Then, without ever peeking at the coins, you sort them into two piles, blindly flipping and shuffling them as if your hands were being guided by the spirit world. You magically wind up with the exact same number of heads in each pile. Every time.
Let's say your spectators tell you that there are six heads-up coins in the pile. All you need to do is grab that number of coins and flip them. Just any six random coins. Take the ones you flipped and move them to their own pile, which we'll call Pile #1. The remaining coins are Pile #2. Both piles will contain the same number of heads.
Why does this work? Because math, that's why. Say you have 12 coins total. Your friend tells you six are heads, so you flip and separate six random ones -- if two are heads and four are tails, you're still left with four heads in each group. Here, we made a chart:
Pro Tip: Don't live in one of those weird countries with coins that have heads on both sides.
Go on, take a hammer to your swear jar and try this. If you're accused of feeling the coins as you go, just repeat it with cards or driver's licenses. And if they still think your super-sensitive fingers can distinguish the images you're touching ... well, just let them think that.