Tokyo night transportation?

I've read about the "last train" problem in Tokyo, ie. that metro lines stop around 1 o'clock.

There are any "night buses" after 1 o'clock?
How people deal with that problem in Tokyo?

Maybe all events finish early to allow people to go back?
There will be a rush hour on saturday night?

Is taxi an affordable option? for example between Roppongi and Shinjuku?

thanks

There are some "night buses" from central Tokyo to the suburbs for the locals, but if you are only going from Roppongi to Shinjuku, then taxi would be the option.

Some locals do that night buses, stay in "capsule hotels" (or other places like "manga kissa" or all-night family restaurants) for the night, etc.

How people deal with that problem in Tokyo?

They either catch the last train or make alternate plans, either staying in a hotel, capsule hotel, restaurant, manga cafe...

Maybe all events finish early to allow people to go back?

Many do yes

There will be a rush hour on saturday night?

The last trains can be pretty full

Is taxi an affordable option? for example between Roppongi and Shinjuku?

It depends on what you consider affordable. Taxi from Roppongi to Shinjuku costs about 2200-2500 yen at night. Cheaper than getting a place to stay, and cheaper even than McDonald's if you're splitting it among friends.

There are some so-called night buses around the center of Tokyo, but their operation time is no later than trains.

Taxi costs around JPY2,500 to JPY3,000 depends on where in Shinjuku. But drivers don't speak English at all. There is a pretty good English speaking driver service in Tokyo, just for your reference. https://www.blacklane.com/en/cities-tokyo

Or, you can just stay until the first train. From Roppongi to Shinjuku, weekday last train is 00:49 and the first train 05:08 (Oedo line). For weekend, pretty much the same. There are bunch of places you can get through the night in Roppongi and take the first train. Bars, clubs, 24h fastfood, Manga cafes, or even hot spring. http://www.japanican.com/en/hotel/detail/4015A10/

Ok, thanks to everybody!
I was hoping indeed for a taxi price cheaper than finding an accommodation for the night.
I guess it will be wise to check first with the taxi driver, but for a couple of people and one night out it looks affordable.

Thanks for the link about English service.