A topological space $X$ is called *(strong) Choquet* if the player II has a winning strategy in the (strong) Choquet game.

It is known that a metrizable space $X$ is

$\bullet$ Choquet if and only if it contains a dense complete-metrizable subspace;

$\bullet$ strong Choquet if and only if it is complete-metrizable.

Since a topological group is complete-metrizable if and only if it contains a dense complete-metrizable subspace, we obtain the following characterization.

Theorem.A metrizable topological group is Choquet if and only if it is strong Choquet.

Corollary.A cosmic topological group is Choquet if and only if it is strong Choquet.

Let us recall that a regular topological space is *cosmic* if it has a countable network of the topology. It is easy to show that a topological group is second-countable if it is cosmic and Baire. That is why Corollary follows from Theorem.

Theorem and Corollary suggest the following intriguing

Problem.Is each Choquet topological group strong Choquet?