# How many times do we have to flip a coin to have it being as close to its true mean of 50%?

#### holygrailseeker

##### New Member
How many times do we have to flip a coin to have it being from its true mean of 50% with a reasonable margin of error say +/- 1%?

We know that flipping a coin, very rarely (but it can happen), that we have 10 heads or tails in a row.
So we definitely need a much larger sample, my guess is at least a few hundred flips to reduce the margin of error to a few %.

#### katxt

##### Active Member
You can get a rough idea of the accuracy using MoE = 1/sqrt(n) for midrange proportions. So, in round numbers, a MoE of 1% for a coin needs about 10000 flips.
The MoE often quoted on political polls is 3% from 1000 people. 1/sqrt(1000) is about 3%.

#### jansch

##### New Member
can you elaborate where the 1/sqrt(n) rule comes from? Thank you

#### katxt

##### Active Member
The actual formula is MoE = z*sqrt(p(1-p)/n) (just google ci for proportion). For 95% z = 1.96 or near enough to 2. p is about 0.5 so MoE = 2*sqrt(.5(1-.5)/n) = 2*sqrt(.5(1-.5))/sqrt(n) = 1/sqrt(n) as a simple rule of thumb.