Mario Kart Tour error code 805-0001 affects a large number of people as they attempt to play the game. If there is an error, players will be notified that they need to update the game, but none. update will only be available at that time. You can try to fix this problem by doing it in a quick and easy way.
Mario Kart Tour Error Code 805-0001 Explained
I imagine the reason for this boils down to two main causes. The first is that an update was not installed correctly, the second is that people are just unhappy and trying to play the game while an update is streaming to their phone. Just follow the steps below to see if that fixes the issues for you.
The first thing to do is to wait a few minutes. If the update is being transferred over the network, the game may wait for it to complete before telling you that it is available for download. Waiting a little while should resolve this issue for you.
If that doesn't work, try restarting your app and then restarting your phone if it still hasn't fixed the issue. Phones, cell signals, and wifi can all be troublesome. If something was wrong with your connection while downloading an update in the background, the app could get stuck until you restart all connections.
If you still cannot get it to work, try reinstalling the app. This shouldn't delete your save files, and you should be able to keep all of your progress.
If none of these fix the problem, then I'm afraid it's a problem on the developer side that they'll have to fix. These events can occur on launch day. The problem should therefore be resolved soon.