suspicious coin flip

Sometimes when you flip a coin, things happen that might appear unusual, but are actually rather ordinary. For example, you might get 8 heads in a row on 8 consecutive flips.

But at a certain point, the odds become ridiculous. Here's my question: at what point would someone educated in math become suspicious about the integrity of the coin toss? 30 consecutive heads? 50 consecutive heads? 100 consecutive heads?

https://youtu.be/XzYLHOX50Bc

Derren Brown did a "trick" some years ago about getting heads 10 times in a row, using multiple cameras filming continuously to prove it's legit.

He later revealed in another video the "trick" was he filmed himself flipping the coin for 9 hours before getting 10 heads in a row. So the trick was just filming nonstop until he eventually got a 10 head streak.

In the initial show it was spun to be some "luck system" where thinking you are lucky makes you lucky or something like that, it's been years since I watched the full show (the coin trick was one part of the show), culminating with making a whole town luckier by installing lucky statues (I think, it's been a while).

Quote: reno

Sometimes when you flip a coin, things happen that might appear unusual, but are actually rather ordinary. For example, you might get 8 heads in a row on 8 consecutive flips.

But at a certain point, the odds become ridiculous. Here's my question: at what point would someone educated in math become suspicious about the integrity of the coin toss? 30 consecutive heads? 50 consecutive heads? 100 consecutive heads?

My starting presumption when someone pulls out a coin to flip is that it’s not fair.

Quote: unJon

My starting presumption when someone pulls out a coin to flip is that it’s not fair.

exactly.
I carry a fair looking 'rounded corners' Die to flip a coin.

let the other select which numbers (3 of them) will be Heads.
still have seen 6,7 Heads in a row with this method while watching that the roll is a fair one.
Makes me wonder

I’d get suspicious at 57 consecutive heads. This is roughly the same probability of someone winning the powerball jackpot twice in a row, which never has happened and never will.

Quote: reno

Sometimes when you flip a coin, things happen that might appear unusual, but are actually rather ordinary. For example, you might get 8 heads in a row on 8 consecutive flips.

But at a certain point, the odds become ridiculous. Here's my question: at what point would someone educated in math become suspicious about the integrity of the coin toss? 30 consecutive heads? 50 consecutive heads? 100 consecutive heads?

Hmmmmm, I'd base my judgement on the totality of my coin flip watching experience.
I.E. I've watched many hours of blackjack spins and a handful of times, the history display has shown a whole long streak of reds or blacks or odds or evens. I'm not for one second inclined to suspect cheating there because it is to be expected that I would see this, over the long time I've spent observing and maybe even playing.
BUT, the total number of times I've spent watching coin toss results is very low. If I see 10 consecutive heads or tails in the next 6 months, that would be exceptional. If I was martingaling those coin tosses and losing, I'd seriously start to suspect mischief after half a dozen losses....
We can judge the mathematical probability based on numbers and simple maths. On judging a wagering situation, we need to account for human nature and potential fraud far more.
If you watch a guy on stage in a black cape take a chainsaw to a lady who just happened to climb in a box, what do you expect? Do you call 911? Nope!
If you encounter a guy with a chainsaw in a dark alley, do you think to yourself 'this will be fun, I'll watch' or do you flee ( or shoot the guy )?
Situation and context matters.

There was a stage magician on tv who showed an experiment. On the street with a small camera crew and sound guy present, he asked young ladies for their engagement rings and then dropped them into the street drain. He then said, 'oh sorry, still, what did you expect?' and he and the camera crewe walked away. The reaction of the 'victims' was priceless. Fortunately for those hysterical ladies, he got their rings back to them later.

Quote: OnceDear

...the history display has shown a whole long streak of reds or blacks or odds or evens. I'm not for one second inclined to suspect cheating there because it is to be expected that I would see this, over the long time I've spent observing and maybe even playing.
BUT, the total number of times I've spent watching coin toss results is very low.

I used coin toss as an example, but you could substitute roulette or craps or blackjack or whatever (though obviously the odds of red on a roulette wheel aren't the same as a coin toss because of the green zero(s).)

If I saw 10 consecutive red numbers winning on a roulette wheel, I wouldn't necessarily be suspicious. But 20 reds in a row? 30? 40? At a certain point, you'd have to wonder.

Just wondering what would raise eyebrows among mathematicians.

At 15 I would be concerned.

Quote: reno

Just wondering what would raise eyebrows among mathematicians.

Context: It's all about context. Why am I watching the coin flips? Does the coin flipper have a vested interest?
There are few situations where I'd be inclined to even watch a short sequence of flips? Those times I would be interested would, by definition, be times when I expected mischief.
Guy on stage? Street hustler? Nephew saying hey look what I can do? Carnival game?
I'd get suspicious after 2 flips the same?
Online simulated coin flip at an online casino? I'd expect about 10% bias at the outset and would not trust it at all.

Nope.... No way I'd trust anyone offering a coin flip demonstration.

At 32 heads in a row, I become suspicious

Quote: DRich

At 15 I would be concerned.

I have seen 20+ consecutive reds and blacks at roulette many times.

Im not saying it is a daily occurrence but it happens more often than you think.

More than 30 consecutive I only experienced once (i was betting and winning with that streak but should have won more. I was playing scared when i should have been pressing)

Never seen more than 30+ so im gonna go with 40 or 50 as suspicious

Quote: darkoz

I have seen 20+ consecutive reds and blacks at roulette many times.

Im not saying it is a daily occurrence but it happens more often than you think.

More than 30 consecutive I only experienced once (i was betting and winning with that streak but should have won more. I was playing scared when i should have been pressing)

Never seen more than 30+ so im gonna go with 40 or 50 as suspicious

I saw the #5 hit on five consecutive roullete spins , which is the equivalent of about 27 heads coin flips in a row.

Quote: michael99000

I saw the #5 hit on five consecutive roullete spins , which is the equivalent of about 27 heads coin flips in a row.

I just saw 4,24,16,5,11,3,32 in that exact sequence!
Wow!
Probability of 1 in 37^7 or 1 in 94931877133. or roughly 1 in 100 billion. Almost unthinkably unlikely.
I was shocked. Sadly, the pattern broke just after I recognised it and 18 did not occur next.

:o)

The problem also has to get over Bayes theorem. You have to show it is more likely that you have a ( biassed coin/wheel/etc. && result ) compared with ( unbiassed && outlandish results ). Thus if you were playing on the back streets then you'd be more suspicious than playing in a regulated casino.

One has seen many threads suggesting something is wrong, you need lots of evidence before you can say for sure something is wrong.

For instance suppose a casino fruit machine is expected to pay out 94% but you've played lots of times and only get 93%. You would have to play over 100 million times before you could seriously consider something was wrong.

Quote: reno

But at a certain point, the odds become ridiculous.

You answered your own question. What do you consider ridiculous odds? Work backwards from there.

Quote: darkoz

I have seen 20+ consecutive reds and blacks at roulette many times.

Quote: AxelWolf

Quote: darkoz

I have seen 20+ consecutive reds and blacks at roulette many times.

Im not saying it is a daily occurrence but it happens more often than you think.

More than 30 consecutive I only experienced once (i was betting and winning with that streak but should have won more. I was playing scared when i should have been pressing)

Never seen more than 30+ so im gonna go with 40 or 50 as suspicious

I just wanted to make sure we got Alan Mendelson JR on record.

p.s. Where have you been for the last few days darkoz, it's not like you to skip a few days of posting? If I recall correctly, you even claimed to be posting while having a "hot" girl in your bed.

Quote: darkoz

More than 30 consecutive I only experienced once (i was betting and winning with that streak but should have won more. I was playing scared when i should have been pressing)

Never seen more than 30+ so im gonna go with 40 or 50 as suspicious

Mehhh....the multiple 1 in 3 million aren't nothing.

I want to quote the 1 in 5.4 billion statement🙄😲🙄

And how he doesn't get suspicious until around 1 in 10 trillion or so......oof....trusting🤣🤣

Quote: MaxPen

Mehhh....the multiple 1 in 3 million aren't nothing.

I want to quote the 1 in 5.4 billion statement🙄😲🙄

And how he doesn't get suspicious until around 1 in 10 trillion or so......oof....trusting🤣🤣

I just wonder what that chapter in his book is going to be called?

Quote: reno

Sometimes when you flip a coin, things happen that might appear unusual, but are actually rather ordinary. For example, you might get 8 heads in a row on 8 consecutive flips.

But at a certain point, the odds become ridiculous. Here's my question: at what point would someone educated in math become suspicious about the integrity of the coin toss? 30 consecutive heads? 50 consecutive heads? 100 consecutive heads?

The question is more complex than simply ONE sequence.
One should be suspicious when recording several 10-runs in a short time, for example.
- -
I doubt anybody in the real world has recorded the outcomes of thousands of coin flips (with the same physical coin). Computer simulations are different: the matter is about the RNG.
No coin is physically exactly fair, of course.
So, for a practical purpose, the question of fairness is unimportant as such: it is the size of the bias that counts. And its importance relies on the number of value laden flips. With the same coin.

In a heads or tails situation, you implicitly admit that there is a probability distribution on the coin selected, before the probability distribution of that one coin sides. On the whole, even Bayesian admit the overall chances are 50/50.

Unless the RuritanIan Mint, e.g., should design one coin, intentionally or other, to fall more often on one side...

- -
There are millions of roulette tables in the world, each running hundreds of spins each day. 3652 days per decade.
The order is around a trillion spins in a decade.
An event that has a 1 in a trillion prob ON ONE SPIN has 36% chance of having happened in the last decade.

But here, we are looking at sequences. So the experiments must be sliced in sessions per individual roulette wheel (I guess having 5 reds just before closing time, then 5 at next mornings opening, don’t count as a 10 run.)
Say what? Five billion sample sessions? A one-in-10-billion chance event happening once in the world during a pre-chosen decade should make eyebrows . Maybe.
(And then there are the other worlds to take into account, including their probability of existence.)
- -

Quote: kubikulann

Unless the RuritanIan Mint, e.g., should design one coin, intentionally or other, to fall more often on one side...

Good question!

In what measure do Mints give importance to the question of Heads-or-tails equilibrium in their coin design?

Quote: Gandler

He later revealed in another video the "trick" was he filmed himself flipping the coin for 9 hours before getting 10 heads in a row. So the trick was just filming nonstop until he eventually got a 10 head streak.

There's a scene in Spider-Man (the 2002 movie) where Mary Jane slips in the high school cafeteria, sending her lunch items flying through the air. Peter Parker uses a cafeteria lunch tray to catch the airborne food items.

Apparently the scene was filmed without the use of digital CGI special effects. They did it the old fashioned way. It took actor Tobey Maguire 156 attempts over 16 hours to catch the items. Aside from the 16 hour day, the only "trick" the film crew used was super glue to attach the tray to Maguire's hand.

Quote: reno

There's a scene in Spider-Man (the 2002 movie) where Mary Jane slips in the high school cafeteria, sending her lunch items flying through the air. Peter Parker uses a cafeteria lunch tray to catch the airborne food items.

Apparently the scene was filmed without the use of digital CGI special effects. They did it the old fashioned way. It took actor Tobey Maguire 156 attempts over 16 hours to catch the items. Aside from the 16 hour day, the only "trick" the film crew used was super glue to attach the tray to Maguire's hand.

In Aliens 4 Sigourney Weaver (now a test tube alien human) is supposed to throw a basketball BACKWARDS WITHOUT LOOKING one handed from 50 feet before the net and its a perfect shot.

They planned to do some cgi on the shot and on the first take, Sigourney weaver ACTUALLY MAKES THE SHOT.

The actor in the scene nearly ruined it. He was so shocked he dropped character. The basketball goes out of frame and then comes back down sadly. They never thought she could actually do it

Quote: darkoz

In Aliens 4 Sigourney Weaver (now a test tube alien human) is supposed to throw a basketball BACKWARDS WITHOUT LOOKING one handed from 50 feet before the net and its a perfect shot.

They planned to do some cgi on the shot and on the first take, Sigourney weaver ACTUALLY MAKES THE SHOT.

The actor in the scene nearly ruined it. He was so shocked he dropped character. The basketball goes out of frame and then comes back down sadly. They never thought she could actually do it

You think that's amazing, well, Evil Knievel broke 433 bones in his lifetime not getting something just right the first time! Yeah, so there.