We will never know exactly. I've been bored and done some testing. I've used 8-12 at once a few times and 2/3 times it'll drop an exotic. If it doesn't though, I don't believe it stacks with the next batch. I say this because it hasn't altered the results of my next method at all.
Going 1 at a time every 20+ minutes is your best bet though. When I waited 30mins between usage I averaged 1 in 3/ 1 in 4. My odds were the same regardless of using 10 at a time on my previous attempt.
I experiment with them so don't think me using 8-12 at once was a waste. It's for science.
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I really appreciate this post, and your effective pursuit of in-game competence. Thank you!