Is there maths behind "divide by 10 for a 1% probability"? I can't tell why that would be the case at a glance.
Right. Divide by 10 for a 1% probability. So base62:6 has about a 1% chance of having at least one collision across your game library. Will probably work, but you're playing with fire. Not much headroom.
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sqrt(-log1p(-0.01)), but really you can just approximate it as sqrt(0.01). Though I got that wrong, it's off by a factor of 2 since the baseline is 50%. Dividing by 10 gives you ~0.5% probability (100 times less).
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