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[WanderingWinder]

And actually, 10s(5-15) in Celsius= cold, 20s= comfortable, 30s= hot also work fine.

In human understanding, there isn't a big difference between -10 and -50, only "very cold" to "colder than the devil's heart".

Whoa, what?  No Canadians here, I guess?  5-15 C is not cold, it's cool.  It's not cold until -20.

And let me tell you, there is a huge difference between -10 and -40 (not going to consider -50, haven't experienced that).  In -10 weather I'm still wearing t-shirts under my fall jacket, maybe with a hoodie.  At -40 I'm wearing long johns and have a giant winter jacket.  -10 is still pleasant.  -40 is not.

Conversely I find 25 C cool. Even 10 C is cold to me. And it's not hot until you hit 35, in all seriousness.  I was stunned that the ESPN guys doing France/England called 86 F "sweltering"...

[eHalcyon]

Conversely I find 25 C cool. Even 10 C is cold to me. And it's not hot until you hit 35, in all seriousness.  I was stunned that the ESPN guys doing France/England called 86 F "sweltering"...

You got me there.  25 C is getting rather warm for me.  I would totally consider 86 F (30 C) sweltering. 

[kilgoretrout103]

I'm interested where your numbers come from. I wish you could see my calculations, as I'd like to have an opinion on whether they make sense or not. PM with your email and I can send a PDF.

I'll do the number of games without Colonies as an example.

Number of Kingdoms without Young Witch: (156 choose 10)
Number of Kingdoms with Young Witch (marked Bane): 42(155 choose 9)
Number of Kingdoms with Young Witch (unmarked Bane): (156 choose 10) - (114 choose 10)
Number of Kingdoms with Black Market -> Young Witch (marked Bane): 41(154 choose 9)
Number of Kingdoms with Black Market -> Young Witch (unmarked Bane): (155 choose 10) - (114 choose 10)

To get the number of Colony games I did the same calculations for all the non-Prosperity cards, then subtracted off the totals.  What I didn't do is subtract off the Prosperity-only games from the non-Colony total, which I should have under the rules you specified.

I can take a look at your calculations if you like.  PM sent.

Ah, crap, you're right. I missed the "marked Bane" distinction, so I treated "10 cards, where Hamlet is in the Kingdom normally and Watchtower is the Bane" as a different case from "10 cards, where Watchtower is in the Kingdom normally and Hamlet is the Bane." So that would significantly reduce the number of possibilities.

[blueblimp]

On the other hand, can anyone tell me why or whether base ten numbers is better than other bases, say, base 8 or base 16?

This was a very helpful post on AskScience Reddit on this question.  Turns out the mathematically "optimal" base is ... e.

That's for a certain model of how computers work. For humans, I figure you want the base to be as big as it can be while still having a reasonably-sized times table, and then it's nice to have convenient factors as a bonus. Since people often learn up to 12x12 anyway, we should be safe up to base 13, but 12 has nicer factors than 13.

[Ozle]

I cant believe there is no exact soecific answer posted yet! Or did i miss it?

[kilgoretrout103]

I cant believe there is no exact soecific answer posted yet! Or did i miss it?

Assuming we're willing to count the same set of 11 cards--but with different cards as the Bane--as different Kingdoms, then I think my original answer of 1.076 x 10^24 holds. Of course, that assumes a 30 card BM deck and strict Prosperity/Colony rules. Modifying those conditions will obviously give you different answers.

[qmech]

I cant believe there is no exact soecific answer posted yet! Or did i miss it?

With a free choice of whether or not to use Colonies and with a distinguished Bane there are 21 614 757 429 266 540 = 2.1... x 10^16 distinct Kingdoms.  (The "Isotropic rules" counts are off because I included Prosperity only games in the non-Colony count.)

It can't be anywhere near 10^24 because 80x(157 choose 10) is a generous upper bound.

[Edit: added extra factor of 2 to cover the cases where Young Witch is in the Black Market deck.]

Back 'on' topic: 15C is warm.  At 25C the good people of Britain collapse in puddles of sweat and fail to get any work done (which is handy because the trains have probably also broken down).

[GendoIkari]

I cant believe there is no exact soecific answer posted yet! Or did i miss it?

Assuming we're willing to count the same set of 11 cards--but with different cards as the Bane--as different Kingdoms, then I think my original answer of 1.076 x 10^24 holds. Of course, that assumes a 30 card BM deck and strict Prosperity/Colony rules. Modifying those conditions will obviously give you different answers.

I definitely think that you should count that same set of 11 cards as a different Kingdom if the Bane is different. Mostly because the strategies could play out very different between the 2.

[werothegreat]

The metric system is the tool of the devil! My car gets 40 rods to the hogshead and that's the way I likes it.

The one big thing that bothers me about the Imperial system is that "pounds" are both a measure of mass, and a measure of force, which is one of the big reasons why most people still have trouble distinguishing the two.  "Hurr hurr, I weight less on the Moon, so I won't have to diet there!"  "... yes, you will, you fut fack."


(wasn't sure if I'm allowed to say naughty words on this forum - and yet spellcheck tells me "fut" is actually a word...)

Actually, pounds aren't a unit of mass. You have the lazy 'poundmass', which is the amount of mass to give you a pound of force under 'normal earth gravity', and you have, more properly but less used, slugs.
Also, I'm not sure why you'd think 'naughty words' are unacceptable, but such obvious spoonerisms (is this technically a spoonerism) are fine...

Apparently naughty words aren't acceptable on here, because my naughty post was deleted.  At any rate, I love how derailed this thread has gotten.

[kilgoretrout103]

I cant believe there is no exact soecific answer posted yet! Or did i miss it?

Final answer! A giant thank you to qmech, who pointed out two things:

 (1) The probability of YW in the BM is irrelevant, and they should both be weighted as 1. (This is a minor change to my original formula)

(2) More importantly, I made a typo when I calculated the results of my formula! It should not be so large. So, without further ado, here is the final answer:

1.2274 x 10^16, or about 12 quadrillion. Much more in line with the upper-bound posited by qmech. Woo!

EDIT: Here is my formula, for those who care:

Case 1: No BM, No YW, No Colonies = (155 choose 10) - (25 choose 10)
Case 2: BM, No YW, No Colonies = 41(154 choose 9)
Case 3: BM, No YW, No Colonies = (155 choose 9) + 41(154 choose 9)
Case 4: No BM, No YW, Colonies = (155 choose 10) - (130 choose 10)
Case 5: BM, YW, No Colonies = 41(154,8)
Case 6: BM, YW, Colonies = 3(154 choose 8 ) + 38*((154 choose 8 ) - (130 choose 8 ))

case1+case2+case3+case4+case5+case6 = 12274208207648045 = About 12 quadrillion

EDIT #2: Getting those formulas to appear without emoticons was non-trivial, haha.

[theory]

And what are the assumptions made in this 12 quadrillion number?

[WanderingWinder]

I cant believe there is no exact soecific answer posted yet! Or did i miss it?

With a free choice of whether or not to use Colonies and with a distinguished Bane there are 21 614 757 429 266 540 = 2.1... x 10^16 distinct Kingdoms.  (The "Isotropic rules" counts are off because I included Prosperity only games in the non-Colony count.)

It can't be anywhere near 10^24 because 80x(157 choose 10) is a generous upper bound.

[Edit: added extra factor of 2 to cover the cases where Young Witch is in the Black Market deck.]

Back 'on' topic: 15C is warm.  At 25C the good people of Britain collapse in puddles of sweat and fail to get any work done (which is handy because the trains have probably also broken down).

Nonsense. 25C is the exact temperature, to degree celsius, I would keep the interior of my house at, were heating/cooling costs not an issue.

[kilgoretrout103]

And what are the assumptions made in this 12 quadrillion number?

Only that the probability of playing with Colonies is equal to the number of Prosperity cards in the Kingdom (including the Bane) divided by 10.

It works for any size Black Market deck (provided it could possibly contain Young Witch).

I count the same Kingdom with different Black Market decks as the same case, but I count the same 11 cards where a different one of those 11 is the bane as different cases.

EDIT: Upon further reflection, if we follow the Prosperity recommendation to the letter, the Bane shouldn't affect the probability of Colonies. If we go by that instead, we change case 6 to:

Case 6: BM, YW, and Colonies = 41*((154 choose 8 ) - (130 choose 8 )), and there are 4,872,533,562,000 fewer possible kingdoms. So then our answer is 1.2269 x 10^16 instead of 1.2274 x 10^16.

[WanderingWinder]

Only that the probability of playing with Colonies is equal to the number of Prosperity cards in the Kingdom (including the Bane) divided by 10. nonzero IFF there is at least one prosperity card, and 1 if all kingdom cards are from prosperity.

It works for any size Black Market deck (provided it could possibly contain Young Witch).

I count the same Kingdom with different Black Market decks as the same case, but I count the same 11 cards where a different one of those 11 is the bane as different cases.

The exact probabilities don't matter, except to break down into 3 cases: 0, 1, or between.
I also don't think you're accounting for what happens if all 2s/3s are in black market along with young witch existing either, though apparently it's not clear what happens in this case....

[kilgoretrout103]

The exact probabilities don't matter, except to break down into 3 cases: 0, 1, or between.
I also don't think you're accounting for what happens if all 2s/3s are in black market along with young witch existing either, though apparently it's not clear what happens in this case....

Interesting thought.

Under my original assumption of a size 30 (or 25) Black Market deck, this is impossible because there are fewer cards in the Black Market deck than potential Banes. But let's say that assumption doesn't hold, and the BM deck consists of every card not in the Kingdom. Then, the only ambiguous case occurs when Black Market is in the Kingdom, but Young Witch isn't. You pick your 10 Kingdom cards, throw the rest in the Black Market deck, go to add the Bane because YW is in the BM deck, but oh look, you can't, they're all in the BM deck.

I don't know of any official rules that cover this case, but if I were making the call, I'd say choose a Bane at random from the BM deck, and put it in the Kingdom instead. If that's our solution, it shouldn't change our count.

[Piemaster]

If we assume that you just chuck every non-kingdom card into the BM (or simply that the choice of what to put in the BM falls outside the scope of the calculation seeing as it is non-random) then this discussion becomes a hell of a lot easier and we might have a prayer at finding an answer.

[Davio]

Don't forget that BM is a Promo card, we keep treating it like it's an official card from one of the expansions.

You shouldn't take Promo cards too seriously.

If you're ever in the situation that all $2 and $3 cards are in the BM, just take a random one out and put a random higher cost in.

Not everything needs a ruling.

[Piemaster]

Don't forget that BM is a Promo card, we keep treating it like it's an official card from one of the expansions.

You shouldn't take Promo cards too seriously.

Really?  I have never seen anything to suggest that promo cards are anything other than legit and balanced cards (albeit thematic ones)

If there was a World Championships do you think they would be included?

[Tables]

I believe the World Championships used the base game only .

Anyway, what's this nonsense about 25 degrees being a sensible temperature? In my house, we stay at about 15 degrees. I've walked in once with it being 18 degrees and immediately taken clothes off for it being too hot. And it's taken the temperature being in single digits before I've decided I need to put something extra back on. 25 degrees, man, that IS swelteringly hot.

Whether Black Market is a serious card or not, it's certainly an option for being in the game, and leads itself to two possibilities: BM contains YW, BM doesn't contain YW (whose probabilities don't matter as long as they aren't 0 or 1 - and it's only 0 if the kingdom contains YW). I think (at a glance) 1.2*10^16 looks right. However, it's of course possible to play with Colony/Platinum without Prosperity. Donald has I believe said it's okay and the recommendation is only that, so I believe such games should be counted.

[WanderingWinder]

Anyway, what's this nonsense about 25 degrees being a sensible temperature? In my house, we stay at about 15 degrees. I've walked in once with it being 18 degrees and immediately taken clothes off for it being too hot. And it's taken the temperature being in single digits before I've decided I need to put something extra back on. 25 degrees, man, that IS swelteringly hot.

You're insane . Remind me to bring a jacket if I go to your house.
25 is totally sensible. I've lived entire summers at 27 without problems really. My totally honestly ideal temperature is between 24 and 25, but probably closer to the 25 side. At 18, I usually need to put more clothes on.

[eHalcyon]

Anyway, what's this nonsense about 25 degrees being a sensible temperature? In my house, we stay at about 15 degrees. I've walked in once with it being 18 degrees and immediately taken clothes off for it being too hot. And it's taken the temperature being in single digits before I've decided I need to put something extra back on. 25 degrees, man, that IS swelteringly hot.

I'm Canadian and this is still too much for me.  I think my ideal room temperature is ~19-22.  Do you live extra far north? 

[clb]

Just so WW doesn't feel all alone - I grew up in southern Arizona, and 25 is a very normal temperature for the thermostat. The electric company would encourage us to set it lower in the winter to conserve energy, but that is a seperate issue.
As to outdoor temperatures, 20-30 is very comfortable, in fact, 30 is as cool as it gets overnight for 5+ months of the year. 35-37 is warm, but we often have 100+ days in a year of highs over 37. 40-43 is where people start complaining about the heat.
On the flipside, 10 was considered pretty cool weather and time to don a sweater (or a jacket if you will be outdoors for long). Now that I live in the Seattle area (almost to the border with our Canadian friends), when the temperature hits 10 in April or so, its time for shorts, t-shirt and maybe some flip-flops/sandals.

[Ozle]

Can only really go by inside (home/Office) temps

21 seems reasonable to me, thats what i would set my car or air conditioning at for comfort.
But anywhere between 18 and 24 is also acceptable to me.
25 I would describe as a bit Warm in the office
And at 27 I would probably be moaning about the heat

[Kuildeous]

Anyway, what's this nonsense about 25 degrees being a sensible temperature? In my house, we stay at about 15 degrees. I've walked in once with it being 18 degrees and immediately taken clothes off for it being too hot.

That must have made for an awkward holiday dinner.

[Kirian]

Yeah, 25 is doable but a bit higher than I would like it.  We generally keep the thermostat near 23 in summer and 20 in winter.  Anything above 27 means I stay in the AC or a pool.  Anything below 20 and I put on a light jacket.

I guess that's what comes of growing up at the border of a Dfa and a Cfa climate (NW Ohio).