I shall hereby present you: The ultimate calculation to lay everyone's rng fears at rest! (assuming they can clear the last map)
First: Look at the min/avg/max table for your stamina. The avg number of crystals should allow you to, after clearing the previous maps, run the last map around 92 times, if you start with full stamina and make full use of what you regenerate. I'll assume the worst case scenario of you having only 12 stamina, i.e. each additional crystal gives you 2 more attempts at the map, and for ease of calculation I will assume that you got absolutely 0 serums from any of the previous maps.
(For those interested in the method to check what I did: C=Number of times you cleared the last map. I calculated the chance of getting at least (1200-C*10)/3 hits out of C*2 rolls)
Here are the results:
Chance of not maxing with +1 crystal: 10%
Chance of not maxing with +2 crystals: Roughly the chance of drawing Nanaly from Premium Summon
Chance of not maxing with +3 crystals: Roughly the chance of getting a 4 of a kind on your opening hand in Poker (regular 5 card draw mode)
Chance of not maxing with +4 crystals: Winning the lottery
So basically, if you have even just a few more crystals than the average from the table, you are fine. On the downside, this also means that you can't hope for luck to save a few crystals either, since the chances behave similarly in the opposite direction.
tl;dr: Expect to pay pretty much the average from the posted table above with almost no deviation. I doubt there will be any player paying more than 3 additional crystals, let alone 4.