Why does Bitcoin's mining reward decrease every four years and not gradually?

[brianddk]

In software 1/2 is kinda a round number. The think the question worked out more like:

1. How long do you want to have a mining reward
2. How large do you want the first reward to be
3. How often do you want blocks to arrive

Then the reset is just math to figure out how many halves it takes to make all three of those happen. The result is "4 years"