Urban Airship spoke in numbers about the benefits of push in games. It turned out that they have a minimal impact on retention, but they stimulate engagement very well.
Users who receive push messages are 26% more likely to open applications. When talking about games, this figure increases to 35% (Average Push Opt-in Rate).
Retention at the end of six months with push – 14%, without push – 9%
In general, games have the lowest average retention rate for the first month: 44% with push buttons, 27% without them.
It’s funny, but pushy at the same time have a very big impact on the level of engagement in games (one of the maximum). The average level of engagement in games with push – 27.4%, without push – 20.3%
A source: http://urbanairship.com/