The Setup: using a totally fair quarter, you and your friend will place bets on which sequence of coin tosses are most likely to come first... while it looks totally fair, you'll have up to a 7 to 1 advantage over them!
The Scam: This is an old math problem called "Penney's Game". In this game, each player chooses a 3-digit sequence of coin flips... a coin is flipped over and over again, and whomever's sequence of heads and tails comes first, wins. in other words, player 1 may choose HTH (heads, tails, heads) as his sequence, while player 2 would choose HHT. when the coin is flipped, the results may be: TTHTTHHT, in which case, player 2 would win.
The Trick: you can always get an advantage over your opponent by going second, and choosing your pattern based on what they pick. The algorithm is simple: just take the first two digits of their pick, and move them to the last 2 spots in your pick. For your first digit, choose the OPPOSITE of whatever your last digit is. For example: if they choose, HHT, you'll take their first two digits (HH) and move them to the back for your pick: _HH. to choose your first digit, pick the opposite of your last digit... so you'd pick THH.
Check out the full wikipedia article for your exact odds, but if you follow these steps, you'll win MUCH more often than lose!