What are the odds that The Patriots won 19 of their last 25 coin tosses, /sci/?
The same as the odds that they lose 6 of their coin tosses out of 25. I'm rusty on my babby probability, but here's a shot: There are 25C6 ways of losing 6 out of 25 coin tosses. There are 2^25 possible outcomes in 25 coin tosses. Hence, the following probability:
If you want to know the odds that the Patriots got at LEAST 19 out of 25, you need to add in the probability of getting 25/25, 24/25, 23/25, 22/25, 21/25, and 20/25. That gives you:
I'm not sure wtf is up with /sci/'s LaTeX, so here's an image of what I intended on showing you.
Here's a better question: what are the odds that *some* team wins 19/25 tosses? I bet it's better than even. And if you pick an arbitrary rolling window of 25 tosses, it's pretty much certain to happen eventually.
Your odds of winning the lottery are basically zero. But someone will win the lottery, and if not this week, then the next week or the one after. Same deal here, but on a smaller scale.
If the coins are fair, then it must happen eventually. The odds are not even outlandish, although surprising. I've played shitty MMORPGs with drop rates as low as 0.01%, and I managed to obtain the items within fair time.
This cannot be determined with the given information. The distribution of the heads vs tails would have to be justifiably suspicious.
>What are the odds that The Patriots won 19 of their last 25 coin tosses, /sci/?
About the same odds that whoever came up with that title isn't salty as fuck wrt: pats undefeated season.
If you actually analyze what goes into a coin flip, you realize what you think is random is actually not random.
It depends on how you hold it, and how you catch it. Also classical probability is based off of really old and thin coins, but most coin flips are done with quarters, which due to their width have an additional probability of landing perfectly on their side.
Coin flips are not a reliably random measure, but they are used because most of the time no one gives a fuck.
Deflategate was only one of numerous times the patriots were suspected of cheating. Remember the super bowl vs the Rams a decade or so ago? Remember how they taped their practices so they knew all their plays?
On a flat surface, sure, the coin might land on its edge, but it's idiotic to think that a coin flip isn't a reliably random measure. It's literally autistic to think that in the long run, the odds of coin flips don't balance to nearly 50%
It depends on how you flip it. I can predict which side it lands on if I practice and time it right.
There has actually been a lot of study on coin flip accuracy, that although it reliably produces the expected probabilities, it is still less purely random than a yarrow stalk method.
There is literally no way you could predict it unless you knew every single factor that contributed to its end state. This would mean air pressure, temperature, force of the flip, weight of the coin, angle of the flip, distance from finger pivot, etc. By the time your calculations were complete, we'd be in the third quarter. And you might still be incorrect.
A better question is "What are the odds that at least one team out of the 32 NFL teams won at least 19 out of 25 coin tosses in any streak of coin tosses?" My feeling is that the odds are pretty good.
You can control for a lot of those factors. By practice you can get the angle and velocity correct, you can even predict the rotations after enough tries. Of course this assumes that you are the one flipping the coin.
And the goal is not to win every single time. It's to get more than 50%. 51% is good enough in vegas.
>By practice you can get the angle and velocity correct, you can even predict the rotations after enough tries.
LMAO... please cite some sources of this. There's no fucking way you can do this.
There's a stats prof at Stanford who did a bunch of experiments and he concluded that it's next to impossible to pull that off unless you have a device that can exert same momentum on a coin every time.
But there’s no fucking way you can do that with a human hand & arm.
odds of winning 19 of 25 coin tosses is
177100/2^25/2^25 = 0.00527799129486083984375
odds of winning at least 19 of 25 coin tosses is
245506/2^25 = 0.007316648960113525390625
now delete this shitty thread
I honestly don't feel you deserve this knowledge, but I am posting for the benefit of others here.
There are many ways to cheat at coins. The simplest way is a little bit of earwax on ole coppernose. When you do the slap, it will come out tails side up.
Sometimes the tactile difference between heads and tails can be enough. Again, look for the nose.
If you toss it up without flipping it, and no one calls you out on it, obviously it will land in the same orientation as when you started.
Like all sleight's of hand, it depends on the vigilance of those you are with. On the playground, where I spent most of my days, chilling out maxin relaxin all cool and shootin bbal outside of the school, people were very dumb and fell for it every time.
> stats prof
> did experiments
> next to impossible
This is why magicians continue to amaze people in the age of technology. Most things that are "next to impossible" are actually completely possible if you're willing to devote enough practice time. That practice time often ends up being surprisingly short; I'd guess maybe a few dozen hours to reliably flip a coin. Easier if you're catching it, but I don't see it being a problem if it's landing on turf.
You don't need the "same" momentum. It just has to be close enough. And you have the ability to control both the rate of rotation of the coin and the rate at which is spins. It's a powerful combination with a lot of room for error, and people can develop pretty fine motor control.
Counting rotations is another level of difficulty, but I can for example stack a couple decks of playing cards, have you call a number from 1 to 100, and pull that many cards off the stack within a second. Sometimes I'm off by 1, but not really often. It wouldn't surprise me to learn that someone can do coin rotations like that (though I'd be impressed by it... probably more so than would a non-magician).
> unless you knew every single factor...
No. You don't need to know the wind currents and temperature and exact mass of the football to catch a pass, do you? You have a brain that handles that shit for you, in real time, and does so with remarkable efficiency.
you mean their "undefeated" "season"?
I think a better question is, what are the odds that a team KNOWN for cheating and general shady behaviour would win coin flips at impossible rate in a legit manner? It's one thing for the Titans or even a middle-tier team to win coinflips like that, but the Cheatriots? naw man, just naw.
tl;dr the randomness of coin flips is very dependent on how the coins are flipped. if you're a shitty flipper you can easily flip it so it looks like it's spinning without it ever spinning
They didn't cheat, they just misinterpreted the rules.
A coin doesn't need long-term 1:1 random behaviour to be fair: all that's necessary is that the person calling the result have no informational reason to prefer one result to another. A referee could even inform players than the coin he intends to use has landed one one given side in 95% of a million trial flips and, so long as he doesn't specify *which* side, tossing the coin and having the player call the side is still a fair selection process.
If you're accusing someone of cheating on coin-flips you're necessarily implying a high level of collusion between the player and the ref, and if that exists there're are dozens of ways to control the outcome of the game which are far less detectable and far more impactful than fixing coin flips.