“…Lastly, given instead a strategy τ ∈ Ψ 2 , let q k,·,τ (u,ex) = max σ∈Ψ1 q k,σ,τ (u,ex) , and let q * ,·,τ (u,ex) = sup σ∈Ψ1 q * ,σ,τ (u,ex) . From very general determinacy results (Martin's "Blackwell determinacy" [Mar98] is one such result which applies to all two-player zero-sum stochastic games with countable state spaces) it follows that the games M A are determined, meaning that sup σ∈Ψ1 inf τ ∈Ψ2 q * ,σ,τ (u,ex) = inf τ ∈Ψ2 sup σ∈Ψ1 q * ,σ,τ (u,ex) . Of course, finite SSGs are even memorylessly determined ([Con92]), meaning that the strategies of either player can be restricted to memoryless strategies which ignore the history prior to the current position, without harming the optimal outcome for that player.…”