Some elements of a possible demonstration of the Collatz conjecture

In this paper we are shown the following facts: The probability of increased $A_{k}=P(T^{k} (x_{0})>T^{k-1} (x_{0}))$, and the probability of decrease $B_{k}=P(T^{k} (x_{0})<T^{k-1} (x_{0}))$ in step $k$ of a Collataz procedure initiated in $x_ {0} \in \mathbb{N}$ arbitrary, they are equal for all values of $k$. This influences on the law that generates the numbers of a Collatz sequence so that it is forced to decrease until the unit. Also is shown in the Collatz conjecture is false for every problem $an +b$ such that $a\geq 5\geq b+2$, and your probabilistic caracter can not be ignored if you want to get to the definitive solution, among other interesting arguments.