The birthday paradox derives from how the chance of somebody there having their birthday on a specific day is 1-in-365 (ish)/nr-of-people hence the chance of two people having their birthday on that specific day is 1-in-365^2/nr-of-people, but the chance of two people having their birthday in the same day out of any days of the year is quite different because it’s not a specific day anymore so it’s quite a different calculation (which I totally forgot ;)).
In here the closest to that paradox would the chance of 2 whistleblowers of any company with whistleblowers dying within a few weeks of each other (which, depending on how many companies have whistleblowers, can be quite high) compared to the chance of 2 whistleblowers of Boeing dying within a few weeks of each other (which is statistically a lot lower unless there are thousands of Boeing whistleblowers).
Edit: actually it’s more the chance of any 2 Boeing whistleblowers dying with a few weeks of each other at any point in time (so this includes long after they did it) vs the chance of any 2 Boeing whistleblowers dying with a few weeks of each other during the time they are blowing the whilstle.
The probability of 2 people having the same birthday is 1 in 365 because it’s the same as picking person A’s birthday as a specific day in the year and checking whether person B has their birthday on that date.
Now, the reason the number is so low is that you are basically comparing pairs and with 23 people there are 253 different pairings (23 choose 2 or 22*23/2). With each pair having a 1/365 chance to have the same birthday and having 253 distinct pairs, you would have to fail a 1/365 check 253 times in a row. The formula you can use for the success rate is 1 - (1-p)^x with p being the probability and x the number of trials, so in this case
1 - (1 - 1/365)^253 = 0.5004
In essence, the unintuitive part of the “paradox” is how fast the number of possible pairs grows the more people you add.
Not really. That is just a fact that there’s only 365 days, and the more samples you make increases the odds it’s a sample that overlaps with another (there are fewer unique options).
What the OP is saying is that sometimes randomness can appear less random than other randomness. True randomness will occasionally give results that closely match something non-random. It’s why almost all music players don’t use true random for shuffle. True random you could have the same song play 15 times in a row. In fact, that is expected to happen eventually (assuming infinite time) just as all other sets of 15 songs are.
My dream is for Spotify (and other music playing apps) to let you customize your shuffle algorithm. Minimum number of songs between repeating an artist or album, that sort of thing.
I made a random character selector app for super smash bros that makes you play through every character before it lets you repeat a character. And it won’t let two people play the same character at the same time. My friends and I like playing random characters, but we kept getting the same characters over and over again, sometimes even in the same colors (online only). I got frustrated one day and made the app.
Yeah, true random sucks pretty badly for any sort of repeated selection. You could make your algorithm potentially even better by grouping characters into different roles and not repeating them in a row either. Never give two sword characters in a row if possible, for example.
That’s a really interesting thought. We do still have issues where we get like Ken then Terry (or Mii Gunner then Mii Brawler) back to back, and for people who don’t like that type of characters, its a bummer.
Each character having a list of groups that they belong to, then not allowing players to play a character in the same group consecutively would probably be a huge improvement. I would need to be careful to make sure too many characters aren’t excluded, though. It would be tough to get right, but I think it would be really good.
Could this be akin to the Birthday paradox?
That was a great read! Not something I’ve heard of before. Thank you!
And yeah it’s related for sure.
The birthday paradox derives from how the chance of somebody there having their birthday on a specific day is 1-in-365 (ish)/nr-of-people hence the chance of two people having their birthday on that specific day is 1-in-365^2/nr-of-people, but the chance of two people having their birthday in the same day out of any days of the year is quite different because it’s not a specific day anymore so it’s quite a different calculation (which I totally forgot ;)).
In here the closest to that paradox would the chance of 2 whistleblowers of any company with whistleblowers dying within a few weeks of each other (which, depending on how many companies have whistleblowers, can be quite high) compared to the chance of 2 whistleblowers of Boeing dying within a few weeks of each other (which is statistically a lot lower unless there are thousands of Boeing whistleblowers).Edit: actually it’s more the chance of any 2 Boeing whistleblowers dying with a few weeks of each other at any point in time (so this includes long after they did it) vs the chance of any 2 Boeing whistleblowers dying with a few weeks of each other during the time they are blowing the whilstle.
The probability of 2 people having the same birthday is 1 in 365 because it’s the same as picking person A’s birthday as a specific day in the year and checking whether person B has their birthday on that date.
Now, the reason the number is so low is that you are basically comparing pairs and with 23 people there are 253 different pairings (23 choose 2 or
22*23/2). With each pair having a 1/365 chance to have the same birthday and having 253 distinct pairs, you would have to fail a 1/365 check 253 times in a row. The formula you can use for the success rate is1 - (1-p)^xwith p being the probability and x the number of trials, so in this case1 - (1 - 1/365)^253 = 0.5004In essence, the unintuitive part of the “paradox” is how fast the number of possible pairs grows the more people you add.
Not really. That is just a fact that there’s only 365 days, and the more samples you make increases the odds it’s a sample that overlaps with another (there are fewer unique options).
What the OP is saying is that sometimes randomness can appear less random than other randomness. True randomness will occasionally give results that closely match something non-random. It’s why almost all music players don’t use true random for shuffle. True random you could have the same song play 15 times in a row. In fact, that is expected to happen eventually (assuming infinite time) just as all other sets of 15 songs are.
My dream is for Spotify (and other music playing apps) to let you customize your shuffle algorithm. Minimum number of songs between repeating an artist or album, that sort of thing.
That would be sick. 🤘
I made a random character selector app for super smash bros that makes you play through every character before it lets you repeat a character. And it won’t let two people play the same character at the same time. My friends and I like playing random characters, but we kept getting the same characters over and over again, sometimes even in the same colors (online only). I got frustrated one day and made the app.
It definitely livens up our game nights.
Yeah, true random sucks pretty badly for any sort of repeated selection. You could make your algorithm potentially even better by grouping characters into different roles and not repeating them in a row either. Never give two sword characters in a row if possible, for example.
That’s a really interesting thought. We do still have issues where we get like Ken then Terry (or Mii Gunner then Mii Brawler) back to back, and for people who don’t like that type of characters, its a bummer.
Each character having a list of groups that they belong to, then not allowing players to play a character in the same group consecutively would probably be a huge improvement. I would need to be careful to make sure too many characters aren’t excluded, though. It would be tough to get right, but I think it would be really good.
Didn’t the iPod have the same “issue” that it sometimes played the same song twice in a row or randomly played the next song in the playlist?
You essentially did what Apple did and made the randomness less random so humans think it’s more random.