From the Super Mario Wiki
Red Rings (also known as Red Coin Rings) are objects present in New Super Mario Bros., New Super Mario Bros. Wii, New Super Mario Bros. 2, New Super Mario Bros. U, Super Mario 3D Land, and Super Mario 3D World. When jumped through, it will make several Red Coins appear, but only for a limited time. In most of these games, eight Red Coins will appear, while in Super Mario 3D Land, there will only be five. The prize for collecting them all always depends on what form the player is in.
In New Super Mario Bros., when Mario or Luigi is in his small or Mini form upon collecting the final Red Coin, a Super Mushroom will appear. If he is in his Super form, a Fire Flower will appear. If he is in his Fire form or Shell form, a 1-Up Mushroom will appear instead. Like mentioned above, the prize always depends on what form the player is in. Each Red Ring is worth 1000 points.
In New Super Mario Bros. Wii, Red Rings serve the same function as before. However, an item will appear for every character that is on-screen and not in a bubble when the final coin is collected. Fire Flowers, Propeller Mushrooms, Ice Flowers or Penguin Suits, depending on the level, will appear for every character who is in their Super form. Anyone who is in their Fire, Ice, Propeller, or Penguin form will gain a 1-Up Mushroom.
Red Rings also appear in Super Mario 3D Land. They now make only five Red Coins appear instead of eight, but other than that they function the same way. Depending on the level, they can yield a Fire Flower, Super Leaf, Statue Leaf or Boomerang Flower when Mario or Luigi are in their Super form. Like always, when all red coins are collected in a powered-up form, a 1-Up Mushroom would appear.
Red Rings reappear in New Super Mario Bros. 2, where they serve nearly the same function as in the previous New Super Mario Bros. games. The resulting Red Coins that appear from passing through the Red Rings can either remain in the air as usual, or slowly descend from the sky with parachutes. If a player collects all of the Red Coins in a Cannon or Rainbow level, they are rewarded with a Gold Flower in their inventory. Either a Fire Flower or a Super Leaf will appear if Super Mario collects the eighth red coin. The 1-Up Mushroom is replaced by a Gold Mushroom in Coin Rush mode.
Red Rings also appear in Super Mario 3D World. This time, like in the New Super Mario Bros. games, eight Red Coins are produced instead of five like in Super Mario 3D Land.
A Red Ring makes its first appearance outside the Super Mario series in Super Smash Bros. for Nintendo 3DS, in the Golden Plains stage. Like in the New Super Mario Bros. games, passing through one spawns eight Red Coins; however, each one is worth five Coins when collected.
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