The calculations made by the Poker Rebuy Calculator are based on a mathematical model of a poker tournament, as described in the next section.
The model is that of Brownian motion, also known as a Wiener process, drunkard's walk, or random walk with very small steps. This walk is in a space whose dimension is the number of players remaining in the tournament.
It is a completely accurate model of a poker tournament if the stacks are all large, and the mechanism of play is that two players are repeatedly chosen at random chosen at random, to toss a penny, the loser giving one chip to the winner.
I believe that this model is a reasonable model of a real poker tournament if all, or all but one, of the stacks are large relative to the blinds. It is also a good model if there is only one prize, or if only two players remain in the tournament.
The model is not a good fit to reality if more than two players remain in the tournament, and more than one of the stacks is less than 20 big blinds, and there are at least two prizes. In these circumstances, it overvalues the equity of small stacks relative to big stacks.
It is also a poor fit to reality if the players are not all equally skilful.