testing data manually) this is considered by most mathematicians to be ‘near certainty’ that the result I am achieving is ‘not random’. I am current in some areas of math and not current in other areas (i.e., I still have yet to take the courses in statistics or teach myself) but I am wondering what variables to plug into the empirical rule to see if I am within 3 standard deviations.
I typically retain 18% of every dollar I win on paper… meaning I will win $100, then lose $82, then win $100 and lose $82, with the 'retained' amount of $18 accumulating over time as I get through larger and larger data sets. In other words, the $18 that my formulas allow me to attain (i.e., the sum of total $ retained (won)), have now accumulated to 57x my random starting sum (i.e., called bankroll by gamblers). E.g. I started with $100 and now have $5700. I am not a gambler, just trying to solve a long thought to be impossible math matter.
What numbers can I plug into 68–95–99.7 rule to ascertain my level of certainty that my formula is working?
Using this formula:
Pr(μ-2σ ≤ X ≤ μ + 2σ) ≈ 0.9545
or
Pr(μ-3σ ≤ X ≤ μ + 3σ) ≈ 0.9973
I know where Χ is “an observation from a normally distributed random variable”, but in my case/scenario what is “X”? The number of ‘Sums/Multiple of starting Bankroll” won? The amount ($) retained (i.e., the net) per $100 of gross winnings? I know it is likely none of these, but what value should I use for X?
μ is the mean of the distribution, and σ is its standard deviation, but in my scenario what numbers do I plug into μ and σ?
My goal is in asking this question is to have some method for determining when I am within three standard deviations, and therefore my result will be considered "significant” and able to qualify as a discovery.
Please do not ask me to share my formulas (in order to allow for peer review), as even my existing formulas, although still being tested/validated) have significant ‘real world’ value that I plan to apply ‘for public good’. I may be young, but as a kid growing up these days, I am not gullible just because I am young : -) [no insult intended]. The internet has made us aware and savvy in terms of gaining real world skills at a young age. Also, I have nearly lost the use of my writing arm because I have spent so many thousands of hours after school (sitting and not moving) and just writing, that I feel like my left arm is atrophying, so for that reason alone I would not share my formulas. I actually want to use what I have discovered to earn a PhD, but not till I have achieved the level of monetization I seek and only then in order to apply such monetization towards a special philanthropy project I have created for the public good. I understand that I will likely be required to share the formulas to attain my PhD, so I will only apply after I monetize my formulas and have my philanthropic efforts well underway.
I hope there are some math majors/professors/teachers/tutors on this forum who understand statistics as applied to games of chance (such as casino table games, which have a built in negative expectation (commonly referred to as the house edge)) who can help me learn what values to plug into X, μ and σ --- so I can apply the empirical rule/68–95–99.7 rule to learn when I have attained ‘near certainty’ and to determine whether my equations are yielding results that are ‘not random’. I know I still must accumulate more results over a larger data set, but how much larger a data set??... and how do I apply the empirical rule to determine whether my results are approaching 'near certainty'? And, how do I apply see if my results fall within the "three-sigma rule of thumb") or five as the case may be for this field of study.
I do have a feeling that for the results I am achieving to be considered "significant" I may have to apply the convention of a five-sigma effect (99.99994% confidence) before my results/formulas qualify as a discovery. At the very least, my existing results do currently have real world value, but once I learn how to code my formulas in order to be able to test data sets in the billions, I can then quickly ascertain where I sit in terms of whether I have achieved the five-sigma effect... (versus the tedious practicality of testing/calculating longhand). However, for now, just using the empirical rule, I cannot figure out what numbers to plug into the variables (X, μ and σ) in this scenario (as referenced above).
Thank you in advance for any assistance.
