The chances of flipping 3 coins at once and then all landing in the same side is 12.5% but if I said they had to specifically all land on heads does that then change the %?

12.5% already is for a specific side: each H is 1/2 so P(HHH)=1/8

P(HHH or TTT) = 25%

Ok heehaw. What is it for all three being different?

I'm going to jump in here and say 0.0%.

I think it may help the OP to expand upon this a little more to show the incorrect reasoning that led the OP to say the probability of flipping three simultaneously and having all be the same is 1/8.

Let's say you flip 1 coin (Coin A) and don't look at the result (you hide it under a cup or something). Then the question becomes what is the probability that when you flip the next two coins that they will match Coin A? It is 1/2 * 1/2, no matter what is under the cup.

Put another way, by saying it's 1/2 * 1/2 * 1/2 you've already decided that Coin A has to be a specific thing to meet the success condition because the probability that Coin A is going to be H or T is 1, not 1/2 (neglecting it landing on its edge or any physical processes that would cause the coin to disintegrate). So it's expressed as 1 * 1/2 * 1/2.

The difference between "named coin" and "any coin" throws up a few interesting apparent contradictions. My favourite one is:

"Flip 10 coins. Is it more likely they will be five of one side and five of the other, or six of one side and four of the other?"

the first post is inaccurate just think of sample space if we said specifically what are the odds of getting three heads then it would be 1/2*1/2*1/2=1/8 or 0.125.

however the odds of getting 3 coins all landing on the same side is not 0.125 it is 0.25.

because we have the odds that all 3 coins land on heads which is 1/2*1/2*1/2=0.125
+ all three coins land on tails which again is 1/2+1/2+1/2=0.125 hence 0.125+0.125=0.25

think of all possible permutations here if we let H be heads and T be tails we have the following possibilities
HTT HTH HHT HHH
THH THT TTH TTT
and you will notice the last two one each row are the sample spaces where we have 3 of the same side which is 2/8.

Yes, brute force (exhaustively listing all permutations) is another way to show that p=0.25 in addition to the other two statements that it's 0.25 before this.