This study delves into the bidirectional link between Algorithmic Trading and intraday tail risk. It reveals that both Proprietary and Agency Algorithmic Traders (ATs), through their order placements and cancellations, contribute to lowering intraday tail risk. Interestingly, this relationship is two-sided: tail risk reduces order activity across trader types. While order placements by all ATs (Proprietary, Agency, and Retail ATs) decrease with rising tail risk, only Agency ATs' cancellations exhibit the same trend. These findings reveal heterogeneity in risk sensitivities and trading responses among ATs.