LogFAQs > #934542633

LordoftheMorons posted...

You actually can extend the binomial coefficients to the reals or even complex numbers! (Though probably not on a TI-83 since iirc you needed an 89 to do integrals?)

Yeah, TI-83 throws a domain error if you feed it even a positive non-integer rational. It's not an issue if all you care about is tracking P(0) since you can represent that particular case without running into that issue since it's not a significant term since it'll always be 1 regardless of n. Which is why initially all I did was graph that as 1-P(0) was still valuable as a basic "chance to not totally fail" figure. Arguably it's more useful in a far-out sense where you're unsure how many rolls you'll have because you can see various breakpoints easily like where you cross 50%, 75%, etc. Since it's obviously over the reals you get a bunch of nonsense stuff too since non-integer values are meaningless since you can't have .4 of a roll but yeah.

The TI-83 can "kinda" do integrals but not really. The TI-89's computer algebra system is OP and it has nothing like that but it can do an "okay" job depending on what you need from it. However, IIRC, it's not true integration and can only give you a numerical answer if you feed it the parameters: function, the variable, a, and b. I'm not sure which approximation method it uses, but I'm pretty sure that's what it's really doing so yeah.

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Anyways, the time has arrived. Some might say that this very moment is the reason I started Fate/Grand Order in the first place. I forget which New Year's was when I marathoned Kara no Kyoukai... 2018? 2017? but really enjoyed it and honestly the more time passes and I look back on it I think I like it more and more so this is kinda big for me. It is time to transform this game into Kara no Kyoukai/Grand Order.

So yeah, for two week starting today some Kara no Kyoukai characters are available in F/GO. Two of which are only obtainable here and now AFAIK. There's Assassin Shiki who is obtained through actually playing the event so I'm not worried at all about her she's a given. Then there's Fujino who AFAIK has only ever been available during this two-week period (the English version of the game runs 2 years behind the Japanese version and she has yet to ever be available again in Japan) and Void Shiki who is I think technically available later on but you need to gamble with real money and again, I'm not about that life. Now! This is it! Now is the time to gacha! Surrender, and be free of pain, or roll, and fight your sorrow! Now is the time to shape our stories. My fate is in the hands of the RNG!

I actually did make an error from my EARLY ACCESS post but it was in my favor. I forgot to account for some pity resources the game gave out for the maintenance period it was down for in preparation of this event so instead of 111 rolls... I've got 112. Now for some despairing odds. Fujino has a 1.5% chance on any given roll. Void Shiki has an even grimmer 0.7% chance. Thankfully for me, that there's a no-roll-dependent Shiki in this event means I can take or leave getting Void Shiki here. It'd be great if I did and I'll aim for it, but I wouldn't be crushed if I fail there. Fujino though... that would hurt.

Mission Objective: Roll and pray the gacha RNG gives me Fujino
Bonus Objective: Hope the gacha RNG also gives Void Shiki

Mission Odds: Chances of obtaining Fujino over 112 rolls: 81.60%. Chance of obtaining Void Shiki over 112 rolls: 54.47%.

Additionally, while this would be a pure bonus, there is a benefit of getting multiple copies of a character up to 5. I... uh... don't think that's happening in either instance. Also in the miracle case where I get both of them fairly quickly without many rolls I don't know if I want to continue there rather than preserve my resources for some future event with other characters I may like. FTR some stats on this: The odds of getting 3 Fujino cards is just slightly lower than missing completely. Getting 5 or more sits at 2.73%. For Void Shiki it's just comical: There is literally only a 0.12% chance of getting 5 over 112 rolls. In what may haunt me should it come to pass there's actually a better chance of getting at least 2 Void Shikis than missing on Fujino which would drive me into Danganronpa levels of despair.

So now, now it is time.

"February 2020. I rolled."

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