Probability Puzzle : Robot and coins Someone walks into your room and dumps a huge bag of quarters all over the floor. They spread them out so no quarters are on top of any other quarters. a robot then comes into the room and is programmed such that if it sees a head, it flips it to tails. If it sees a tail, it throws it in the air. the robot moves around randomly forever. Will there be a convergence in distribution of heads vs. tails?
I am trying this puzzle for the past two days . But got lot of confusions !! As i don't know what is convergence in probability,i cannot proceed further. Please don't provide a link to wikipedia for convergence in probability.Can someone give me a simple definition of convergence in probability and explain the solution to the puzzle ? 

Let $h$ be the proportion of heads among the coins and $t=1-h$ the proportion of tails.  In a stationary state, the chance of a transition heads$ \to $ tails must equal the chance of a transition tails$ \to $heads  So we have $h=\frac t2$ and the equilibrium state is  $\frac 13$ heads and $\frac 23$ tails.
