Li, Li, and Dai's Contribution to the Discussion of "Estimating Means of Bounded Random Variables by Betting" by Waudby-Smith and Aaditya Ramdas

We congratulate Waudby-Smith and Ramdas for their interesting paper \cite{waudbysmith2022estimating} in generating confidence intervals and time-uniform confidence sequences for mean estimation with bounded observations. Their methodology utilizes composite nonnegative martingales and establishes a connection to game-theoretic probability. Our comments will focus on numerical comparisons with alternative methods.