If you need to flip a coin - that is, make a random yes/no decision - in your mind, use the following procedure:

  1. Think of any number with about five digits. The digits shouldn't be too small. No 10001, 12000 or 20001. Also, don't use the same number again for another decision, since you'll already know the result.
    Example: 63194
  2. Now add all the digits.
    6 + 3 + 1 + 9 + 4 = 23
  3. Repeat step 2 until you have a single-digit number.
    2 + 3 = 5
  4. If the resulting number is odd, the answer is yes. If it is even, the answer is no.
    5 is odd -> Yes

There is no way you can know whether a five-digit number will add up to be odd or even (unless the digits are too small). This method has two advantages: You don't need another person to help you, and you don't have to gesticulate. Nobody'll notice if you cast your vote for a random president.

Fordprefect informed me that for this method to work fairly, you need to pick an odd digit (say, 1) and throw out the result if you get it. Otherwise there are 5 odd possibilities and 4 even ones. 0 never happens.