Best way to Measure High but Short Current Draw

If I had a strobe light goes off for 250ms once every minute and I wanted to know the average current draw to calculate my battery life, what's the best way to do that? The strobe would draw a lot of power for a very short amount of time.

I assume either use a scope to measure the current draw during an strobe event, then create a per minute average current draw, and from there estimate my battery life, or use an Arduino with a really fast ADC and measure the current draw at a high rate for a strobe light to be on or over the course of a minute?

0.25 seconds / 60 seconds = 0.00416666666667 * pulse current. That’s a dead slow “strobe”, you’re not going to do any “stop action” with that. Real xenon strobe pulse lengths are in the microsecond range.

Most probably each pulse draws a constant amount of energy from the battery. An Arduino ADC is capable of measuring a constant current within 250ms, but for an unknown pulse shape a fast scope is a better tool.

You can use a RC filter to get the average current consumption. A shunt resistor as large as possible (depends on the peak current) and a huge capacitor in parallel.

By 'strobe light' do you mean a xenon discharge tube or something else? Please explain what this strobe light is, and provide some product details.
Thanks

a strobe light goes off for 250ms

Where did the "250ms" figure come from? That seems highly unlikely for a strobe.

It was just an example of an idea. Probably use a strobe as a locator in the dark when I want to save battery and run for as long as possible. So not for a camera flash but really any very fast but infrequent current draw is what I was wondering.