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to think about no doots in n pulls in this simplified case, you evaluate (1 - 0.0085) ^ n
to convert pulls to coinflips, the value of the above expression must evaluate to 0.5 (50%). doing some brain stuff will tell you that n must equal 81.1 for the previous statement to be true. therefore, in every 81 pulls, you will find at least 1 doot in the pile of pets half the time.
this compounds btw, so in 2 piles of 81 pets, you will only find that none of the piles have a doot 1 in 4 times you run this test. kind of expensive test to run imo so good thing we can use brain to run it first
edit: since it is 250 gems per pet at T5, you use 20250 to get each pile of pets, which translates to $222 per pile of pets