# Thread: Outcomes of coin toss with restrictions?

1. ## Outcomes of coin toss with restrictions?

Hey guys,

Apologies if this is in the wrong area.

I'm busy with a non academic project at the moment, and I need to determine the number of possible outcomes of a two outcome system, such as a coin toss.

The problem comes in with the fact that I need to include restrictions of the type

"Outcome one cannot occur x more times than outcome 2"
and
"Outcome two cannot occur y more times than outcome 1"

So in laymans terms, there can never be a certain number more heads recorded than tails.

I have no idea how to calculate this, barring using excel and some form of numerical methodology, but I'm quite unfamiliar with that, and it seems daunting to calculate as the number of tosses increase.

Thanks for the help

2. ## Re: Outcomes of coin toss with restrictions?

hi,
do you have some restriction like, outcome after N tosses?
regards
rogojel

3. ## Re: Outcomes of coin toss with restrictions?

Forgive me, but I don't fully understand what you are asking.

I need to work out how many possible outcomes there could be, after N tosses of the coin.

Any "probability branch" wherein rule 1, or 2, is broken is to be ignored.

As an example, assuming 3 tosses, and a rule that heads can never occur more than tails, give us 3 possible solutions.

TTT
TTH
THT

I now need to do the same, for N number of tosses, with the rules stated in my first post.

4. ## Re: Outcomes of coin toss with restrictions?

Originally Posted by GTG
I need to determine the number of possible outcomes?
Forgive me for asking even though your text is quite explicit about the matter: But do you really need number of possible outcomes or probabilty of number of 1's?

5. ## Re: Outcomes of coin toss with restrictions?

Really what I'm after is the ratio of those that fulfill my criteria, to those that don't.

As the total number of possibilities is simple 2^n, n being the number of tosses, either the number of those that fulfill it, or those that don't, will do.

In another thread I realized I had been a bit unclear about my terminology, so just for insurance I'll rephrase what I'm after.

Giving a starting value of a 100, adding one for every head, and subtracting one for every tail, I want to find out in how many possible outcomes the value never ever reaches 0 or 200 at any point.

6. ## Re: Outcomes of coin toss with restrictions?

Seems you are just consider a symmetric random walk with two boundaries as the absorption state; and asking the probability of not absorbing at time

The "probability" here is equivalent to the number of paths when the random walk is symmetric as each non-absorbing path is equally likely.

7. ## Re: Outcomes of coin toss with restrictions?

That does seem to be along the lines of what I am looking for.

Sadly a lot of the mathematics behind random walks is going over my head at the moment, but I am looking into it

8. ## Re: Outcomes of coin toss with restrictions?

Originally Posted by GTG
Giving a starting value of a 100, adding one for every head, and subtracting one for every tail, I want to find out in how many possible outcomes the value never ever reaches 0 or 200 at any point.
hi,
this seems to be quite different from the original question. Is there some restriction on the number of times a head can occur vs. a tail?

regards
rogojel

9. ## Re: Outcomes of coin toss with restrictions?

No, there wouldn't be any restrictions of that nature.

So for instance after a 100 coin tosses, there would only be 2 possible outcomes that would be excluded (100 heads, 100 tails).

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