coin flips: In a thousand coin flips, how many times will I lose five in a row?

[kini]

How to solve: in a thousand coin flips, how many times will I lose five in a row?

 

[Dr.Peterson]

Let's start by clarifying your question. We can't know what will happen in any given set of random events. Are you looking for the expected number of times out of the 1000 flips that five flips in a row will be ... uh, heads? tails? I don't know what "lose" means! Also, if I "lose" 6 in a row, does that count as one or two times I lost 5 in a row?

We have to be specific in probability questions.

Also, what help do you need with this? Our main goal is to help you figure things out for yourself.

 

[Steven G]

Please state what win and lose means. You can win (or lose) if you get three heads followed by 2 tails or maybe you win (or lose) if you get 17 heads or tails in a row. Do you see that your question is not clear?

 

[pka]

How to solve: in a thousand coin flips, how many times will I lose five in a row?

This is an interesting example that illustrates how a simply put question can require a complicated answer.
There is a whole area of cryptology known as "runs": SEE HERE It an't easy to study this area.

 

[kini]

Let's start by clarifying your question. We can't know what will happen in any given set of random events. Are you looking for the expected number of times out of the 1000 flips that five flips in a row will be ... uh, heads? tails? I don't know what "lose" means! Also, if I "lose" 6 in a row, does that count as one or two times I lost 5 in a row?

We have to be specific in probability questions.

Also, what help do you need with this? Our main goal is to help you figure things out for yourself.

Hey sorry. "Lose" means you guess incorrectly before the flip. And I'm going to say for the sake of simplicity that we restart the counting after five. And yes, "expected number" of times.

I want to know how to calculate this generally. I'm not a math student so I'm unsure where to begin.

This is an interesting example that illustrates how a simply put question can require a complicated answer.
There is a whole area of cryptology known as "runs": SEE HERE It an't easy to study this area.

Thanks.

 

[Steven G]

If you like, you can assume that you always pick heads for each toss. In this case your problem is tossing a tail 5 times in a row means that you lose.
I do not think that there is an easy way to do this especially with starting the tails count at 0 after 5 consecutive tails.

 

[kini]

Hmmm, is there a way to approximate it then, to make it easier?

 

[Steven G]

Personally I would run away from this problem and I like challenges.
I just can't think of how to handle more than 5 tails in a row.