At a local country fair, a volunteer fire department has a fundraising booth with a game of chance. In the center of the booth there is a large square board with 100 non-overlapping red circles of equal size. Players throw nickels (5 cent coins) and the object is to have your coin come to rest completely inside a circle.

While playing the game I wondered what would happen if one were allowed to throw dimes (10 cent coins) instead. Being smaller makes it easier to land inside the red circle, but being of higher denomination you are throwing more money away^*.

Is there a size circle for which it wouldn't matter?

A nickel has a 21.21mm diameter whereas a dime is only 17.91mm. The board looked to be a square about 8 feet on a side. Any other assumptions may need to be left up to you.

^*Quite literally, but the money is for a good cause. The prize is a box of candy worth about a dollar.