Coin flip problem

There are three coins. They look and feel identical. Two are fair and the third comes up heads 60% of the time. The objective is to determine which coin is unfair.

You are allowed a total of 4 flips. Meaning you could flip one coin all 4 times, or 2 and 2, or 1, 1, 2, etc. Any combination as long as you only make a maximum of 4 flips.

What flipping strategy should you use? And given that strategy, how often will you correctly choose the biased coin?

Pasghettos said:

There are three coins. They look and feel identical. Two are fair and the third comes up heads 60% of the time. The objective is to determine which coin is unfair.

You are allowed a total of 4 flips. Meaning you could flip one coin all 4 times, or 2 and 2, or 1, 1, 2, etc. Any combination as long as you only make a maximum of 4 flips.

What flipping strategy should you use? And given that strategy, how often will you correctly choose the biased coin?

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Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

If you had only one flip then your chances would be 1/3*.6 + 2/3*.5*.5 = 36.6~%

That is, the 1/3 chance you randomly selected the biased coin to flip multiplied by the 60% chance you landed heads, plus the 2/3 chance you selected a fair coin to flip multiplied by the 50% chance of a tail, multiplied by the 50% chance you happened to choose correctly between the unflipped coins. From there I get lost, I have no idea how to account for a second flip, much less 4 flips.

Because the previous poster was so bold.
I will, like him or her, use my 2nd post to take a stab while I wait to see if someone answers my 1st post.

STRATEGY or how to apportion 4 flips:
Flipping one coin once obviously provides no information about bias. (And obviously I am not facile with the theorems of probability).
Since flipping an unbiased coin 2x must produce either 'the same side up' or 'opposite sides' and both are equally likely, I don't think that would help ID the biased coin either.
Flipping any one coin only 3x, means the last flip is wasted (for reason#1), so my gut says choose any one of the three coins and flip it all 4 times.

If the same side shows all 4x, you'd be right in saying that was the biased coin all but 2 out of 16 times, i.e., you'd have a 87.5% probability of being correct,
because an unbiased coin would behave this way only 2 times out of 16 in the long run.

A fair coin (flipped fairly) should show 3 heads or 3 tails half the time in the limit and
2 heads and 2 tails 6/16*100% in the limit.

I think my analysis already, at the minimum, shows how much more efficient it would be to use universally-recognized notation and terms and to base arguments on theorems rather than enumeration of all possibilities.

Hopefully my 1st post is answered now by someone employing both of these advancements.