Partial identification (PI) presents a significantchallenge in causal inference due to the incomplete measurement of confounders. Given that obtaining auxiliary variables of confounders is notalways feasible and relies on untestable assumptions, researchers are encouraged to explore theinternal information of latent confounders withoutexternal assistance. However, these prevailing PIresults often lack precise mathematical measurement from observational data or assume that theinformation pertaining to confounders falls withinextreme scenarios. In our paper, we reassess thesignificance of the marginal confounder distribution in PI. We refrain from imposing additional restrictions on the marginal confounder distribution,such as entropy or mutual information. Instead,we establish the closed-form tight PI for any possible P(U) in the discrete case. Furthermore, weestablish the if and only if criterion for discerning whether the marginal confounder informationleads to non-vanilla PI regions. This reveals afundamental negative result wherein the marginalconfounder information minimally contributes toPI as the confounder’s cardinality increases. Ourtheoretical findings are supported by experiments.