I forget how long ago but there was a guy who could flip a silver dollar and have it come up what he wanted something better than 90% of the time. Something I found interesting was that he could do it with a half-dollar but only about three-fourths of the time and as I recall with a quarter but only three-fifths of tosses.
I read about it in a science magazine where the writer posited that the larger mass of the silver dollar made for better control, assuming that the force applied to any given coin was the same.
Then there was the assignment in a probability course to flip a penny a thousand times. Two results stood out: first, the longest string of the same result was seven ‘heads’ in a row; second, overall – the total results of forty-some in the class – tails came up 52% of the time.
[The results led to an interesting question: was forty people flipping coin a thousand times each the same as one person flipping a coin forty thousand times? The professor answered with a question: what about forty thousand people each flipping a coin once?]
At any rate, the 52% was obviously a surprise, and if my math is right we should have expected a string of nine matching results in that many tosses.
Of course this was the introduction to a longer lesson, beginning with “What if the coins had three equal sides? four?” etc. – which points towards the difference in possibilities when shuffling cards as compared to coin tosses: increase the number of possible results and the space of actual results expands immensely.
It’s a philosophical question of what true randomness means. If the outcome is predictable on a larger scale, tending towards an equal distribution of results, then the process is not truly unpredictable or random.
What is the probability a program chooses 3 natural numbers that are identical?
One option for the string length is that people with no intent to manipulate the results tend to have the coin flip over relative to how it was sitting on their hand just before the flip slightly over half of the time and end up the same as it was slightly under half of the time. In the case of pennies, the heads side seems to be slightly heavier than tails, so a slight preponderance of tails is expected, especially if some of the coin flips landed on a hard surface before being read off, instead of a hand.
A random process is where individual outcomes are not predictable, even if the results are bounded by a known distribution. That would be the case for truly random processes.
100% if it is programmed to spit out 3 identical numbers. In Python:
I think I am somewhat intelligent, and I can say with great confidence that the Python script I showed you has a 100% probability of choosing 3 identical numbers.
Interesting. I do not have enough math background to calculate, but sure that 1000 flips while a lot, is not enough to determine whether a 52% tails result is real or purely chance in one student, though very suggestive when 40 students do it. In medicine, sometimes it takes years and large numbers to determine whether a treatment has adverse effects or not, and even then it is sometimes unclear. For example, the risk of breast cancer from hormone replacement therapy is real, but only 5 per 1000 women treated above the background rate of about 1 in 8, which means an individual physician can not see the risk in their practice above baseline. If my aging memory is correct, the study that found the difference followed 50,000 or so women. Of course, there is still the question of whether the benefits justify that risk.
There are AI programs that produce random numbers. You could probably look through their documentation to see what those probabilities are if you want.
For 1000 flips of a fair coin, getting 520 tails is about 1.26 standard deviations away from the expected mean of 500 tails. So you’re right - 1000 flips (with that result) would not have been enough to distinguish any real signal from purely random there. With 10,000 flips, though, getting 5200 tails would be 4 standard deviations out which would be a very suspicious circumstance indeed!
It’s a philosophical question of what true randomness means, and what happens when a computer is not using a psuedo-random number generator to produce numbers. It’s a foreseeable possibility quantum computing will allow for a computer to choose numbers.
I feel confident when that happens all probabilities are off (or on) the table. But emotions are something else altogether from the ability to choose.
I experienced grief today with the loss of a family pet. It has been a while since I felt deep grief and experienced how vividly it brings up memories. In a small way, it was as if my life passed before my eyes.
It would be one thing if HAL learns (or mimics) this behavior from its vast resources of data it draws on, but in the case of biological life, it is astounding how this would be an emergent property.
That makes sense. I know that long before I’d finished even a hundred flips I got tired of catching the coin and just let it land on the table, and then it wasn’t long before that got old and I tossed it into an old cigar box; table landings too often meant having to retrieve it from the floor while the cigar box caught it most of the time.
Which makes me think of a very human result from the experiment: no one actually sat down and just tossed the penny a thousand times through, in fact most of us ended up doing it while watching TV.
I sometimes think it would be fun to learn Python. Then I ask myself what I would actually use it for.
Given how vague that instruction is, it would depend on how the AI understood it. Writing a Python script illustrates the point; to get clear results you need clear instructions.
[Which is a point I made as Game Master to fantasy RPG players when their character(s) had a Wish to use.]
Given the point that @Paraleptopecten made, I wonder two things: was the choice of a penny deliberate on the part of the instructor; what if we’d done the experiment using blank metal disks (like unstruck coins) instead?
Real numbers? natural numbers? prime numbers?
How many attempts? Is there a limit to the number of digits? Where is it getting the numbers – reading license plates passing by? simulated coin flips? simulated die rolls – and if so, what kind of dice, just six-sided or any regular polyhedron? observing the shapes of clouds?
No probability can be assigned without knowing the specific parameters involved.
