We prove an elliptic Harnack's inequality for a general form of a parabolic equation that generalizes both the standard parabolic 𝑝-Laplace equation and the normalized version that has been proposed in stochastic game theory. This version of the inequality does not require the intrinsic waiting time and we get the estimate with the same time level on both sides of the inequality. M S C 2 0 2 0 35K55 (primary), 35K67, 35D40 (secondary) 1 𝛾 −1 sup 𝐵 𝑟 (𝑥 0 ) 𝑢(⋅, 𝑡 0 ) ⩽ 𝑢(𝑥 0 , 𝑡 0 ) ⩽ 𝛾 inf 𝐵 𝑟 (𝑥 0 ) 𝑢(⋅, 𝑡 0 ).

We prove an elliptic Harnack's inequality for a general form of a parabolic equation that generalizes both the standard parabolic p-Laplace equation and the normalized version that has been proposed in stochastic game theory. This version of the inequality doesn't require the intrinsic waiting time and we get the estimate with the same time level on both sides of the inequality.