  Can an absorbing game with rational data have an irrational limit value? Yes:
In this note we provide the simplest examples where this phenomenon arises.
That is, the following $3\times 3$ absorbing game \[ A = \begin{bmatrix} 1^* &
1^* & 2^* \\ 1^* & 2^* & 0\phantom{^*} \\ 2^* & 0\phantom{^*} & 1^*
\end{bmatrix}, \] and a sequence of $2\times 2$ absorbing games whose limit
values are $\sqrt{k}$, for all integer $k$. Finally, we conjecture that any
algebraic number can be represented as the limit value of an absorbing game.
