European vanilla call/put option, when volatility increases, how will gamma changes?

according to the BS formula, $\gamma = \frac{N'(d_1)}{S_0\sigma\sqrt{T}}$, gamma will decrease when volatility increase.

How does it intuitively make sense? rather than from the formula.

• $d_1$ is a function of the volatility. So even if you restrict yourself to the BS model, ignoring smile dynamics, it is not true that gamma will always decrease when when volatility increases. I would be glad to read a practitioner's opinion about sensibility of gamma wrt vol though. – AFK Jan 30 '15 at 22:03