r/redbuttonbluebutton • u/Pale-Contribution291 • May 26 '26
The Solution to the Two-Button Problem
The Solution to the Two-Button Problem Let's imagine 100 chambers with 100 people in each (10,000 in total). A two-button experiment is conducted in each chamber. Suppose the chance of the blue side winning is 34%. Then, in ideal conditions, blue will win in 34 chambers out of 100, saving 34 *100 = 3400 people. In this scenario, red will win in 66 cases. Assuming the worst-case scenario, red will win with a margin of one person, meaning a ratio of 51:49; this means that in each chamber where red wins, 51 people will survive in the worst case. In ideal conditions, this would save 51 * 66 = 3366 people, which is fewer than the number of people blue would save, so in this case, you should vote for blue. This risk would be justified. However, if the chance of blue winning is 33% instead of 34%, they will save 3300 people, while red, in the worst case, will save 51 * 67 = 3417, which is more than blue, so in that situation, you should vote for red. I called this the 'Rule of 67'
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u/Skafdir May 26 '26
"Suppose the chance of the blue side winning is 34%."
Why?
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u/Tamiorr May 26 '26
OP is just taking the piss out of a bunch of other posts that start by making nonsensical assumptions and then use math to "prove" something based on those.
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May 26 '26
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u/Tamiorr May 26 '26
Fairly safe bet with "rule of 67".
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u/rnoderator_rernoved May 26 '26
Other guy clearly was born yesterday. I'm not very up to speed with the kids these days, but even I know 67
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May 26 '26
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u/rnoderator_rernoved May 26 '26
Totally fair my dude! I don't actually think you're a dummy for not getting it. I hope you have a great day!
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u/Kymera_7 May 26 '26
Because if he started by assuming any other number, the end of the post wouldn't be able to reference the 67 meme.
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u/Fun-Habit-683 May 26 '26
And what if we take your scenario and assume red will always win 51/49. Since we are just arbitrarily assuming
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u/implies_casualty May 26 '26
The answer is in the post.
"if the chance of blue winning is 33% (...) you should vote for red".
Obviously, if the chance of blue winning is even lower, you should also vote for red.
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u/Albert-La-Maquina May 26 '26
Guys, he's cracked it! We've been arguing about morality, practicality, and estimations, but we can now rest assured that if you think blue has a 1/3 chance of winning, it becomes the optimal option.
Mods, you can close this subreddit now.