Chance theories are based on the assumption that "Absolute asymmetric synthesis, i.e., the formation of enantiomerically enriched products from achiral precursors without the intervention of chiral chemical reagents or catalysts, is in practice unavoidable on statistical grounds alone".
Consider the racemic state as a macroscopic property described by a binomial distribution; the experiment of tossing a coin, where the two possible outcomes are the two enantiomers is a good analogy. The discrete probability distribution  of obtaining n successes out of  Bernoulli trials, where the result of each Bernoulli trial occurs with probability  and the opposite occurs with probability  is given by:
The discrete probability distribution  of having exactly  molecules of one chirality and   of the other, is given by:
As in the experiment of tossing a coin, in this case, we assume both events ( or ) to be equiprobable, . The probability of having exactly the same amount of both enantiomers is inversely proportional to the square root of the total number of molecules . For one mol of a racemic compound,  molecules, this probability becomes . The probability of finding the racemic state is so small that we can consider it negligible.
In this scenario, there is a need to amplify the initial stochastic enantiomeric excess through any efficient mechanism of amplification. The most likely path for this amplification step is by asymmetric autocatalysis. An autocatalytic chemical reaction is that in which the reaction product is itself a reactive, in other words, a chemical reaction is autocatalytic if the reaction product is itself the catalyst of the reaction. In asymmetric autocatalysis, the catalyst is a chiral molecule, which means that a chiral molecule is catalysing its own production. An initial enantiomeric excess, such as can be produced by polarized light, then allows the more abundant enantiomer to outcompete the other.