I found it hard to find good numbers, so hopefully this research will be of use to other people:

Yesterday, Uber co-founder Garrett Camp wrote "Uber has become a global service providing roughly 15 million rides per day across 500 cities" at https://medium.com/@gc/ubers-path-forward-b59ec9bd4ef6

The most recent estimate I could find on Didi Chuxing is 20 million rides per day as of October, 2016 as stated at https://www.techinasia.com/china-didi-chuxing-20-million-dai...

It's reasonable to assume that Didi has noticeably grown since October 2016, but none of these numbers are easily verifiable externally to these companies.

(Lyft's market share is unclear to me, but perhaps 2 million rides per day, more or less?)

Kind of unfair to compare Didi (or any Chinese company) with the free market alternatives. If you're given state sponsorship from one of the largest countries, then you should easily be able to do more rides than Uber.

I don't think that UberChina's failure to win against Didi was due to state sponsorship. Didi had a better product tailored to the Chinese market, better operations people who conducted local campaigns in more cities, and only one market to compete in, as opposed to Uber's worldwide competition.

It was apparent that Didi had achieved the network effects necessary to overcome Uber in volume. Both companies wanted to focus on revenue so it was savvy of Didi to purchase UberChina so they could reduce ride subsidies.

I think that the success of UberChina, along with Yum! and Wal-Mart, demonstrate that it is possible to prevail in the difficult Chinese market.

> a better product tailored to the Chinese market

What were the differences?

According to HN commenters in China, Didi understood that government employees needed a standard voucher so Didi made its generation automatic in the app. UberChina apparently never did.

It was used as an example to illustrate that Didi did the little things that remove friction for its customers. Didi also recruited drivers in smaller cities; its coverage was superior to UberChina's.

and MUJI, also very successful in China

I think there's a case to be made that the tax policies that apply to investor organizations and participants qualifies as a form of state sponsorship.

Do they nearly guarantee people will buy the app despite foreign competition? This sort of thing happens in China more than over here. U.S. consumers use or buy products from many places with significant percentage coming from China at some point. Something just being American sponsored doesn't usually cut it.

There's also Per Capita to consider. Obviously an anything in China will have more actual humans using it - there's a billion of them there.

Aside: is there anything to be said for doing well in lots of countries vs a monopoly in one?

It seems to me that to be successful in certain countries requires skills that don't translate internationally - for example, understanding the quirks of one big country, or negotiating the political situation.

Well, largest by revenue :-)