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One of Warren Buffett's primary fears is weapons of mass destruction, I think since the 70s (as stated in his semi-autobiography, Snowball). During the cold-war

One of Warren Buffett's primary fears is weapons of mass destruction, I think since the 70s (as stated in his semi-autobiography, Snowball). During the cold-war, he put things like this (paraphrasing from memory): if there's a 4% chance of nuclear war per annum, there's a 70% chance of it happening over the next 30 years. If we reduce the annual chance to 2%, we reduce the 30-year chance to 45%.

VWWHFSfQ 7y ago
for some reason those numbers are not adding up to me. do the chances compound year-over-year? how is the 4% any different in year 1 than in year 30? or any year in between? how does this add up to 70% over a 30 year period
- zamfi 7y ago
  If you assume 4% each year independently of each other year, then the chance of not having nuclear war is 96% in any given year. Over 30 years, your chance of no war is (0.96)^30 = 30%.
  - dragonwriter 7y ago
    > If you assume 4% each year independently of each other year, then the chance of not having nuclear war is 96% in any given year. Over 30 years, your chance of no war is (0.96)^30 = 30%. It's clearly not independent though, but this calculation remains true if you assume only that not having a nuclear war doesn't change the odds for future years, even if having one does.
    - zamfi 7y ago
      My apologies, you are right -- I should have said "4% each year independently of each prior year" -- and it's true that only the negation needs to be independent.
- deleted 7y ago
  [deleted]
- ekosz 7y ago
  You can try it yourself without any of the math with just a little bit of programming. function calc30(odds) { for (let i = 0; i < 30; i++) { if (Math.random() < odds) return true; } return false; } Array.from(Array(10000)).map(() => calc30(0.04)).filter(Boolean).length //=> 7022 or ~70% Array.from(Array(10000)).map(() => calc30(0.02)).filter(Boolean).length //=> 4545 or ~45%

VWWHFSfQ 7y ago

for some reason those numbers are not adding up to me. do the chances compound year-over-year? how is the 4% any different in year 1 than in year 30? or any year in between? how does this add up to 70% over a 30 year period

zamfi 7y ago
If you assume 4% each year independently of each other year, then the chance of not having nuclear war is 96% in any given year. Over 30 years, your chance of no war is (0.96)^30 = 30%.
- dragonwriter 7y ago
  > If you assume 4% each year independently of each other year, then the chance of not having nuclear war is 96% in any given year. Over 30 years, your chance of no war is (0.96)^30 = 30%. It's clearly not independent though, but this calculation remains true if you assume only that not having a nuclear war doesn't change the odds for future years, even if having one does.
  - zamfi 7y ago
    My apologies, you are right -- I should have said "4% each year independently of each prior year" -- and it's true that only the negation needs to be independent.
deleted 7y ago
[deleted]
ekosz 7y ago
You can try it yourself without any of the math with just a little bit of programming. function calc30(odds) { for (let i = 0; i < 30; i++) { if (Math.random() < odds) return true; } return false; } Array.from(Array(10000)).map(() => calc30(0.04)).filter(Boolean).length //=> 7022 or ~70% Array.from(Array(10000)).map(() => calc30(0.02)).filter(Boolean).length //=> 4545 or ~45%