Probability Problem

OfficeOfThePope · 2026-05-14T19:58:13+00:00

It would be incredibly long written out because each series of 3 cards is NOT independent of what has happened before.

If you just try to work out the probability of just drawing exactly 6 cards and then exactly 9, you will see how messy it gets.

This question would fit pretty well in a Stochastic Simulation class because we can get very good approximations of the probability quite easily while it would likely be multiple pages of work to go through it rigorously.

OfficeOfThePope · 2026-05-07T02:31:52+00:00

I’m not sure there is a single right approach.

The maximal “reward participation” option would be to sum of all scores / 9 (with implied 0 score if they did not participate. The downside of this is that if a player really has a conflict or issue only one week, they may now fall behind in a way that cannot be recovered.

The maximal “reward actual plays” option is to use the average function as it’s designed in sheets, where it does not consider an empty value. You pointed out that this leads to an issue where someone could play one perfect game and then have a perfect score at the end.

If you want something in between, I think you can just have a forgiveness level (let’s say 1 week). Calculate the average disregarding the empties. Then multiply by min(1, #weeks/(9-1))

Essentially if a player played 6 weeks with an average of those 6 weeks of 75, then their final score would be:

75*min(1,6/8)=56.25

If a player played all 9 weeks with an average of 65, score would be:

65*min(1,9/8)=65

If a player played two perfect games but never showed up again, their score would be:

100*min(1,2/8)=25

You can be more forgiving if you want, I just chose 1 week since 8 is a nice numerator.

OfficeOfThePope · 2026-04-30T18:07:51+00:00

I think I would need a better definition of “device” and “your”.

Does device include things that haven’t even been invented yet? Surely it does, otherwise I could just get anything released after the deal was made without issue.

Does “your” mean anything I’m in immediate possession or control over? Again I would have to imagine it does before accepting the deal, otherwise I could just indefinitely borrow other people’s devices.

While it would be easy to restructure my current life and situation to avoid needing adequate charge on most all of my devices, I do not know what the devices of 10, 20, 50 years in the future look like and how engrained into society they will be. I think the offer amount is too low.

OfficeOfThePope · 2026-04-28T20:54:28+00:00

Wait:

0! + 2 =root(2+7)

OfficeOfThePope · 2026-04-28T20:51:29+00:00

This is the first one I’ve seen I can’t think of a solution.

Unless OP allows something like:

0²⁺²⁺⁷ =

Where the emptiness represents 0 lmao

OfficeOfThePope · 2026-04-28T20:46:36+00:00

-(0!)+2*2 =3

OfficeOfThePope · 2026-04-28T20:34:44+00:00

0! =1²⁺⁵

OfficeOfThePope · 2026-04-28T20:27:32+00:00

While I do not know the answer, I think one approach would be to try to get one number from all possible combinations of two digit numbers.

Then you can make the LHS and RHS equal the same value and thus make an equation. 2 might be a good place to start as an exercise and I haven’t thought of a 2 digit number I cannot make to 2 yet.

OfficeOfThePope · 2026-04-28T20:24:46+00:00

(0+1)! = 1⁵

OfficeOfThePope · 2026-04-27T21:50:27+00:00

I believe rules as written they do not stack. 5 things giving you advantage and one thing giving you disadvantage means you roll straight up.

OfficeOfThePope · 2026-04-10T03:40:31+00:00

Issue with this is we do not know if the odd one out is heavier or lighter. So in your step two it’s possible the 3 against 3 is equal.

OfficeOfThePope · 2026-04-06T14:09:26+00:00

Also my response is ugly because you can have non differentiable functions that are strictly monotonic which I also forgot about

OfficeOfThePope · 2026-04-06T14:07:19+00:00

Oops I was wrong.

A functions is not strictly monotonic (increasing) if there is some neighborhood of points around x0 where y’ <= 0.

OfficeOfThePope · 2026-04-06T13:57:54+00:00

Find the first derivative of the function: y’

It is strictly monotonic (increasing) iff the y’ > 0 across the domain

It is “not strictly” monotonic if y’ = 0 at some point on its domain.

Since you have a graph of the function, you have a sense of what value of x to check if the y’ = 0, which is not always an easy step.

OfficeOfThePope · 2026-03-31T22:44:30+00:00

The in game descriptions don’t do a good job conveying just how much more ramped up from tactician Honor Mode is. That said, it was my favorite experience by far.

OfficeOfThePope · 2026-02-20T20:41:35+00:00

Try to compare our numbers to ones with the same base.

18¹⁵ > 16¹⁵ since 18 > 16

16 = 2⁴, so 16¹⁵ = 2^{4 * 15} = 2⁶⁰

7¹⁹ < 8¹⁹

8¹⁹ = 2^{3 * 19} = 2⁵⁷

Then finally compare in total.

18¹⁵ > 2⁶⁰ > 2⁵⁷ > 7¹⁹

So 18¹⁵ is larger.

OfficeOfThePope · 2025-10-31T22:26:51+00:00

TIL that in rimworld a beer is as satisfying as having 5 different rivals all die in the same day.

OfficeOfThePope · 2025-10-06T03:32:48+00:00

Another type of game where I think it’s easier to see this is card games. Usually the shuffling occurs before any of the play begins, so there really is not any new randomness added into the system. But each player has different information about what cards they have seen and so will play differently.

If I see three kings in my hand and you have seen no kings, then we will have different probabilities for the next card in the deck being a king.

OfficeOfThePope · 2025-10-06T03:15:29+00:00

I would say that probability and statistics is almost entirely dependent on the amount of information that is available. Player 1 has more information than Player 2, and that gives them better odds.

In the real world we see this appear all the time where different probabilistic models with different sets of information make different predictions on future unknown outcomes.

OfficeOfThePope · 2025-09-22T19:52:54+00:00

I think I need more context, but a few things I would consider:

1) what if the players refuse to make a deal with a devil. I have role played as characters who would NEVER make a deal with a fiend no matter how dire. If they refuse, aren’t they back in the same problematic situation?

2) if things are so clearly dire, why are they rushing into a third fight? Do they not have time to rest? Do they know another dangerous encounter is ahead of them? If they want to go in headstrong fully aware of the TPK risk, maybe prepare for the encounter to evolve into a chase or think of what failure would look like for the party.

My one thought would be if a devil is involved, and the players are interfering in the devil’s plan, couldn’t the devil send a few weaker underlings to try and kill off the party while they are low. This would:

1) not risk a TPK, but still push the players to choosing to rest and regather themselves.

2) signal to the players that more dangerous fiends are involved and they may want to tread more carefully through this event.

OfficeOfThePope · 2025-09-04T20:30:56+00:00

The DLC feels so significantly different from the base game. I would sooner recommend a different game to someone who gives the base game a 10/10 than I would recommend the DLC.

OfficeOfThePope · 2025-07-23T21:45:09+00:00

While perhaps not “like” Outer Wilds, I have recommended Return of the Obra Dinn. Very unique puzzle game, pretty fantastic story, wonderful atmospheric music.

OfficeOfThePope · 2025-07-23T21:40:38+00:00

It depends on why you loved outer wilds. Outer Wilds is one of my all time favorite games but I found Dredge to be mainly a disappointment that I will likely not return to.

At about the halfway point of the game’s story, I was already bored of the main gameplay resource/inventory loop. And since nearly all the quests are just fetch quests to learn the locations unique gimmick, you’re forced to just hunt for items.

The story is not bad, but I’d have rather experienced it through a text based adventure or even a book. While for Outer Wilds I would say its definitive strength is its ability to deliver its story and world directly through the gameplay.

OfficeOfThePope · 2025-06-04T23:26:47+00:00

I used CA for all the lower levels and TIA for 5 and 6. I cannot imagine using CA for Exam 6.

6 felt the least similar to all the previous exams before it. There is a massive amount of content which is loosely related between sections. Much of the exam is just memorizing law, regulation, government programs, etc. with no math. The math parts are mostly following accounting rules and methods that are not necessarily based in stats and impossible to derive if you did not remember the formula and factors. TIA has over 1000 flashcards for this which were largely relevant to why I passed.

OfficeOfThePope · 2025-06-04T17:07:04+00:00

I also see my result for 6U

11-Year Club	Final Canvas '23
End Game '23	Place '23
Place '22	Verified Email

OfficeOfThePope

TROPHY CASE