# Recursive Pareto ðŸ”—

One formulation of the Pareto principle is that with 20% of the work you get 80% of the benefit, and it takes the remaining 80% of the work to get the remaining 20% benefit.

This makes it sound like we should stop after the first 20% of work. But we can apply the Pareto principle recursively to the remaining work and benefit.

In the second iteration, with 20% * 80% of the work, you get 80% * 20% of the benefit. In other words, with 16% of the work you get 16% of the benefit.

Overall, after two iterations, you did 20% + 16% of the work and got 80% + 16% of the benefit. With 36% of the work you got 96% of the benefit.

Here is a table with 7 iterations:

iteriter worktotal workiter benefittotal benefit
120%20%80%80%
216%36%16%96%
312.8%48.8%3.2%99.2%
410.24%59.04%0.64%99.84%
58.192%67.232%0.128%99.968%
66.554%73.786%0.026%99.994%
75.243%79.028%0.005%99.999%

After 7 iterations you did 79% of the work and got 99.999% of the benefit.

iteriter workiter benefitwork / benefit
120%80%0.25
216%16%1
312.8%3.2%4
410.24%0.64%16
58.192%0.128%64
66.554%0.026%256
75.243%0.005%1,024

The work of the 7th iteration is 1024x the benefit (4^(7-2)).

itertotal worktotal benefit1 / missing benefit
120%80%5
236%96%25
348.8%99.2%125
459.04%99.84%625
567.232%99.968%3,125
673.786%99.994%15,625
779.028%99.999%78,125

After 7 iterations you are still missing 1 / (78 thousand) of the benefit.

itertotal worktotal benefit1 / missing benefit
883.223%99.999744%390,625
986.578%99.9999488%1,953,125
1089.263%99.99998976%9,765,625
1191.410%99.99999795%48,828,125
1293.128%99.99999959%244,140,626
1394.502%99.99999992%1,220,703,064
1495.602%99.99999998%6,103,513,664

After 14 iterations you did 95% of the work and are only missing 1 / (6 billion) of the benefit.

If we imagine that the benefit corresponds to how you compare with other people, you could now be close to being the world’s best.

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