Forgive me, I do know that many questions do not contain MWEs. There are several reasons for using them. If there is an error of some kind, producing an MWE may lead to the questioner finding the reason for the error, or at least the smallest combination of packages and commands that causes the problem. Of course, this is not the case here, but another point is actually that it is a courtesy towards those who would help you. I'm not claiming that it is a big job to make a complete document in this case, but everything takes time, and not having to do that saves a little. Also, it's not always obvious (at least for me ...) which packages and/or libraries have been used, and then having an MWE saves having to figure out that.
Now, I don't know which version of breqn you have, but in the one I have, v0.98a from 2009/08/07, the breqn environment is undefined, hence your example does not work for me. Perhaps it existed in older versions, I do not know.
Back to the question at hand, breqn does both line breaks and, when a line break has occurred, indentation of the second line, automatically. None of your lines are so long that they require a line break, though breqn still adds a couple (see below). You could use an align* environment (from amsmath), and as Peter Grill mentioned in a comment add a \qquad or two at the beginning of the line. This didn't work in the environments provided by breqn when I tried, but \hspace*{<dimension>} did. Kind of hackish really, you may well get better solutions from other users.
In the code below I've added three examples: one with align*, one with breqn environments and no \hspace, and the final breqn environments with \hspace. All are unnumbered in this case. Do you want numbering, and in that case one number per line, or a single number for the entire thing?

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{verbatim}
\usepackage{breqn}
\begin{document}
% ...
% A long eq which I want better indented, with tabs, so it is easier to read
\begin{align*}
&\forall \text{game}\in[2,5]\in\mathbb N \\
&\forall \text{player}\in[1,10]\in\mathbb N \\
% I want 1 pc of TABs HERE
&\qquad\text{potentialTiredness}[\text{player}][\text{game}] \\
% I WANT 2 pcs of TABs HERE
&\qquad\qquad=\left(
\sum_{\text{game2}\in[1,\text{game}-1]}x[\text{player}][\text{game2}]/5
\right)
+
\frac{x[\text{player}][\text{game}-1]}{10}
\end{align*}
\vspace{1cm}
\begin{dgroup*}
\begin{dmath*}
\forall \text{game}\in[2,5]\in\mathbb N
\end{dmath*}
\begin{dmath*}
\forall \text{player}\in[1,10]\in\mathbb N
\end{dmath*}
\begin{dmath*}
% I want 1 pc of TABs HERE
\text{potentialTiredness}[\text{player}][\text{game}]
\end{dmath*}
\begin{dmath*}
=\left(
\sum_{\text{game2}\in[1,\text{game}-1]}x[\text{player}][\text{game2}]/5
\right)
+
\frac{x[\text{player}][\text{game}-1]}{10}
\end{dmath*}
\end{dgroup*}
\vspace{1cm}
\begin{dgroup*}
\begin{dmath*}
\forall \text{game}\in[2,5]\in\mathbb N
\end{dmath*}
\begin{dmath*}
\forall \text{player}\in[1,10]\in\mathbb N
\end{dmath*}
\begin{dmath*}
% I want 1 pc of TABs HERE
\hspace*{1cm}\text{potentialTiredness}[\text{player}][\text{game}]
\end{dmath*}
\begin{dmath*}
% I WANT 2 pcs of TABs HERE
\hspace*{2cm}=\left(
\sum_{\text{game2}\in[1,\text{game}-1]}x[\text{player}][\text{game2}]/5
\right)
+
\frac{x[\text{player}][\text{game}-1]}{10}
\end{dmath*}
\end{dgroup*}
\end{document}
\quadand\qquad. – Peter Grill Nov 24 '11 at 21:44documentclassand adocumentenvironment which is necessary in that respect. But as thebreqnpackage does not provide an environment calledbreqn, even with those added it wouldn't work. – Torbjørn T. Nov 25 '11 at 0:12