50/50 probability on a coin flip?

Each flip is 50/50 (unless you shave the edge). You can get ‘heads’ one zillion times in a row (unlikely but statistically possible). The odds on the one zillionth and first toss are still 50/50.

it is not exactly 50/50. the coin can also land upright.

50/50 each time. The coin has no memory.

The occurrences of a coin landing on its edge would be statistically insignificant.

Using a USA quarter, the chances of it being tails are JUST slightly higher for tails because the heads side weighs a little more. The difference is far from statistically significant, but it is interesting to note.

Even if you got tails 10 times in a row, that doesn’t change the odds. That act itself is statistically improbable because of the 50/50 odds stating that half will probably be heads. But that still wouldn’t mean that tails or heads would be more or less likely to come up.

@ragingloli: What does upright mean? That sounds like the the same thing as heads to me….

Each flip is independent. Getting heads GIVEN that you have already gotten heads is the original probability of getting heads. HOWEVER getting heads twice in a row is a 25% probability.

This is because there are four available outcomes:
HH
HT
TH
TT

If you assume that you got heads first, that only leaves HT and HH. And it’s 50–50.

@La_chica_gomela
landing on its edge

@Bri_L: Actually in a stat class I took once, we flipped pennies hundreds of times, and you’d be surprised how many runs we got (such as ten heads in a row). Try it sometime!

But take, instead of the coin, a peanutbutter-sandwich and you’ll find that it’s no longer 50/50.

Ask Marilyn, she always knows.

@rebbel: If the pb and j is an open sandwich, the odds are likely that you get only one toss.

@gailcalled I didn’t take that in consideration.
In that case it is 50/50, i guess.

@rebbel: “It is a truth universally acknowledged that” bread or toast always falls jam- or butter-side down.

@gailcalled
only if you brush it off the table, because the toast has not enough time to make a full revolution.
if you drop it vertically it becomes 50/50 again.
they did that on mythbusters

They don’t call me “butterfingers” for nothing. I beat the house when I drop toast.

@La_chica_gomela – Right I agree, but my point, and I don’t think I made it very clear, was that run or no run the odds don’t change. Even if you got 10 out of 10 tails, the next is still 50/50. I loved stats in college. It really helped me learn how the media and politics can manipulate.

I don’t have any webpage references but I do know that my STATS teacher teacher told us that there is actually a slightly higher chance to flip heads. He said it had something to do with the weight distribution of the coin. Like I said, I have nothing to back that up except his word. I just thought it was worth putting into the discussion.

edit:: whoops @torch81 beat me to it. AND I was wrong. My apologies for not reading every response. That’ll teach me.

@gailcalled ^ ^

@PrancingUrchin: Torch81 said this:^^ “Using a USA quarter, the chances of it being tails are JUST slightly higher for tails because the heads side weighs a little more. The difference is far from statistically significant, but it is interesting to note.”

I may be wrong here, but as I calculate it, the chances of having at least one run of five flips in a specific configuration is over 95%. That is to say, if you decide to look for a certain ordering of flips- 5 heads in a row, 5 tails, h-t-h-t-h, or whatever- then you will find it 19 out of 20 times. The chance of a run of 10 specified flips is 8.5%.

My calculation is 1—(1—.5^X)^(Y-X+1)
where X=number of flips in the ‘special’ string and Y=total number of flips

Isn’t it like 60/40 for a penny because heads or something weighs more so it will land heads down? I thought I read that somewhere…

@Bri_L: Oh I completely agree with your main point, I was just making discussion about the side-point.

@Parrappa: That may be true of quarters, as @torch81 suggests, but from personal experience, I can tell you that pennies are almost exactly 50/50. I believe out of 200 flips, I got a percentage of 51.7% heads.

The statistics assume you have a “fair” coin and the same flipping flip every time and no tail winds or electric fans.

If the coin is tossed and caught, it has about a 51% chance of landing on the same face it was launched. (If it starts out as heads, there’s a 51% chance it will end as heads).

If the coin is spun, rather than tossed, it can have a much-larger-than-50% chance of ending with the heavier side down. Spun coins can exhibit “huge bias” (some spun coins will fall tails-up 80% of the time).

If the coin is tossed and allowed to clatter to the floor, this probably adds randomness.

If the coin is tossed and allowed to clatter to the floor where it spins, as will sometimes happen, the above spinning bias probably comes into play.

A coin will land on its edge around 1 in 6000 throws, creating a flipistic singularity.

The same initial coin-flipping conditions produce the same coin flip result. That is, there’s a certain amount of determinism to the coin flip.

A more robust coin toss (more revolutions) decreases the bias.

—————

From Bruce Shneier’s blog: http://www.schneier.com/blog/archives/2009/08/non-randomness.html

the paper it comes from

@phoenyx is right. I was talking about a coin tossed and allowed to “clatter to the floor” (or whatever flat surface it falls on).

I would love to witness a flipistic singularity. Has it ever been captured on film/video? And not as part of a magician’s act?

@La_chica_gomela – I remember that task of flipping coins. It was amazing how exciting it got trying to beat the record of “number in a row”. Wild.

It’s a paradox, but yes, the coin has no memory.

This reminds me of a conversation I had recently. This guy was trying to tell me that your chances are less with the powerball lottery than with the TN lottery, because more people play the powerball. I tried to expalin to the guy that the same amount of random numbers are used no matter how many people play. It is not like a raffle ticket in a hat. The guy could not get it.

Ah yes, the old Monte Carlo fallacy.