From this excellent YouTube video, the summary is that there is a slight bias in coin tosses. Professor Persi Diaconis has proven that coins have a 51% tendency to land the way they started. In short, if you want a coin to land heads up, you should start flipping it in your hand heads up!
Another short video about whether you should catch a tossed coin or let it rotate slowly on the table.
One good book by Professor Persi Diaconis is:
Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks
. A professional mathematician and also a magician, Persi Diaconis reveals the secrets of amazing, fun-to-perform card tricks--and the
profound mathematical ideas behind them--that will astound even the most
accomplished magician.
