# The odds of flipping a coin heads 100 times in a row!

## The closet answer to the odds of flipping heads 100 times in a row

• ### The answer is actually greater than option 2!

• Total voters
18

#### Cardcounter

##### Well-Known Member
What is closer to the true odds of flipping a coin heads a 100 times in a row?

#### Thunder

##### Well-Known Member
I would think assuming the coin isn't weighted , that it's .5^100

#### Cardcounter

##### Well-Known Member
Yep it is not weighted or rigged in any way it is a fair coin with odds of fliping heads at 2 to 1.

#### SleightOfHand

##### Well-Known Member
1,267,650,600,228,229,401,496,703,205,376:1

PS: I hear that coins are actually slightly biased because one side is barely heavier than the other (well, at least US Quarters). But yea, 2^100:1

Last edited:

#### Canceler

##### Well-Known Member
Not to get technical or anything, but...

SleightOfHand said:
1,267,650,600,228,229,401,496,703,205,376:1
I get 1 out of 1,267,650,600,228,229,401,496,703,205,376

or

1,267,650,600,228,229,401,496,703,205,375 to 1

#### SleightOfHand

##### Well-Known Member
Canceler said:
I get 1 out of 1,267,650,600,228,229,401,496,703,205,376

or

1,267,650,600,228,229,401,496,703,205,375 to 1
Odds of flipping 100 heads, not what fair betting odds would be

##### Well-Known Member
The odds are irrelevant. My 10 yo would intercept It long before 100 trials and spend it in some machine somewhere.

#### FLASH1296

##### Well-Known Member
The odds are "long" only if you predetermine when the series of coin flips begins.

If you flip a coin endlessly it is a tautology that indeed you WILL ultimately flip 100 heads in succession, presuming that you live long enough.

I would like to know what is the probability of this occurrence within any 100 consecutive flips out of a series of 100,000,000 coin flips.

Seriously, I would.

#### 21gunsalute

##### Well-Known Member
It depends on which direction and how hard the wind is blowing.

#### StandardDeviant

##### Well-Known Member
FLASH1296 said:
If you flip a coin endlessly it is a tautology that indeed you WILL ultimately flip 100 heads in succession, presuming that you live long enough.
I love it when you talk like this

#### StandardDeviant

##### Well-Known Member
FLASH1296 said:
I would like to know what is the probability of this occurrence within any 100 consecutive flips out of a series of 100,000,000 coin flips.

Seriously, I would.
See this:

#### Attachments

• 12.7 KB Views: 749

#### StandardDeviant

##### Well-Known Member
21gunsalute said:
I'd much rather look at your avatar than that formula.
But you'll have better chances with the formula.

#### fredperson

##### Active Member
If you flipped the coin for eternity, it would happen an infinite number of times.

#### StandardDeviant

##### Well-Known Member
fredperson said:
If you flipped the coin for eternity, it would happen an infinite number of times.
Only if I flipped the coin an infinite number of times. If I flipped the coin 99 times and then waited an eternity, it wouldn't even happen once.

##### Well-Known Member
StandardDeviant said:
Only if I flipped the coin an infinite number of times. If I flipped the coin 99 times and then waited an eternity, it wouldn't even happen once.
Stop! You are killing me with your wit and logic! :laugh:

#### Kasi

##### Well-Known Member
FLASH1296 said:
If you flip a coin endlessly it is a tautology that indeed you WILL ultimately flip 100 heads in succession, presuming that you live long enough.
Indeed. What a tautology - how to flip "endlessly" and yet live "long eough".
Hmmm....

Sure, as long as you flip that coin once a second and live 400 million billion years.

Or flip it 400 million billion times a second and then you only have to live one second. That's the way to go when you think about it - flip it really really quickly enough and you won't actually have to live that long after all.

Presuming you live long enough? What in the world are you talking about?
You won't. You can't. It probably will not have happened even once yet since the universe began.

If it were to happen in one's puny lifetime all it would mean is that it was not a fair coin in the first place. It could not be otherwise.

And you're worried about 100,000,000 coin flips? I don't know. I guess you'd have 99,999,900 separate sequences of 100-in-a-row coin flips. On the 99,999,901st flip there won't be enuf room for another 100-flip sequence.

Take it from there. Change the 31st decimal from a 1 to a 2 to account for the diff rom zero.

Whatever. Funny, silly stuff. 100 heads-in-a-row.

What would be your terms if I could come to your house and stay for x years while you flip a coin as often as quickly as you can? I will show up tomorrow with certified funds of \$1MM payable to you should it happen in 6 months and only ask \$200K in return if it does not happen. To make it fair you can hire up to 1000 people 24/hrs/day for those 6 months flipping a coin as often and as quickly as they can.

Oh hell. Make it 10,000 people if you want.

Oh hell, make it 100,000 people.

Want to bet on that tautology? :laugh:

#### Nynefingers

##### Well-Known Member
Kasi said:
And you're worried about 100,000,000 coin flips? I don't know. I guess you'd have 99,999,900 separate sequences of 100-in-a-row coin flips. On the 99,999,901st flip there won't be enuf room for another 100-flip sequence.
Splitting hairs here, but there would be 99,999,901 separate 100-in-a-row sequences of coin flips. On the 99,999,901st flip, you only need 99 more to complete the 100-flip sequence. How many 100-in-a-row sequences are there if you flip 100 times? Obviously 1. You get (#_flips - 99) 100-in-a-row sequences. Still, that wasn't your point, and your point still stands. :joker:

#### StandardDeviant

##### Well-Known Member
Nynefingers said:
Splitting hairs here, but there would be 99,999,901 separate 100-in-a-row sequences of coin flips. On the 99,999,901st flip, you only need 99 more to complete the 100-flip sequence. How many 100-in-a-row sequences are there if you flip 100 times? Obviously 1. You get (#_flips - 99) 100-in-a-row sequences. Still, that wasn't your point, and your point still stands. :joker:
And then there's this.