What are the differences between zombies and normal sims?
notovny:
Quote from: Garnet Avi on 2008 April 22, 07:24:57
Quote from: notovny on 2008 April 21, 10:38:34
Yep. Cumulative chance of achieving at least one abduction with 28 nights of 7PM to 4AM stargazing under the same assumptions is 74.1%.
Isn't this "gambler's fallacy"? The way I understand it, the odds do not increase the more you stargaze:
No, it is not the gambler's fallacy.
If what I was doing was figuring the odds over one stargazing cycle after having spent 28 days stargazing, you would be correct. But that's not the question I'm answering there.
The question I'm answering is "What is the chance of achieving at least one abduction, during 28 nights of stargazing."
If I flip a coin once, I've got two options H and T. The chance of getting heads 1 or more timesis 50%. If I flip a coin twice, or use two coins, there are four results possible: HH HT TH TT. The chance of getting heads at least once is 75%. For three coins, it's 87.5%, and so on. For each individual flip, the odds remain the same, but the more times you flip the coin, the more likely you are to have a rare result show up in the string of all the results you get.
I'm not looking at any individual roll of 0.05%, I'm looking at the chances of succeeding one or more times when I roll against 0.05% odds 2749 times.
n = (28 days * 9 stargazing hours / day * 60 minutes/hour ) / (5.5 minutes/stargazing cycle) = 2749.09 cycles.
The probability p of getting an abduction in one cycle is p = 0.0005.
The probability q of not getting an abduction in one cycle is q = 1-p = 0.9995.
The potential results can be grouped into two categories: No Abductions at All, and One or More Abductions.
The probability Q of getting No Abductions At All in 2749 cycles is Q = q^n = 0.2529.
The probability P of getting One or More Abductiions in 2749 cycles is consequently P = 1-Q = 0.7471, or 74.71%.
cwykes:
That coin toss stuff brings back lots of memories of maths and stats lessons!
Another question, if you don't mind...
Why choose to quote odds for 7pm-4am rather than 7pm-6am? Is the chance of getting abducted really lower after 4am or is it just that sims don't have the stamina for more than 9 hours of stargazing? I guess active sims can manage longer than lazy sims.
TreyNutz2 says "TIME: The earliest I had an abduction in my testing was 8:56pm, and the latest was 4:16am.... I have read reports of abductions as late as 4:30am."
I agree, btw, that Free Time changed something for sims who are stargazing at 6am. They used to keep "stargazing" in their queue until they stopped, but as of Free Time "stargazing changes to "look through the telescope" at 6am. Sims used to go on earning logic points after 6am, but I guess they were no longer "at risk" of abduction or we'd have heard about 10am abductions by now surely!
gjam:
Quote from: notovny on 2008 April 22, 10:35:27
n = (28 days * 9 stargazing hours / day * 60 minutes/hour ) / (5.5 minutes/stargazing cycle) = 2749.09 cycles.
Aha! That's why I'm getting slightly different results than you for the 28 day odds. (The difference isn't enough to matter for gameplay purposes. It's only relevant to math geeks. ;D )
There are either 2744 or 2772 cycles in 28 days. Not 2749. This is why:
(9 stargazing hours / night * 60 minutes/hour ) / (5.5 minutes/stargazing cycle) = 98.18 cycles/night
0.18 cycle * 5.5 minutes/cycle = 1 minute
The end of the 98th cycle occurs at 3:59AM. The following night, the stargazing starts over at the beginning of a new cycle, so the extra 1 minute is lost. OTOH, if the abduction check is made at the very beginning of the cycle, or if the complete cycle is executed once it's begun, it's possible for that 1 minute to effectively become a 99th cycle. But there are an integral number of cycles per night; either 98 or 99. No fractional cycles are carried forward to the next night, which your calculation is doing.
notovny:
True. However In the long-gone Varioussimmers thread twoJeffs mentioned that the stargaze animation was 5-6 minutes long, so I just went with 5.5 as a reasonable estimation, though having not timed a lot of them myself, I don't know whether the true time is closer to 5 or to 6 minutes (or even, come to think of it now, whether twoJeffs just pulled the number out of thin air.). Given how important that number winds up being over thousands of repetitions, though, I suppose there's a case for just throwing the raw number in there.
Quote from: cwykes on 2008 April 22, 13:51:09
That coin toss stuff brings back lots of memories of maths and stats lessons!
Another question, if you don't mind...
Why choose to quote odds for 7pm-4am rather than 7pm-6am? Is the chance of getting abducted really lower after 4am or is it just that sims don't have the stamina for more than 9 hours of stargazing? I guess active sims can manage longer than lazy sims.
TreyNutz2 says "TIME: The earliest I had an abduction in my testing was 8:56pm, and the latest was 4:16am.... I have read reports of abductions as late as 4:30am."
I blame treacherous memory.I might have had a reason to just do 7PM to 4AM, based on vague recollection of a long-gone thread at varioussimmers. But going with 7PM to 4:30AM results in numbers even closer to 5% with the 5.5 minute assupmtion I'd been using. So at this point, I'll retreat a bit from probably unwarranted precision and call the odds of getting abducted once or more times in a full night of 7PM-4:30 AM stargazing to "about 1 in 20" and the odds of getting abducted once or more times in a full adult lifetime of such stargazing to "about 3 in 4."
gjam:
I'd been wondering how exact the 5.5 minutes was.
I just enjoy playing with the numbers. Looking at the range of possibilities, I get:
Assuming 4:00AM to be the latest possible abduction time
5 min/cycle --> 5.3% per night; 78% per adult lifetime
6 min/cycle --> 4.4% per night; 72% per adult lifetime
Assuming 6:00AM to be the latest possible abduction time
5 min/cycle --> 6.4% per night; 84% per adult lifetime
6 min/cycle --> 5.4% per night; 79% per adult lifetime
Meh. So the answer is somewhere between 4.4% and 6.4% for one full night, and between 72% and 84% for 28 nights. I can't quarrel with "about 1 in 20" and "about 3 in 4". That's close enough, and easier for most simmers to understand.
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