From the Super Mario Wiki
Frog Mario is an alternate form of Mario and Luigi that can be attained by acquiring a Frog Suit in the game Super Mario Bros. 3. Frog Mario can swim faster than regular Mario, allowing him to overcome currents in his path Controlling Mario while swimming is also easier, as he can stop instantly, in a single spot in the water, and swim in any direction. However, Frog Mario's walking and running ability is greatly decreased. In fact, Frog Mario can only hop on the ground like a Frog. As such, Frog Mario's jumping ability is greater than regular Mario's. Frog Mario was of great help in World 3 of Super Mario Bros. 3, Sea Side. Also, Frog Mario can run when carrying an item such as a Koopa Shell. It will also prevent Big Bertha from eating the player.
In The Adventures of Super Mario Bros. 3, Princess Toadstool and Toad were also able to use the Frog Suit to transform into Frog Toadstool and Frog Toad respectively. King Koopa also had the ability to transform himself into Frog Koopa by the use of a Power Pendant.
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