Randomness and the Misinterpretation of Random Behavior

I know "randomness" is an important concept in the field of mathematics, probability and statistics and much study is devoted to this. I do not profess to have spent time studying this myself.

I think because our brains are bad at understanding--or even recognizing--randomness, we have a difficult time accepting some notions of probability due to paradoxes and surprises with which we encounter--particularly in the casino.

I read about a party trick. Take two people and ask one person to flip a coin 30 times and write down the order of heads and tails. The other person will only imagine flipping a coin 30 times, and that person will write down the order of heads and tails that he or she has visualized. Without you knowing which person took which role, you are then presented with their two lists. You may be surprised to discover that you are able [edited] to spot which list comes from flipping the real coin and which list was for the imagined coin.

The human brain finds it incredibly difficult, if not impossible, to fake randomness. Consequently, when we are presented with randomness, we often interpret it as nonrandom.

For example, I read that when iPod launched its shuffle feature to play songs in a random order, customers complained that it favored certain bands. If songs are chosen randomly, it is very possible--even likely--that there will be clusters of songs by the same artist. Steve Jobs was very serious, in response to the outcry, "We're making the shuffle less random to make it feel more random."

I can think of other examples. Such as the Birthday Paradox. Take a randomly selected group of 23 people, and it is more likely than not that two people in the group will share the same birthday. Though there is nothing self-contradictory about the result, it does appear to fly in the face of common sense.

Interestingly, the proof of the Birthday Paradox is similar to the proofs for rolling certain combinations of dice.

These thoughts occurred to me as I considered some of the remarks on other threads involving such things as dice control and biased dice. I think it is easy for many people to misinterpret what actually happens--whether it be at the craps table or at a slot machine or practically any other game in the casino--as nonrandom outcomes when, in fact, such outcomes are totally random.

Our instincts take over, causing us to reach some incredible conclusions, resulting in beliefs, myths and superstitions which we embrace in our quest to beat the casino.

We also succumb to gambler's fallacy by believing the deviations from expected behavior with which we observe will some how indicate that future deviations in the opposite direction will then be more likely to occur.

I don't know where this thread will lead (definitely not a discussion on dice control). It may die a quick death. But I throw these thoughts out there for your consideration.

Our brains constantly strive to make order
out of chaos. So we see things that don't
really exist in random outcomes. Thats why
the drop from roulette went up 30% overnight
when casinos started installing electronic tote
boards. people could see the random outcomes
and their brains saw order where there
was none.

"Without you knowing which person took which role, you are then presented with their two lists. You may be surprised to discover that you are unable to spot which list comes from flipping the real coin and which list was for the imagined coin."

You are UNABLE to spot? Or are able to spot? I would have thought it would be easier to spot the human list. Or more likely, people would assume the random list wasn't very random, and say that was the human list.

Quote: Jimbo

I read about a party trick. Take two people and ask one person to flip a coin 30 times and write down the order of heads and tails. The other person will only imagine flipping a coin 30 times, and that person will write down the order of heads and tails that he or she has visualized. Without you knowing which person took which role, you are then presented with their two lists. You may be surprised to discover that you are unable to spot which list comes from flipping the real coin and which list was for the imagined coin.

The human brain finds it incredibly difficult, if not impossible, to fake randomness.

Sorry, I don't get it.

If you *cannot* distinguish between a random and a human written list of imaginary coin flips, this does not support your thesis ("humans are unable to fake randomness"). In the contrary, if you could distinguish between both lists, then I would agree that it is difficult to fake randomness.

Quote: MangoJ

If you *cannot* distinguish between a random and a human written list of imaginary coin flips, this does not support your thesis ("humans are unable to fake randomness"). In the contrary, if you could distinguish between both lists, then I would agree that it is difficult to fake randomness.

Yeah, that's exactly what I was thinking.

You are right--I mis-wrote in the original post "unable" instead of "able" and I will correct this in an edit (and probably thereby further confuse some people).

I also apologize if I was otherwise inarticulate about the party trick and flipping of a real coin and an imagined coin. It's been some time since I read about this.

I recalled at the time when I did read this that the main thrust of this exercise was to demonstrate that the list for the imaginary coin toss would appear to be less random than the list for the real coin.

For example, we may look at the maximum runs of heads or tails on the two lists. One list may have a maximum run of 4 heads and the other list may have a maximum run of 5 tails. The probability of a run of 5 in 30 flips is almost two thirds, so it is more likely than not that 30 flips will give us a run of 5. But for most people making up an imaginary list, they would not ascribe a run of 5 in 30 flips since it will seem too deliberate to be random.

If the person (who is trying to pick which list is fake and which list is not) knows this, then he will have a good idea that the list with only a maximum run of 4 heads is the fake list.

Secondly, we can look at the how frequently the heads and tails alternate. Due to the fact that each time you flip a coin, the chances of heads and tails are equal, you would therefore expect each outcome to be followed by the same outcome half the time and followed by a different outcome half the time. We would therefore expect the list for the actual random coin toss to alternate 15 times.

Again, if the person who is trying to pick the fake list knows this, then he will know that if one list alternates considerably more or less than 15 times, then that would suggest it is the fake list.

Thirdly, when imagining coin flips, our brains tend to alternate outcomes more frequently than what actually occurs in a random sequence. So after a couple of heads, our instinct is to compensate and imagine an outcome of tails, even though the chance of heads is just as likely. (An experience which probably occurs frequently at the roulette wheel.)

The person knowledgeable of randomness will, again, likely recognize the fake list for the inclusion of these compensating outcomes.

Some years ago there was a fun applet on the net that
showed this very thing. It had you guess the outcome
of a coin flip as randomly as you could and if you were
close to random, the meter stayed in the center. But
if you strayed, it went to the left or right. The computer
analyzed your guess and it was impossible to guess in
a random manner for long. I bet its still out there.

Quote: Jimbo

I recalled at the time when I did read this that the main thrust of this exercise was to demonstrate that the list for the imaginary coin toss would appear to be less random than the list for the real coin.

Okay, then I perfectly agree on your thesis - it is difficult to produce random-looking lists of coin flips by pure imagination.

What would be the reason for that ? There are tons of statistical tests you can run on a sample and figure out how likely they are following a given statistical model. And these tests are quite strong. The longer the list to be written, the more accurate are those tests.

Failing in most of these statistical tests, the conclusion must be: Pure imagination is not sufficient to produce a truely random list.


What would be the implication ? My thesis is: We must abandon the concept of "free will". A free will could act, by the very definition of "free", totally independent from any events in the world or current (or past) states of the mind. And as such one would produce a truely random list of any given length - simply by choosing heads or tails in a fashion utilizing that very free will.
However, this is not observed by statistical analysis. So we are not free to choose heads or tails randomly for some reason. Whatever the "will" is, it is definetly not "free".

Like the guy being introduced to some weird hop bet at craps... it won. They went to four different casinos that night and kept winning with this really weird hop bet. A license to print money thought the neophyte.

I think he learned a little bit more about randomness on his next trip when he tried to repeat his great income producing bet.

Isn't there order in random events? A simple coin toss trial of 100 flips generally delivers predictable results. Right? I'm not trolling.....back-off troll hunters.

[delete]

Quote: treetopbuddy

Isn't there order in random events? .

No. Thats rather the point of using them in casino
games.

Quote: Jimbo

the party trick and flipping of a real coin and an imagined coin. It's been some time since I read about this.

A certain Professor Hill got well known for having half his students write down their results for flipping coins and had the other half fake flipping a coin, writing down fake results. The actual group in which the turned-in results belonged to was hidden from him. In the next class he was able to sort out which group a result belonged to in seconds, wowing the students. The key was the absence of long streaks of either heads or tails in the faked results, the faking students always cutting off short such sequences.

There were probably a few data-takers modifying their results from real flips to shorten such streaks, figuring "he'll think I made this up".

this can be googled but it's hard to find a good readable link.

Confirmation bias is our brain's tendency to confirm our belief by looking for things that will support it. On top of that, I do believe that our brain looks for patterns.

Now with a coin, yeah, the result comes out random, and our brain understands that, but to truly understand that, one has to understand the nature of streaks. In a hundred toss set, it wouldn't be unusual to see 7 or 8 head, even 9 heads (or tails) in a row. Even 14 or 15 heads in a rows wouldn't be unheard of. Someone tossing 68 or more heads in 100 trials, while unusual, is quite possible. Our brain doesn't get that.

Once our brain understands what random is, you might be able to write down a sequence that appears indistinguishable from a RNG set.

Quote: boymimbo

I do believe that our brain looks for patterns.

This is certainly the foundation for gambler's fallacy.

We prefer to see patterns when there are none.

It's been said that it is about control--that, as humans, we feel the need to be in control of our environment. If events occur randomly, then we feel we have no control over them. On the other hand, if we do have control over other events, then they are not random.

By seeing patterns when there are none, we are trying to recover that feeling of control.

Quote: boymimbo

Confirmation bias is our brain's tendency to confirm our belief by looking for things that will support it.

I think "confirmation bias" definitely plays an important part in our misinterpretation of random behavior.

We can talk about countless examples in casino settings--which is what prompted me to commence this thread.

Consider the classic situation of taking one's bets down when the dice fly off the table.

****

I am reminded of a comedian's comment about playing blackjack. He said the dealer had a tattoo of an Ace on one finger and a King on another finger. The comedian said that he was prompted to also get a tattoo reminiscent of his own play. He'd get a tattoo of a 10 and a 2. Then later he'd add a tattoo of a face card.

The reason, of course, this is funny is that many are convinced that bust card comes every time when they hit that 12 (and, naturally, never for the dealer).

We know, intellectually, the odds or chance of drawing a 10 or face card and busting on a 12 is 30.8% (16 out of 52). But our confirmation bias and our misinterpretation of random behavior convinces us otherwise.

Maybe hitting the 12 and busting isn't the best example--but it allowed me to pass along what I thought was a funny joke.

Quote: Jimbo

our confirmation bias and our misinterpretation of random behavior convinces us otherwise.

Speaking for myself, anyway, I don't instinctively evaluate correctly what "just happened here" when both the dealer and the player bust. IIRC the Wizard has said this is the sole source of the house advantage in BJ. Instead I just get the impression the dealer is 'luckier' when it comes to busting . Of course, often the dealer need not check to see if he would have busted.

Quote: odiousgambit

I just get the impression the dealer is 'luckier' when it comes to busting . Of course, often the dealer need not check to see if he would have busted.

Another good example.

I know I have walked away from a disappointing experience at the BJ table thinking "how is it that I always bust and the dealer never busts." And then, of course, it occurs to me that I go first.

But instinctively it is difficult to dismiss the notion that the dealer is "luckier."

This is especially true for me when I so rarely win on a 20. I have often remarked that I would own the casino if I got paid on 20s!

Along the lines of confirmation bias and the op.

When a person gradually loses their hearing, in the beginning it's confusing.

Later in an attempt to understand voices they are always saying hunh?

Then when someone is speaking to you, if you can't read lips your mind takes a second
then interprets what would make the most sense out of what it thinks it heard. Often incorrectly.

It can be a little humorous when it gets to that stage, then it's not funny anymore.
Hearing loss goes thru those stages as well, denial , anger, acceptance.

I thought this correlated to the OT.The brain automatically try's to find patterns
by analysing garbled noises and attempting to find order in the chaos.