Coin tossing simulation 2 - difference of heads and tails

Two players are playing a game with coins. Player A wins 1 euro if the result of a coin-toss is head, player B wins 1 euro if the random toss gives tail. Repeat the simulation several times. Observe the frequency of the difference of heads and tails obtained.
What are the possible values of difference of heads and tails? What values of difference occur more frequently? What is the probability that the game ends tied (the difference of heads and tails is equal to 0) ? What is the type of this distribution?