The top face will be more probable
Quote: billryanQuote: AlanMendelsonKeep in mind the Super Bowl toss is on turf. No bounce. Gravity.
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turf or astroturf? Indoors or outside? Wind direction and velocity? Dew point?
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The scientists say that they found that air drag and atmospheric conditions can be ignored in their modeling of coin flips -they found no statistically significant effect.
Perhaps this is an opportunity to learn, rather than to mock. Basically what the scientists are saying is that while various initial conditions of the coin flip are unknown and essentially unknowable that there is one important initial condition that is known, i.e., which side of the coin is initially on top. And that that particular initial condition is not completely randomized by the variability in the other initial conditions.
Rule of nature: Learn or get eaten.
In the meantime, until I see evidence that a coin lands exactly the same on grass, turf and artificial turf, I'll question any conclusions drawn from this.
Remember that these are academic scientists with expertise in non-linear mathematics, chaos theor y and numerical modeling of mechanical systems attempting to discern whether the unknowable initial conditions of a coin toss (angle of trajectory, force of throw, angular momentum, height above the ground, elasticity of the ground, atmospheric conditions, frictional drag terms of the ground, etc.) makes the coin toss truly chaotic and thus random. And they've determined both through theory and some experiments that there is an element of determinism in the outcome tied to the initial position of the coin (i.e., which face of the coin is up). The later paper on throwing dice (which are 3-d cubes) apparently claims the same thing. These papers have been peer-reviewed.
You and everyone else are of course free to have whatever opinions that you wish. That makes a forum interesting. I'm just trying to interpret what the paper seems to be saying and explain it.
Quote: AlanMendelsonQuote: Ace2Slightly = not enough to make any noticeable difference in your craps resultsQuote: lilredroosterQuote: AlanMendelsonI think everyone will agree that this opens up some validity for dice setting. Maybe it's not a whole lot of validity but it's no longer superstition.
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no I don't agree
from the article:
"they show that dice thrown with a 1 on top are 𝙨𝙡𝙞𝙜𝙝𝙩𝙡𝙮 more likely to land as a 1___________"
they do not define slightly___________which is unfortunate____________even so
I would tend to believe that to a scientist "slightly" means far less than what would be necessary to overcome the HA
until they clearly define what 𝙨𝙡𝙞𝙜𝙝𝙩𝙡𝙮 means, dice setting remains a pipe dream
.
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So... is being a little bit pregnant being pregnant?
If dice can be influenced by even one-one-thousandth of one percent aren't they still being influenced?
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Not sure if you’ve read my dozens (hundreds?) of posts regarding dice setting. I always say that there is no one who can, with a legal toss, set the dice in a way to overcome the house edge. I have not eliminated the possibility of some infinitesimally small alteration of results from a purely random roll. But I know there is no one who can change the house edge to a player edge. So if I agree with you that it is possible for a thrower to ‘influence’ the dice, but not to any real world amount, are we agreeing with each other or disagreeing with each other?
Quote: DeMangoYes indeed when it comes to dice the laws of physics are suspended..
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That's the way eyeroll.
Quote: SOOPOOQuote: AlanMendelsonQuote: Ace2Slightly = not enough to make any noticeable difference in your craps resultsQuote: lilredroosterQuote: AlanMendelsonI think everyone will agree that this opens up some validity for dice setting. Maybe it's not a whole lot of validity but it's no longer superstition.
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no I don't agree
from the article:
"they show that dice thrown with a 1 on top are 𝙨𝙡𝙞𝙜𝙝𝙩𝙡𝙮 more likely to land as a 1___________"
they do not define slightly___________which is unfortunate____________even so
I would tend to believe that to a scientist "slightly" means far less than what would be necessary to overcome the HA
until they clearly define what 𝙨𝙡𝙞𝙜𝙝𝙩𝙡𝙮 means, dice setting remains a pipe dream
.
link to original post
link to original post
So... is being a little bit pregnant being pregnant?
If dice can be influenced by even one-one-thousandth of one percent aren't they still being influenced?
link to original post
Not sure if you’ve read my dozens (hundreds?) of posts regarding dice setting. I always say that there is no one who can, with a legal toss, set the dice in a way to overcome the house edge. I have not eliminated the possibility of some infinitesimally small alteration of results from a purely random roll. But I know there is no one who can change the house edge to a player edge. So if I agree with you that it is possible for a thrower to ‘influence’ the dice, but not to any real world amount, are we agreeing with each other or disagreeing with each other?
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Unfortunately these scientists didnt give statistics about casino craps and dice throwing.
The only thing they said is that a thrower can put some influence on dice.
There is no indication that the influence can beat the edge which is determined by the payouts.
I'm just happy to read that these scientists have determined dice influencing is real. They didnt say anything about using influence to beat the house edge.
If they published info which said the house edge cannot be beaten but dice influencing can still have an effect, I would accept that.
Again. The scientists did not say anything about the house edge at craps.
`I do count dice. Results go through a computer program with a built in Chi Square test. every now and then a perfect score = .0000 !! Such to be you!Quote: billryanForget dice control. Learn how to count dice. It's more fun and every bit as effective.
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Quote: DeMango`I do count dice. Results go through a computer program with a built in Chi Square test. every now and then a perfect score = .0000 !! Such to be you!Quote: billryanForget dice control. Learn how to count dice. It's more fun and every bit as effective.
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Does quitting while ahead help?
Why quit when you have an advantage?Quote: billryanQuote: DeMango`I do count dice. Results go through a computer program with a built in Chi Square test. every now and then a perfect score = .0000 !! Such to be you!Quote: billryanForget dice control. Learn how to count dice. It's more fun and every bit as effective.
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Does quitting while ahead help?
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also avoids inter-dice collisions or contacts with side walls, puck, chips,
floor, money, etc.
Why?
Because such tosses are not completely under the control of the shooter
and the real result is UNKNOWN from a DI's point of view. All BT and CHI Sq
results are marred by unknown results that we all know are more likely to be a
7 than, let's say, the hard 8 that resulted when the left die was prematurely
stopped when it hit the puck.
For 99.99% that means their "skill" at avoiding the seven is poorly measured
and dubious at best.
I'm not disputing DM's Chi results. I personally am highly skeptical, however.
'
IMO, the facts speak for themselves. The DI community is in complete denial
when it comes to using BT to measure their "skill". While thousands of DI's
have boasted their results of SRR's/CHI that profess their awesome skills at
avoiding the seven, these flashes in the pan are invariably cherry-picked
sessions that never can be reproduced and just qualify as variance.
At poor skill levels, which is probably 99% of DI-wannabees, the dice will
encounter interference as I stated previously, which makes the result of the
toss meaningless as far as the toss being under shooter control.
From a DI's point of view, Shooter-control vs. Interference is the difference
between Valid DI-toss results and Invalid DI-toss results. (We're not talking
about "legal" tosses which are easily thrown by any chimpanzee or human.)
To measure skill, an SRR must be measured by CONSECUTIVE legal tosses with no
intervening UNKNOWN results which results would be more likely a seven than not...
Pepper your awesome CHI or BT with a few sevens from those interfered-with
tosses and see where you skills or lack thereof lay.
Quote: onebokOf course numbers lie if they are not measuring what you think they are!
IMO, the facts speak for themselves. The DI community is in complete denial
when it comes to using BT to measure their "skill". While thousands of DI's
have boasted their results of SRR's/CHI that profess their awesome skills at
avoiding the seven, these flashes in the pan are invariably cherry-picked
sessions that never can be reproduced and just qualify as variance.
At poor skill levels, which is probably 99% of DI-wannabees, the dice will
encounter interference as I stated previously, which makes the result of the
toss meaningless as far as the toss being under shooter control.
From a DI's point of view, Shooter-control vs. Interference is the difference
between Valid DI-toss results and Invalid DI-toss results. (We're not talking
about "legal" tosses which are easily thrown by any chimpanzee or human.)
To measure skill, an SRR must be measured by CONSECUTIVE legal tosses with no
intervening UNKNOWN results which results would be more likely a seven than not...
Pepper your awesome CHI or BT with a few sevens from those interfered-with
tosses and see where you skills or lack thereof lay.
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Even if someone is a master at influencing dice there is still a luck factor. Just like there's a luck factor in golf and baseball and football and darts and shooting marbles.
think they've finally reached DI-nirvana.
Quote: onebokI totally agree. I would view that as most likely a cause for those monster rolls that make the DI-Wannabee
think they've finally reached DI-nirvana.
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Card counters and those who play abandoned multipliers need luck too.
Quote: AlanMendelsonQuote: onebokI totally agree. I would view that as most likely a cause for those monster rolls that make the DI-Wannabee
think they've finally reached DI-nirvana.
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Card counters and those who play abandoned multipliers need luck too.
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Card counters do not need luck. All they need is a fair game.
Craps is a game of luck. For some, BJ is a game of skill.
Quote: DeMangoNumbers don't lie. "Marred by unknown results" Perfect double speak. Try again.
'
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Two great memorable quotes:
"There are three kinds of lies: Lies, Damn Lies and Statistics."
and
"If you torture numbers, they will confess to anything."
https://aip.scitation.org/doi/pdf/10.1063/1.4746038
for $35 or through your institution if they have a subscription.
I don't have access through an institution. Does anyone else have access? If so, would you be willing to share the pdf of this article through email or however?
Quote: gordonm888The pdf of the article ""The three-dimensional dynamics of the die throw" can be accessed here:
https://aip.scitation.org/doi/pdf/10.1063/1.4746038
for $35 or through your institution if they have a subscription.
I don't have access through an institution. Does anyone else have access? If so, would you be willing to share the pdf of this article through email or however?
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I hear rumors that many in academia are allowed to email you copies of their published papers, and are thrilled to get fan mail from people outside their buildings.
I do not, unfortunately, have the email addresses of any of the authors.
Quote: DieterQuote: gordonm888The pdf of the article ""The three-dimensional dynamics of the die throw" can be accessed here:
https://aip.scitation.org/doi/pdf/10.1063/1.4746038
for $35 or through your institution if they have a subscription.
I don't have access through an institution. Does anyone else have access? If so, would you be willing to share the pdf of this article through email or however?
link to original post
I hear rumors that many in academia are allowed to email you copies of their published papers, and are thrilled to get fan mail from people outside their buildings.
I do not, unfortunately, have the email addresses of any of the authors.
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I am not intend to ask anyone to do something that is ethically wrong. Many academics have a personal webpage in which links are provided to PDFs of their older journal articles (say, > 1-2 years old). And there are usually no conditions or restrictions on transmitting these PDFs to other interested persons. I'm still working through the authors of this dice throwing paper, but so far I have not located a publicly offering of the PDF of this obscure 2012 paper. I will continue to work it.
Edit: I have found a link for a pdf of a related article by many of the same authors: "Can the Dice be Fair by Dynamics" https://www.researchgate.net/publication/220265123_Can_the_Dice_be_Fair_by_Dynamics
ExactlyQuote: billryanQuote: AlanMendelsonQuote: onebokI totally agree. I would view that as most likely a cause for those monster rolls that make the DI-Wannabee
think they've finally reached DI-nirvana.
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Card counters and those who play abandoned multipliers need luck too.
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Card counters do not need luck. All they need is a fair game.
Craps is a game of luck. For some, BJ is a game of skill.
link to original post
Quote: gordonm888The pdf of the article ""The three-dimensional dynamics of the die throw" can be accessed here:
for $35 or through your institution if they have a subscription.
I don't have access through an institution. Does anyone else have access? If so, would you be willing to share the pdf of this article through email or however?
link to original post
To what e-mail address do I send it?
Quote: DieterI predict a surge in PM traffic in the coming hours.
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I’ll send an email to gordonm888 and he can handle it from there.😎
Quote: AlanMendelsonEven if someone is a master at influencing dice there is still a luck factor. Just like there's a luck factor in golf and baseball and football and darts and shooting marbles.
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Mr. Mendelson: Perhaps the most prominent name in DC/DI is Frank Scobleet. For years he admittedly scammed wanabees with classes, paraphernalia, lectures, and web sites. He eventually came clean and divorced himself from all the huckstering. I can not be sure, but my thoughts believe someone sued. There is no science or meaningful performances of DI/DC that show actual DC/DI on a statistical level for consistent winning.
Your second sentence above, IMO, is an over the top generalization. You did provide a caveat using the term "factor." Could more readily define, perhaps, by percentage, what the "luck factor" is in the sports shown above. For example, could you tell us what the "luck factor" was for Tiger Woods winning 82 PGA tournaments including 15 majors as well as another approximately 19 other overseas tournaments? That would be a good start.
tuttigym
J. STRZALKO, J. GRABSKI, A. STEFANSKI and T. KAPITANIAK
Division of Dynamics, Technical University of Lodz,
Stefanowskiego 1/15, 90-924 Lodz, Poland
International Journal of Bifurcation and Chaos, Vol. 20, No. 4 (2010) 1175–1184
c World Scientific Publishing Company
DOI: 10.1142/S021812741002637X
https://www.researchgate.net/publication/220265123_Can_the_Dice_be_Fair_by_Dynamics
Here is my attempt to relate the findings in this article in straightforward language for a cube-shaped die thrown onto a hard flat (planar) surface.
The authors calculated the difference between the average probabilities of the cubical die landing on the initial bottom face and the theoretically expected random probability, 1/6, for different (randomly selected) values of height above the table and initial angular momentum components in three dimensions, i.e., for the spatial components of ω0. The average has been calculated over two million simulations for mass m = 0.016[kg], and χ = 0.5 where χ is the coefficient of restitution of the bounce, χ = vAz/v'Az, in which v'Az and vAz are the projections of the velocity of the point of the dice vertex A that hits the table in the direction (z) normal to the impact surface, before and after the impact, respectively. (Note: χ = 0 represents a soft surface with essentially no bounce.) The simulations used these randomly chosen initial conditions:
- Initial height above the table z0 ∈ [15a, 20a] where a is the dimension of the die 0.02m,
- Initial precession in the frame of the die, ψ0 ∈ [0, 2π],
- Initial nutation in the frame of the die ϑ0 ∈ [0, 2π],
- Initial spin (intrinsic rotation) in the frame of the die ϕ0 ∈ [0, 2π].
It is not stated whether the randomly chosen conditions are from a normal distribution or for a flat distribution within the stated boundaries. Note that atmospheric drag was ignored because it had been previously found to have negligible effects.
Result for cube-shaped die with 6 faces
When the die is thrown from the hand or the cup in these simulations the realistic values of initial angular momentum, ω0 are reported to be in the range 20–40 [rad/s] (the latter value said to represent a vigorous throw) and the typical number of bounces was found to be about 4–5.
- For initial angular momentum 20 rad/sec the die was seen to land with the same top side up with a probability of 1/6 *(1 + 0.101).
- For initial angular momentum 40 rad/sec the die was seen to land with the same top side up with a probability of 1/6 *(1 + 0.063).
One comment by me
In my reading of the article, it appears that the authors may have used a fixed (unchanging) value of initial translational velocity of the die in the x,y and z direction. This would be equivalent to taking all the randomness or uncertainty in initial kinetic energy as randomness or uncertainty in the angular momentum components of the dice (rather than randomness in the translational momentum). My initial inclination is to assume the authors knew what they were doing when making this assumption, but any and all comments are welcome.
One way-cool graphic from the article
Quote: gordonm888(snip)
- For initial angular momentum 20 rad/sec the die was seen to land with the same top side up with a probability of 1/6 *(1 + 0.101).
(snip)
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I am often not good at reading/understanding these kind of articles, but does this mean that the chance of rolling a 7 goes from 6/36 (1/6) to ~ 1/5.988 (see example below)
example: if you had a 1 on one die and a 6 on another die as the "top side up" and managed to "perfectly" roll them with an "...initial angular momentum 20 rad/sec...", then the chance of getting any seven goes from 1/6 to about ~1/5.988 (16.70067%).
Am I correct for the above example?
Please reply with the correct answer if mine is wrong, thanks.
tuttigym
Quote: tuttigymI personally did not spend the time to read this "research." I did read Mr.G888's summary. IMO this "research," as it relates to the game of craps, is worthless because (1) it was done by computer simulation, "calculated of over 2 million simulations," (2) there were no hand tossed dice throws, (3) a craps table or any table for that matter was not used, and (4) there was no wall with pyramids rebounding done. In short, there was no performance of any real science, just hypothetical conjecture which is basically worthless and beyond unreliable.
tuttigym
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It's fascinating that hypothetical and computer simulations are valid for some discussions but not for others.
And what happened with the cameras shooting 1500 frames per second?
Quote: tuttigymI personally did not spend the time to read this "research." I did read Mr.G888's summary. IMO this "research," as it relates to the game of craps, is worthless because (1) it was done by computer simulation, "calculated of over 2 million simulations," (2) there were no hand tossed dice throws, (3) a craps table or any table for that matter was not used, and (4) there was no wall with pyramids rebounding done. In short, there was no performance of any real science, just hypothetical conjecture which is basically worthless and beyond unreliable.
tuttigym
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My understanding is that some craps games with electronic wagering also do not involve pyramid walls, tables, or hand tossed dice.
Quote: DieterQuote: tuttigymI personally did not spend the time to read this "research." I did read Mr.G888's summary. IMO this "research," as it relates to the game of craps, is worthless because (1) it was done by computer simulation, "calculated of over 2 million simulations," (2) there were no hand tossed dice throws, (3) a craps table or any table for that matter was not used, and (4) there was no wall with pyramids rebounding done. In short, there was no performance of any real science, just hypothetical conjecture which is basically worthless and beyond unreliable.
tuttigym
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My understanding is that some craps games with electronic wagering also do not involve pyramid walls, tables, or hand tossed dice.
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So, how does that relate to this thread? The "research" discusses dice tossing, so your point is?
tuttigym
Quote: ksdjdjQuote: gordonm888(snip)
- For initial angular momentum 20 rad/sec the die was seen to land with the same top side up with a probability of 1/6 *(1 + 0.101).
(snip)
link to original post
Please reply with the correct answer if mine is wrong, thanks.
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(1/6) * (1+0.101) = (1/6) * (1.101) = .1835
1/.1835 <> 1/5.45
/web/20151210043949id_//papers/2012/Strzalko_Grabski_Wojewoda_Wiercigroch_Kapitaniak.pdf
Quote: tuttigymCan you link to a source please?Quote: AlanMendelson
Mr. Mendelson: Perhaps the most prominent name in DC/DI is Frank Scobleet. For years he admittedly scammed wanabees with classes, paraphernalia, lectures, and web sites. He eventually came clean and divorced himself from all the huckstering.
link to original post♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
Quote: tuttigymCan you link to a source please?Quote: AlanMendelson
Mr. Mendelson: Perhaps the most prominent name in DC/DI is Frank Scobleet. For years he admittedly scammed wanabees with classes, paraphernalia, lectures, and web sites. He eventually came clean and divorced himself from all the huckstering.
link to original post♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
this goes back pretty far and maybe most already know about it but maybe some don't
there was a challenge to dice influencing that included betting that involved Stanford Wong, one of the greatest blackjack authors ever, who wrote a positive book on dice influencing called "Wong on Dice." Mike was involved in this.
there were 2 sessions_____________the first session involved Wong and somebody called "Little Joe"
the first test involved 500 decisions and Wong and Little Joe won__________indicating they were successful at dice influencing
but Little Joe came back for a 2nd bet involving 1,000 decisions and lost -
and adding up the 2 sessions_____________the number of 7s that came out was almost exactly what randomness would predict
later, Bryce Carlson, another superstar blackjack author, posted on this forum, (linked) indicating that it appears that Wong was backtracking on his claim that dice influencing could be a legitimate AP technique
https://www.lasvegasadvisor.com/gambling-with-an-edge/a-look-at-wong-on-dice/
https://wizardofvegas.com/forum/gambling/craps/7093-wong-and-dice-control/7/
.
Quote: UsernameRemorseThis is a related paper written by the same authors:
/web/20151210043949id_//papers/2012/Strzalko_Grabski_Wojewoda_Wiercigroch_Kapitaniak.pdf
link to original post
Please PM the link to a moderator for approval.
Looks like the spam filter got hungry and ate this one.
Quote: tuttigymI personally did not spend the time to read this "research." I did read Mr.G888's summary. IMO this "research," as it relates to the game of craps, is worthless because (1) it was done by computer simulation, "calculated of over 2 million simulations," (2) there were no hand tossed dice throws, (3) a craps table or any table for that matter was not used, and (4) there was no wall with pyramids rebounding done. In short, there was no performance of any real science, just hypothetical conjecture which is basically worthless and beyond unreliable.
tuttigym
link to original post
First, this scientific article was not written about gambling nor about craps. I think the authors' only citation to a gambling source was a 1956 book on casino games, LOL!. Virtually all the regulars on this forum probably know far more about gambling than the authors, who don't claim to be knowledgable on that subject. This article documents new knowledge about determinism versus chaotic "randomness" on a well-defined case: throwing a die on a "hard" flat planar surface. Whether that new knowledge is applicable to anything any of us care about is for each person to determine.
They did do experimental research on dice throws with a high speed camera, mentioned in this article and more prominently discussed in other articles.
They also documented their observations about the intermingling of basins of attraction as a function of number of bounces, which is germane to chaos theory and nonlinear mathematics. That was a primary point for doing the research. The fact that you don't understand chaos theory and what those words mean doesn't make this paper worthless, IMO.
The requirement that the dice bounce off the back wall of a craps table is definitely an added randomization feature not covered in this article. No one is claiming that this work involved modeling the specific case of dice thrown on a craps table.
tuttigym
Quote: UsernameRemorseQuote: ksdjdjQuote: gordonm888(snip)
- For initial angular momentum 20 rad/sec the die was seen to land with the same top side up with a probability of 1/6 *(1 + 0.101).
(snip)
link to original post
Please reply with the correct answer if mine is wrong, thanks.
link to original post
(1/6) * (1+0.101) = (1/6) * (1.101) = .1835
1/.1835 <> 1/5.45
link to original post
Yes, I agree with the figure for one die, as I used that figure as a starting point in working out my attempt at an answer for "rolling a 7" when they are thrown separately***.
***: I know the above is a hypothetical scenario that would "never happen in a real life Craps game, even if you were allowed to roll the die separately" (but I was still interested).
----
Did it another way by using a spreadsheet instead of a calculator, and I am almost certain my original answer of ~16.7% was correct.
Important: Based on the assumption that all other numbers (besides the "top face" before the roll) would have an "equal chance of coming up after the roll" (I am guessing it would be a more complex formula, IRL, but I don't know what that formula would be).
---
Since the chance of getting "any 7" doesn't change "very much", a better example to use for "Craps hypotheticals" would have been 1-1 or 6-6, because you can bet on a "30-1 spot" for those options (see 1-1 example, below).
1-1 example: If both die are rolled with a 1 as the top face, then 3.367225% would have been the chance of getting 1-1^^^ (if you were allowed to / and could physically roll the same way that was done in the article).
^^^: Under this specific hypothetical scenario, the player would have almost a 4.4% advantage over the casino.
M. Kapitaniak, J. Strzalko, J. Grabski, and T. Kapitaniak
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science 22, 047504 (2012); doi: 10.1063/1.4746038
You may download the pdf of this article here: PDF link
This is a later paper by the same authors, a "review of the subject" with some interesting historical comments about scientists looking at this subject over the centuries (including Diaconis) and an interesting list of references. It is easier to read than the previous article, i.e., more accessible to the layman reader. It covers some new ground, such as throwing dice onto an oscillating surface (which I suspect may resemble a "Magic Fingers" mattress more than the back wall of a craps table.) Not much new information here that is relevant to people trying to understand whether dice setting might be possible in even a marginal way.
I'm happy to email the pdf to anyone who would like to receive it in that way rather than download via the above link. Just send me a private message here on the forum with your email address.
I was not very impressed with the mathematical rigor of that paper. However, I probably would agree with the bottom line premise. I think any bias towards the top side of the dice is very negligible at a craps table, probably worth under a penny with thousands of dollars bet, but that is just conjecture.
I think the reason is the same as that of a coin flip -- where the coin is slightly more likely to land on the side that started in the up position. This can be proven mathematically if we assume the number of rotations of the coin follows a Poisson process, regardless of the mean number of flips.
At Quora, we find the following post:
Quote: Richard Engelbrecht-Wiggans (Professor Emeritus, Business Administration at University of Illinois at Urbana-Champaign)
Originally Answered: Is flipping a coin really a 50/50 chance? I am often able to control the speed and number of rotations of the flipped coin.
You mention controlling the speed and number of rotations. When I filmed my coin tosses many years ago as part of science experiment, the coin made roughly three complete rotations during the flip before I caught it on its way down. Half a flip more or less than three rotations is plus or minus about 17%. It is relatively easy to train oneself to repeat physical tasks to within less than plus or minus 17%; for example to make a free throw shot in basketball requires more accuracy than plus minus 17%.
I was able to train myself so that I caught the coin with the same side up as I started well over 90% of the time. My brother, who more determined, eventually managed to make 100 tosses in a row where he caught the coin with the same side up as he started. However, you have much less control over things, and the outcome is much closer to 50–50, if you let the coin drop to the floor (and bounce and/or roll around) before it comes to rest rather than catching it on the way down.
Note: Emphasis mine.
If we assume an average of three complete rotations and the actual number follows a Poisson process, I show the probability the coin lands on the starting side is 0.5000030721.
I can prove this to be true, but will save that for later. Again, it works for any mean.
I submit for the consideration of the forum that the die conjecture is just an extension of the coin conjecture, which has a lot of mathematical and physical evidence is true. Look it up, there are a surprisingly lot of academic papers on the topic.
Finally, I've noticed in playing Risk some players seems to get a LOT of high numbers. They do a very gentle controlled roll just above the board with a minimum of dice rotations, when the last roll was good. If the last roll was bad, they mix it up more. Maybe this is confirmation bias, but I believe so strongly in this that I won't play with players who do this twice.
Quote: ksdjdj
-snip-
Important: Based on the assumption that all other numbers (besides the "top face" before the roll) would have an "equal chance of coming up after the roll" (I am guessing it would be a more complex formula, IRL, but I don't know what that formula would be).
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My reading of the article is that the top face (in the initial position) is most probable and that the bottom face is less probable. The other four faces would have an unchanged probability, i.e., 1/6.
Quote: gordonm888Quote: ksdjdj
-snip-
Important: Based on the assumption that all other numbers (besides the "top face" before the roll) would have an "equal chance of coming up after the roll" (I am guessing it would be a more complex formula, IRL, but I don't know what that formula would be).
link to original post
My reading of the article is that the top face (in the initial position) is most probable and that the bottom face is less probable. The other four faces would have an unchanged probability, i.e., 1/6.
link to original post
Makes sense, thanks.
Update (about 1920, Pac Time):
When I put those numbers in the spread sheet, I get a slightly different chance figure of ~16.72% (instead of the ~16.70% figure I had in my earlier posts).
