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Messages - Doom_Shark

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51
Wait, the integral thing: will that actually get me what I want? If I integrate f(x) from say, 1 to 300, will I get the same result as calculating f(1) + f(2) + f(3) + ... + f(300)? I barely remember AP calculus AB, so I'd love to hear from someone better at calculus than I am.

That is definitely not true in general:

∫₁⁵ x dx = 12
1 + 2 + 3 + 4 + 5 = 15

Ok, is there a way to do that where I don't have to individually calculate (or rather, type into wolfram alpha) f(x) for each integer value in the range?

The best thing to do would be to look for a closed-form solution of the sum, which is nontrivial.  Wolfram Alpha can sometimes figure it out for you.  Actually, you could just type in your formula and tell it to do a sum.  That should work as well.

So it did! Cool. Back to work.

52
Dominion General Discussion / Re: The most setup
« on: March 24, 2020, 01:40:46 pm »
Before renaissance and menagerie came out, I did a similar thought experiment. The goal was not most setup overall, but to have as many piles of cards as possible and generally be as confusing as it could be for new players, all without touching Black Market:

Kingdom Cards:
1, 2) Page and Peasant each add 4 extra piles. Peasant also adds the 4 vanilla bonus tokens for Teacher, and the Tavern Mat.
3) Druid adds Boons, Will-o-Wisp, and the three set aside ones.
4) Fool gives us the lucky coin heirloom, and Lost in the Woods.
5) Young Witch. Obviously. It's basically a free extra pile with all of these $2 cards.
6) Bishop adds VP chips, and is a Prosperity card, allowing us to add Platinum and Colony. Bonus points for caring about costs, since we'll be adding a potion cost card in a bit. For extra setup, could get out the VP mats since this is from Prosperity rather than Empires.
7) Marauder gives us Ruins and Spoils. It's also from Dark Ages, allowing the use of Shelters.
8 ) Tournament gets us prizes.
9) Exorcist gets us the other two spirit piles
10) Vampire gives us Hexes, states for said hexes, and the Bat pile.
11) Finally, Possession, for potions, but also because of all the rules wackiness and various errata. Who knows what this card does anymore?

As for landscapes, I went with the following:
1) Inheritance. Only three things here can't be Inherited: Possession and Vampire cost too much, and Vampire and Exorcist are Nights, not Actions. This was also done pre-2019-errata (since, ya know, no renaissance), so there was all the shapeshifting to consider, and bonus confusion points for things like exchanging an estate for a warrior, or being unable to reveal am estate if you inherit a bane card.
2) Mountain Pass. Read it a dozen times and still be confused about it. Also, what the heck is debt?

So, the final tally:
11 kingdom piles (10 standard + Bane)
11 base cards (7 standard, Platinum, Colony, Potion, Ruins)
14 non-supply piles (8 traveler upgrades, 3 spirits, Spoils, Prizes, Bat)
10 landscape piles (Boons, Hexes, 3 set-aside Boons, Deluded/Envious, Miserable/Twice Miserable, Lost in the Woods, Inheritance, Mountain Pass)
Total: 46 piles of cards on the table

Bonus:
4 replaced starting cards (3 Shelters, Lucky Coin)
2 mats per player (Tavern Mat, Prosperity vp mats)
5 player tokens (4 vanilla bonuses, Estate Token)
VP tokens
Debt tokens

This could get even cwazier now:
1) Replace Fool with Border Gaurd. We lose Lost in the Woods and Lucky Coin, but we add two Artifacts.
2) Replace Inheritance with Way of the Mouse - Pixie. We lose a player token, but we get a new Heirloom to replace losing Lucky Coin above. Besides, most of the rules confusion with Inheritance was lost anyway with the 2019 errata, so now we get all sorts of new wackiness where the 9 leftover boons are shuffled and can be cycled through, but you can never receive them because Pixie can't trash itself.

53
Now that I'm understanding the order of operations, I think the reply below might not have been a complete answer:

Lantern modifies what happens due to following the instructions on Border Guard. With Enchantress in effect, you ignore those instructions, so Lantern does nothing.

Yes, with Enchantress in effect, you are ignoring the instructions, so Lantern does nothing. But the question remains: What if you apply Lantern before Enchantress? Are you then ignoring the instructions so that Enchantress can't find the very specific thing it's looking for?
Lantern never gets involved; we never reach the point at which Lantern would do anything.

So I was right in the rules thread; lantern is timed as when-would-reveal, not when-would-resolve.

54
Wait, the integral thing: will that actually get me what I want? If I integrate f(x) from say, 1 to 300, will I get the same result as calculating f(1) + f(2) + f(3) + ... + f(300)? I barely remember AP calculus AB, so I'd love to hear from someone better at calculus than I am.

That is definitely not true in general:

∫₁⁵ x dx = 12
1 + 2 + 3 + 4 + 5 = 15

Ok, is there a way to do that where I don't have to individually calculate (or rather, type into wolfram alpha) f(x) for each integer value in the range?

55
Wait, the integral thing: will that actually get me what I want? If I integrate f(x) from say, 1 to 300, will I get the same result as calculating f(1) + f(2) + f(3) + ... + f(300)? I barely remember AP calculus AB, so I'd love to hear from someone better at calculus than I am.

56
So, I'm going to assume that since we don't care about ruins order, knights order, or which card obelisk picks, we also don't care which card specifically is the bane, only that there are 11 kingdom cards including young witch, and at least one of them costs $2 or $3.

I would agree.

The best way to calculate that would probably be to calculate the # of kingdoms, pretending Young Witch wasn't even a card, and then double-count all the kingdoms with cards costing or .

Way ahead of you there. Black Market is hard though. Busting out integrals for that so I don't have to write a different equation for each possible size. Still working out the various formulas, by the way.

Not following... the Young Witch Kingdoms would have 11 piles instead of 10; which would do a lot more than just double count wouldn't it?

The eleventh pile is Young Witch herself. So if we get a bunch of 10-card kingdoms, all of which have at least one or card, then add Young Witch to that kingdom, it becomes a valid kingdom.

57
So, I'm going to assume that since we don't care about ruins order, knights order, or which card obelisk picks, we also don't care which card specifically is the bane, only that there are 11 kingdom cards including young witch, and at least one of them costs $2 or $3.

58
And here I was hoping for some precise combinatorials involving Young Witch's bane and Way of the Mouse, as well as an adjustment factor for kingdoms that include both.

I am disappoint.
Don't forget Obelisk, the ordering of the Knights pile, and the ordering and composition of the Ruins pile.

The ordering of the Knights pile or the Ruins pile doesn't make different kingdoms, though. Yet, the composition of the Ruins pile do. This will also vary depending on the number of players from two to six.
I'd argue that a Kingdom where Dame Anna is the top Knight plays vastly differently from one where Dame Josephine is, and thus it makes sense to call these different kingdoms.

For the Ruins pile of course it matters less, though occasionally it is relevant whether the top Ruins is RUined Market.

I agree that it plays vastly different from other Knights games, but you're talking about different experiences, not different kingdoms. Every shuffle makes each game unique as well, so those should also count, if that's the case. For every shuffle during the game, by the way. Would you say that identical kingdoms are different for two players and six players? Maybe we should multiply everything by five to take that into consideration as well? I don't know. Maybe OP can give us some more guidelines.

I think one valid definition is "what set of cards and card-shaped things are available this game"? Available meaning "could possibly be available depending on how the game plays out"; so the bottom Knight is considered "available". Under this definition; order of Knights and Black Market cards don't count. Obelisk pick doesn't count. Way of the Mouse and Druid choices do count. Which Ruins are in the game count, but not which order they are in.

I'm inclined to agree with this definition. I'm currently working out the formulas with pen and paper. The question now is: what to do about the Black Market deck? On the one hand, there's what should technically be done, which is just one of everything (with the exceptions of only one card from each split pile, one knight, and one castle). On the other, there's how most people play it: with a deck of only 25-30 cards. Thoughts?

59
Variants and Fan Cards / Re: Actually Passable Card Ideas
« on: March 23, 2020, 08:49:18 am »
LOL! The f.ds extension picked up on Fair !

I've also seen that with Haven't. (it interprets the apostrophe as an end-of-word marker, I think)

Which makes sense, as we tend to use possessives when talking about cards, such as Young Witch's bane.

60
There's a total of 376 kingdom cards (including the removed cards,
??? I count 366 (truth: table sheet does)

Ah, you're right, I somehow added 10 cards. That's what I get for doing complex math at 2 am.

61
And here I was hoping for some precise combinatorials involving Young Witch's bane and Way of the Mouse, as well as an adjustment factor for kingdoms that include both.

I am disappoint.

The issue with that is you'd have to figure out how to control for what 2's and 3's are already in the kingdom, which makes it hard. Like I said at the beginning: I'm lazy.

62
Dominion General Discussion / How many possible kingdoms are there?
« on: March 23, 2020, 02:50:05 am »
I know this has been posited before, but that was a while ago (before Renaissance, and I think before Nocturne). I'm also too lazy to hunt down the thread. Dominion setup rules have gotten pretty complex over the years, so I'm going to do this in parts. As I keep the running totals, I'll be correcting rounding errors by just adding the formulas together in Wolfram Alpha, rather than adding the rounded numbers. With all that out of the way, let's do some math!

First, let's do just the kingdom cards. There's a total of 376 kingdom cards (including the removed cards, since they are still techincally possible dominion games). So, without any landscapes, and excluding different possibilities for Young Witch's bane card or shenanigans with the Black Market deck, that gives us 376!/(10! * 366!), or 13.8 quintillion kingdoms, rounded to the nearest 100 quadrillion.

Now, for each of them that has prosperity, there's actually two kingdoms, one with platinum/colony and one without. So how many have prosperity? If we subtract the 25 prosperity kingdom cards from the 376, that leaves us with 351 cards. Using that, we calculate the number of games that don't have prosperity (351!/(10! * 341!)) and subtract that from our 13.8 quintillion to get 6.9 quintillion kingdoms that include platinum/colony.
Running total: 20.7 quintillion kingdoms

Now we add shelters. We do the same thing we did for prosperity, but with dark ages. 376 total cards - 35 Dark Ages cards = 341 non-Dark-Ages cards. 13.8 quintillion kingdoms - (341!/10! * 331!) kingdoms without Dark Ages gives us 8.7 quintillion kingdoms with shelters.
Running total: 29.4 quintillion kingdoms

Now the math starts to get weird, because we need to add the kingdoms that have both platinum/colony and shelters. If we take the number of games without Prosperity and subtract the number of games without Dark Ages or Prosperity, that leaves us with the number of games with Dark Ages and not Prosperity. Subtract that from the 8.7 quintillion total kingdoms with Dark Ages, and we get 4.2 quintillion kingdoms with both.
Running Total: 33.5 quintillion kingdoms

Now we start with landscapes. Each of those kingdoms could be paired with any one of the 115 landscapes. So we multiply that 33.5 quintillion by 116 (adding one for the "no landscape option).
Running Total: 3.9 sextillion kingdoms (rounded to the nearest 100 quintillion)

Now because ways are weird, there's gonna be two parts to having two landscapes. First, we go back to the 33.5 quintillion and multiply that by all the possible combinations of two non-Way landscapes (95!/2 * 93!), giving us 149.8 sextillion kingdoms. That's quite a jump!
Running Total: 153.7 sextillion kingdoms
Note: At this point, Wolfram Alpha broke when I tried to have it run and add all the formulas. So much for correcting rounding error.

Finally, two landscapes, one is a Way. We take our 33.5 quintillion again, multiply by 20 Ways, and then multiply by 95 other landscapes, giving 63.7 sextillion kingdoms.

Grand Total: 217.4 sextillion possible kingdoms

63
Dominion General Discussion / Re: Mouse as other Ways
« on: March 21, 2020, 04:39:05 pm »
Can't have Ambassador for Way of the Mouse though. Only does or cards.

As for Pixie, that doesn't work because of the lose track/stop moving rule. Pixie expects itself to be in play, so it can't trash itself to get the Boon. You'll just continue to cycle through the stack without actually receiving any of them.

Edit: Was thinking of Advisor. Silly me.

64
Rules Questions / Re: Does Lantern override Enchantress?
« on: March 21, 2020, 01:26:14 am »
Now, as I was reviewing the wall of text that was typed below, you posted something else that finally showed me what you were trying to say the entire time: that Enchantress should still able to do its thing with Way of the Chameleon because it should be able to replace the "Follow this card's instructions" bit on Chameleon with "+1 Card, +1 Action," and if it can't, then Lantern should override enchantress as well. This seems much more reasonable of a viewpoint to me. With this in mind, the I think the debate shouldn't be, "Does Lantern override Enchantress?" but rather, "Should Way of the Chameleon be an exception to the rule in this case?"

I will leave this argument here for posterity's sake anyway:
I just came up with what might be a better way to explain this:

You're reading lantern as "Instead of following Border Guard's instructions, follow them, revealing 3 cards instead of two."

We're reading Lantern as "When you would reveal 2 cards by following the instructions of Border Guard, reveal 3 instead."

Yes, I was going to write more or less the same thing.

So, when I posted those earlier, I failed to realize that there was an entire 3rd page of discussion that I hadn't read. That's on me. That said, I'm going to do my best to go through your post point by point:

Quote
First of all, even with the latter interpretation, your are definitely not only following Border Guard's instructions, some of them are interrupted and replaced on the fly with Lantern's (unlike what you said before). Whether this should count as resolving Border Guard so that Enchantress overrides it, I don't know

I think the difference here is that Enchantress and Ways replace the entire card's instructions before they happen, while the latter interpretation of Lantern replaces one subset of the instructions as they happen. This is much like reacting to Workshop with Trader. Workshop is still resolving, but Trader is replacing the gain event.

Quote
but whatever the case, Chameleon should work the same way.

I disagree with you on this. Way of the Chameleon has to replace the entire card's effect due to being a Way. That is how Ways work; Chameleon is worded the way it is due to that constraint, and is why it has this weird interaction with Enchantress. Lantern has no such card-type-based limitations.

Quote
Second, even that interpretation is adding stuff that is not in the wording. It's no more or less valid than my interpretation from the actual card text.

I'll concede that.

Quote
The reason my interpretation is more valid,

Alright, now you're contradicting the above statement. This doesn't add anything to the discussion, I'm just trying to inject humor by being pedantic.

Quote
is that it fits with all other such when-would effects that we have; it follows precedent. I explained this before.

I'm not sure what precedent you are referring to here. You may or may not have already explained this; I'm not entirely sure. If you have, I lost it in all the other discussion/arguing that's happening around this.

Quote
I also said this (and now we have established that Lantern does replace at least some of the instructions):

I, at least, never intended to imply that Lantern did not replace any instructions. I do, however, believe that the replacement is much more limited in scope than Way of the Chameleon; see above.

Quote
"That leaves the question of the timing. The natural interpretation is that it does this just as you're about to do it, just like all other cards like this. To conclude that it triggers several times during your resolution of Border Guard seems very forced to me. It seems to be a rule invented just to avoid a certain interaction."

Ah, the crux of the miscommunication (as I see it, anyway). I see the "natural interpretation" of the timing for Lantern as being when would reveal rather than when would resolve. This goes back to the two different interpretations issue. There's nothing saying this somehow triggers multiple times; I'm not sure where you're getting that from, and I could just be reading too much into rhetorical hyperbole.

Quote
You are also assuming that Chameleon replaces the whole instruction, but I can't see that you have any basis for that.

The basis for this is the rules for how Ways function; see above.

Quote
See my last post, which nobody has responded to. Why is Magic Trick fundamentally different from Chameleon?

I don't see it as fundamentally different; rather, it is only different enough to matter in this specific edge case involving Enchantress. This question is like asking why first and second edition Cellar are fundamentally different; on a fundamental level, they aren't, but it matters for an edge case involving one particular card-shaped thing.

Quote
To me your whole basis for this is circular; it's based on the fact that Chameleon is a Way to conclude that therefore it works as a Way.

Yes, much like saying a Nissan Leaf is a car; therefore, it works like cars do. The rulebook defines the behaviors of Ways; Chameleon is cleverly worded to work within those bounds, but at its core, it is still a Way.

65
Rules Questions / Re: Does Lantern override Enchantress?
« on: March 20, 2020, 10:37:51 pm »
Chameleon/Enchantress replace the whole effect.

Lantern replaces the specific action of looking at the top cards.

The difference here is while Lantern doesn't shapeshift Border Guard anymore, it still only replaces part of the effect when you play Border Guard.

I just came up with what might be a better way to explain this:

You're reading lantern as "Instead of following Border Guard's instructions, follow them, revealing 3 cards instead of two."

We're reading Lantern as "When you would reveal 2 cards by following the instructions of Border Guard, reveal 3 instead."

66
Rules Questions / Re: Does Lantern override Enchantress?
« on: March 20, 2020, 09:56:09 pm »
Right, this is the big difference that I've been trying to point out. Lantern does not contain an instruction to follow, Ways do.

It sounds like you think Lantern still causes shapeshifting, telling you to replace numbers in the card text. Lantern does contain instructions to follow. It is to reveal 3 instead of 2 cards, etc. I can't believe this part is controversial.

I have been saying this before, look:
But Lantern does actually tell you to do something instead of what you would normally do. Lantern doesn't shapeshift Border Guard anymore. So there are alternate instructions. I don't know how you can deny that. "Simply replaceing the 2 with a 3", etc, is also providing alternate instructions.
What's your response?

Chameleon/Enchantress replace the whole effect.

Lantern replaces the specific action of looking at the top cards.

The difference here is while Lantern doesn't shapeshift Border Guard anymore, it still only replaces part of the effect when you play Border Guard.

67
Rules Questions / Re: Does Lantern override Enchantress?
« on: March 20, 2020, 04:34:41 pm »
"when you play a Border Guard, you may instead follow its instructions revealing 3 cards instead of 2 and discarding 2 instead of 1"

Except that's not what lantern says. It says "Border Guards you play reveal 3 cards and discard 2." It has nothing saying either way that it's completely replacing Border Guard's text or just modifying what's there. I'm inclined to the direction that it's modifying what is already happening, as it says nothing about "instead of following its instructions."

68
Dominion General Discussion / Re: bounty hunter is really good, right?
« on: March 20, 2020, 04:16:09 pm »
Top 3 $4 card.

But is it the #3 $4 in the top 5?

69
Rules Questions / Re: Way of the Mouse and Setup Rules
« on: March 20, 2020, 04:13:40 pm »
This matches Black Market, right? Anything in Black Market is considered to be in the game; so you follow all setup instructions for it, including Heirlooms.

Yeah. Black Market was the reason I thought of it, actually. Funny enough, Black Market could be the mouse

70
Rules Questions / Re: Way of the Mouse and Setup Rules
« on: March 20, 2020, 08:46:40 am »
Way of the Mouse. Wacky card. Do I perform Setup instructions for the card set aside for this? Like, if I set aside Trade Route, for example, do I get out the mat and put coin tokens on the victory piles?

Edit: Damn, cardImage tags from the extension didn't work on Way of the Mouse.

This was answered in the rulebook, and the answer is yes. So if you set aside e.g. Pixie, you start with Goat.

Ah. I need to learn to read. Thanks

71
Rules Questions / Way of the Mouse and Setup Rules
« on: March 20, 2020, 07:44:14 am »
Way of the Mouse. Wacky card. Do I perform Setup instructions for the card set aside for this? Like, if I set aside Trade Route, for example, do I get out the mat and put coin tokens on the victory piles?

Edit: Damn, cardImage tags from the extension didn't work on Way of the Mouse.

72
Variants and Fan Cards / Re: Really bad card ideas
« on: March 20, 2020, 07:17:18 am »
Illegal Goods
$5
Event
Reveal the top Event of the Illegal Goods pile. Do its effect, then put it on the bottom.
-------
Setup: Make an Illegal Goods pile of 10 unused Events and set it aside.

I appreciate that you included an upper limit. Good on ya m8.

73
Weekly Design Contest / Re: Weekly Design Contest Thread
« on: March 20, 2020, 07:16:04 am »
It is a Courtier variant. And while it is hard to judge whether this is better or worse than Courier, it is definitely not that much better that it is worth $6.
Furthermore, the below-card in a split pile can always be a bit stronger than a card which is immediately available. See Plunder.

Alright, let's make the plunder comparison:

Plunder is a treasure that has the same abilities as a terminal action (Monument) and costs more than that action.

Your card is a terminal action that, if it were a treasure, would cost . By this comparison, making it cost makes sense.

Also, I would say it's really not a courtier variant, as courtier has, well, variance. You're not guaranteed to be able to make more than one choice in any given kingdom. And in (albeit very rare, depending on what expansions you're using) others, you might be able to get all four (Dame Josephine or Werewolf).

74
Weekly Design Contest / Re: Weekly Design Contest Thread
« on: March 19, 2020, 10:50:09 pm »
Goods (Action, $5)
[...]
Obviously this plays well with any discarder, with Warehouse being a great example.

It's also strictly better than gold. Cheaper, has +buy, and plays itself on discard.

It's an Action, not a Treasure.

Whoops. Still probably worth , though you could probably justify in that case

75
Weekly Design Contest / Re: Weekly Design Contest Thread
« on: March 19, 2020, 07:23:24 pm »
Goods (Action, $5)
[...]
Obviously this plays well with any discarder, with Warehouse being a great example.

It's also strictly better than gold. Cheaper, has +buy, and plays itself on discard.

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