The Independent Chip Model is a model that output's a player's overall equity in a tournament, given the stack sizes of players at the table.
An assumption underlying the calculations in the model is that the probability of a player coming 1st is equal to the proportion of chips the player has at the table.
Taking heads up as a simple example, a player with 1000 out of 9000 chips has a 1/9 chance of placing 1st, while a player with 8000/9000 chips has a 8/9 chance.
This linear relationship between chip proportion and probability of winning seems reasonable and simple, however is there a theoretical basis for this assumption?
For example, could it be a non-linear relationship, where someone with 8/9 of the chips may have a greater than 8/9 chance of winning (and someone with only 1/9 of the chips may have a lower chance of winning than 1/9)?