the rules we have formulated for our evolution of chances above: after each roll of the dice, your winning chances are "hit" from above or below and therefore rise or fall by a certain random value, in a way that is independent of what has gone before. a first model of our random process therefore would be given by a stopped random walk which starts at 0.5 and jumps after each roll of dice by an independent randomly distributed value. it is stopped once it falls below 0 or rises above 1. we call the first time that either of these events happens the stopping time.
if we take into account 