  We have developed a heuristic showing that in the Dirichlet divisor problem
for the almost all $n \in \mathbb{N}^{+}$: $$ R(n) \leq
O(\psi(n)n^{\frac{1}{4}}) $$ where $$ R(n) = \Big\lvert
\sum_{x=1}^{n}\Big\lfloor\frac{n}{x}\Big\rfloor - n\log{n} - (2\gamma-1)n
\Big\rvert $$ and $ \psi(n) $ - any positive function that increases
unboundedly as $ n \to \infty $. The result is achieved under the hypothesis:
$$ \Big \{\frac{n}{x} \Big \} \sim w_x $$ where $ w_x $ is uniformly
distributed over $ [0,1) $ random variable with a values set $ \{0, \frac {1}
{x}, \ldots, \frac{x-1}{x} \} $ and the value accepting probability $ p =
\frac{1}{x} $.
  The paper concludes with a numerical argument in support of the hypothesis
being true. It is shown that the expectation: $$\mu_{1}
\Big[\sum_{x=1}^{n}\Big(\frac{n}{x} - \frac{x-1}{2x}\Big) \Big]=
(2n+1)H_{\lfloor\sqrt{n}\rfloor} - \lfloor\sqrt{n}\rfloor^{2} -
\lfloor\sqrt{n}\rfloor + C$$ has deviation from $D(n)$ is less than $R(n)$ in
absolute value for all $n < 10^{5}$.
