  We describe an efficient algorithm to compute solutions for the general
two-player Blotto game on n battlefields with heterogeneous values. While
explicit constructions for such solutions have been limited to specific,
largely symmetric or homogeneous, setups, this algorithmic resolution covers
the most general situation to date: value-asymmetric game with asymmetric
budget. The proposed algorithm rests on recent theoretical advances regarding
Sinkhorn iterations for matrix and tensor scaling. An important case which had
been out of reach of previous attempts is that of heterogeneous but symmetric
battlefield values with asymmetric budget. In this case, the Blotto game is
constant-sum so optimal solutions exist, and our algorithm samples from an
$\varepsilon$-optimal solution in time $\tilde{\mathcal{O}}(n^2 +
\varepsilon^{-4})$, independently of budgets and battlefield values. In the
case of asymmetric values where optimal solutions need not exist but Nash
equilibria do, our algorithm samples from an $\varepsilon$-Nash equilibrium
with similar complexity but where implicit constants depend on various
parameters of the game such as battlefield values.
