Does anyone know why gamma is always positive for call and puts?
Gamma is positive for â€ślongâ€ť calls and puts (when you buy options). Perhaps someone can explain it better than me, but here goes:

Gamma = measure of how Delta changes when the price of the underlying stock moves up or down. It is a change measurement for Delta. (Remember that Delta = change in the option value due to a change in the underlying stock price).

When you buy options, youâ€™re adding positive Gamma. When you sell options, youâ€™re adding negative Gamma. You can be Gamma neutral if you combine buying and selling options into one strategy.

Long story short  positive Gamma for long calls and puts means: (a) the Delta of â€ślongâ€ť calls will become MORE positive (approaching +1) when the stock price rises, and LESS positive (approaching 0) when the stock price falls; and (b) the Delta of â€ślongâ€ť puts will become MORE negative (approaching 1) if the stock price falls, and LESS negative (approaching 0) when the stock price rises.
Thatâ€™s as I understand it anyway, someone might have a better explanation.
Cheers  good luck  you got this
Makes sense. Thanks.
The price curves for call options and put options are convex (mathematicians would say, "concave upward). The second derivative of a convex (concave upward) function is positive; the slope of the tangent line (delta) is increasing from left to right.
Thanks.
Donâ€™t ignore the â€śsquaredâ€ť in the second order derivative.