Big and small number biases are fundamentally difficult to grasp. But to gain an intuition, try to visualize a stack of 1,000,000,000,000 quarters. Now visualize a stack of 1,000,000,000,000,000 quarters. If you are like most people, the height of each of these stacks is initially quite similar. In reality, the second stack is 1000x higher than the first stack. (Of course it is! But our brains don’t see those numbers accurately.)
Similarly, imagine a cup of water. Now try to imagine pouring all but 0.00003% of the water out. How much exactly would be left? Trying to visualize this, most people would say a few drops, or just enough to keep the bottom layer of the glass wet. In a 16oz cup, .0000048oz, or about 136 micrograms. That’s less than the weight of 3 grains of salt.
These biases extend further into our perception. For example, when we see “99.999% chance”, we perceive it to be further from 100% than 99%. We’re less likely to spend resources to improve life saving treatments from 93% to 96% effectiveness than we are from 99% to 100%. This “cure” effect is similar to the “possibility” effect: we buy lottery tickets because our chances of winning the lottery are non-zero (“possible”).