From the Super Mario Wiki
The Checkpoint Flag (also known as a midway point or a Warp Flag) is a recurring object that signifies a checkpoint in several Mario games. They are similar to the Midway Gates from Super Mario World. If Mario loses a life after touching a Checkpoint Flag, he restarts where the Checkpoint Flag is. If Mario is in his small form, the flag almost always restores him to Super Mario. When the player touches a Checkpoint Flag, they will be rewarded with 2000 points in some games.
New Super Mario Bros.
Midway points first appear in New Super Mario Bros. as white flags with a picture of a Mushroom on them. They are only visible on the touchscreen map after Mario reaches a checkpoint zone (similar to Super Mario Bros.), although not all courses have checkpoints. If Mario loses a life, he will restart the course from the checkpoint. However, if the player exits the course, plays another, then returns to said course, or gets a Game Over, they will have to start from the beginning.
New Super Mario Bros. Wii
Midway points reappear in New Super Mario Bros. Wii. In this game, they appear as black flags with Bowser's symbol on them. The first character who touches a midway point changes the flag's design to their own (Mario and Luigi's flags have the same colors and symbols as their caps (red with an "M" for Mario, green with an "L" for Luigi), and the Toads' flags become their colors with their heads), and they gain 2000 points. Additionally, if a player character is in Small form when they touch the midway point, they are restored to Super form, similarly to the Midway Gates in Super Mario World.
If the character who touched the flag drops out of the multiplayer session after all players lose a life, the remaining players must start over from the beginning of the level. This is only possible with Luigi and the Toads, as Player 1 can only play as Mario and cannot drop out.
Super Mario Galaxy 2
Checkpoint Flags reappear in Super Mario Galaxy 2, replacing invisible checkpoints from the previous game. Due to the game having a health meter and no score system, Checkpoint Flags merely save Mario's progress in the mission. Depending on which galaxy and mission the player is playing, there may be anywhere from one to several Checkpoint Flags positioned between the beginning and the end of the level. Some missions, such as The Perfect Run, may not feature any Checkpoint Flags at all. In addition to having Checkpoint Flags activated by Mario or Luigi themselves walking into them, they can also be activated by the Co-Star Luma or by Yoshi's tongue.
Super Mario 3D Land
Checkpoint Flags reappear in Super Mario 3D Land, acting similar to how they did in New Super Mario Bros. Wii (as the game lacks a score system), and like before, some stages, like World 2-1, may not have Checkpoint Flags at all.
New Super Mario Bros. 2
Checkpoint Flags reappear in New Super Mario Bros. 2, acting as they do in New Super Mario Bros. Wii. In Coin Rush, touching the flag does not give points, but adds 50 or 100 seconds to the time limit. They also do not appear in every level of the game, like in Rainbow and Warp Cannon Courses.
New Super Mario Bros. U / New Super Luigi U
Checkpoint Flags appear in New Super Mario Bros. U and New Super Luigi U, acting as they did in prior 2D games. In the Coin Battle mode, touching the Checkpoint Flag rewards the player ten coins. The hoist of the flag is now wrapped around the pole.
Super Mario 3D World
Checkpoint Flags reappear in Super Mario 3D World, looking and acting as they did in New Super Mario Bros. Wii. As in home console New Super Mario Bros. games, their color and emblem corresponds to the character who touched it. Ergo, Mario and Luigi retain their flag designs, Peach gets a pink flag with her crown, Toad has a blue flag with his face, and Rosalina's cyan-colored flag shows a Grand Star.
Super Mario Maker / Super Mario Maker for Nintendo 3DS
Checkpoint Flags are included in Super Mario Maker in an update released on November 4, 2015, and return as a base element in Super Mario Maker for Nintendo 3DS, gaining new sprites for the Super Mario Bros., Super Mario Bros. 3, and Super Mario World styles; they replace the Midway Gate in the latter style, despite the Giant Gate still being present. They also appear slightly smaller than in New Super Mario Bros. U. They can be placed in a course by shaking an arrow sign, and like an arrow, can be rotated. If a Checkpoint Flag is placed in a level, then in addition to clearing the course normally, players must also be able to clear the course from the checkpoint to upload their levels. Two Checkpoint Flags can be placed per stage, one in the main area of the course and one in a sub-area.
Super Mario Run
Checkpoint Flags appear in Super Mario Run in Toad Rally mode, having the same design as in the New Super Mario Bros. games. They are placed roughly halfway through the level, and whichever of the two players passes by the flag first earns 10 coins. Once one player activates it, it has no effect on the other player if they pass by it themselves. If the player activates it first, the flag will change into the current character's respective emblem. If the opponent activates it, the flag will turn gray with Bowser's emblem still on it. Unlike previous games, Checkpoint Flags do not turn Small Mario into Super Mario.
Super Mario Odyssey
Checkpoint Flags make a reappearance in Super Mario Odyssey, providing a fast travel system. Every kingdom has multiple Checkpoint Flags, and one also appears on the exterior of the Odyssey. When Mario touches one of them, the area's name is displayed, and Mario is able to travel directly to the location by selecting it on the map. Touching checkpoints also restores Mario's health, along with creating a bubble if it is underwater.
The color of the Checkpoint Flags' poles vary by kingdom, and correspond with the color of the kingdom's Power Moon.
Super Mario Maker 2
Checkpoint Flags reappear in Super Mario Maker 2; in the New Super Mario Bros. U style, the flag is triangular instead of rectangular to better fit with the other checkpoint appearances in other styles. Despite the addition of Slopes, Checkpoint Flags can now only be set in four directions instead of eight, and they provide no power-up effect by default in Course Maker. Instead, each Checkpoint Flag can hold a specific power-up, such as a Fire Flower or Super Star, whose effect will be provided when the player character activates the checkpoint.
Super Mario 3D Land
New Super Mario Bros. 2
New Super Mario Bros. U
Super Mario 3D World
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