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Dominion General Discussion / Re: Musings and Pixie strategy
« on: March 26, 2020, 09:34:48 am »
Given how turn 3 went he was guaranteed a $5 hand on turn 4 (he had a 6 card hand and only 1 Estate).
Drawing Goat, Village Green, and an Estate on turn 3 was pretty lucky.
But I'm not sure how central Festival was to his plans, it looks incidental to me. Like it's a silver with +buy which is great, but he could've just picked up a silver instead, and only gotten 4 Destriers on turn 9.

Dominion General Discussion / Re: The most setup
« on: March 24, 2020, 12:08:04 pm »
swamps gift doesn't give wishes...just will o' wisps.

Leprechaun/Secret Cave could get you wishes, but no boons.

Dominion General Discussion / Re: Menagerie Bonus Previews
« on: March 17, 2020, 08:11:26 am »
Bonus Preview 11: Desperation

It's the Event version of Cursed Gold. You can have more money, if you want it badly enough.

Is the person on the art missing a hand?
Looks like they've been caught stealing once before...

Dominion General Discussion / Re: Menagerie Bonus Previews
« on: March 12, 2020, 08:47:14 am »
Feels like Workshop is better, because you can actually gain Gardens with it.  Eventually with Camel Train you'll need to figure out how you're going to consistently hit 4 while flooding with Gardens.

Beggar has that same advantage, flooding your deck with stuff and also helping you actually get Gardens.

Rules Questions / Re: Militia rule change
« on: March 10, 2020, 04:10:40 pm »
I haven't seen anyone mention that the ruling here could force additional cards to be discarded after reaching the hand size.

I have bought Sewers and have five cards in hand, including Tunnel and Watchtower.
Opponent plays Militia.
I discard Tunnel.
I reveal Watchtower to trash the gained Gold.
I use Sewers to trash a card from my hand.
I now have three cards left in my hand.

If I discard until I have 3 cards left then I'm done, but if the number of cards to discard is decided when Militia is played I must still discard one more and will end up with just two cards left.
You're creating an odd scenario where you discard 1-at-a-time, to a set number determined at the start.  I believe the two options are:
Discard 1 at a time until 3 cards or less in hand. (can react after each discard)
Discard all at once down to 3 cards or less in hand. (only react after all are discarded)

Now option 2 combined with Sewers and Tunnel and Watchtower can result in a 2-card hand, because you react after the discard, and choose to trash 1 of your remaining cards.  But it's not because you have a discard leftover after reaching 3 cards.  Option 1 you would discard 1-at-a-time and end after trashing.

I think though that for the discard-gain gold, trash something from hand, draw a card (Catacombs+Blessed Village, or just Overgrown Estate or Rats).  This actually gets you to 3 cards and 2 discarded + 1 trashed either way.  The only difference is whether you can discard the drawn card/watchtower or not.

Option 1 goes: discard-trash-draw, at 4 cards, discard again.  Option 2 goes: discard 2 (at 3)-trash-draw, at 3 cards now.  You'd need to be able to trash due to discard from outside your hand to cause the issue that Village Green causes.

So, option 1 you can discard the drawn card or Watchtower, whereas option 2 you must discard an original non-Watchtower card.

EDIT: it's also possible that option 1 terminates the discard while you're mid-reaction since you reached 3 cards at some point.

I just played a game that included Populate, Way of the Ox, and Prince.  I bought Populate, and so Prince was one of the cards I got.  I chose to set aside Catapult with the Prince (that was pretty much the only decent cheap Action in that kingdom).  Way of the Ox was very useful, because in turns where I wouldn't want to trash any of the cards in my starting hand, I could simply use Way of the Ox on the Catapult.  There's a lot of other combinations with Prince that would also benefit from Way of the Ox

That seems like it shouldn't work. Wouldn't Prince fail to set aside Catapult if Way of the Turtle already set it aside?

Is the expansion symbol in a different place for these landscapes? Is that so more of them can fit on two lines?

Also is the ironic toiling a reference to ironic tilling from Guilds? Yay for self-referential jokes!
He was using Way of the Ox not Way of the Turtle.

General Discussion / Re: Maths thread.
« on: January 30, 2020, 10:17:04 am »
For hat-problem number 2 I don't know the probability, but the strategy that produces better than a 50% chance is:
If you see an even number of hats of each color, guess whichever color you see fewer of. If you see an odd number, don't guess.
This cannot be the best strategy. Consider e.g. the 5 player scenario: You have 2 cases of all same hats, which you get wrong; 10 cases where only a single player has a different hat, which you get right; and of the remaining 20 cases, which have a 3-2 distribution, you get only 50% correct. So overall you get 20/32 = 62.5% correct answers.
This is less than the 3 player solution (guess the opposite color if everyone else has the same hat), which is correct 75% of the time. So player 4 and 5 passing and otherwise using the 3 player strategy is stronger.

Doesn't it make sense that you'd win more with less hats? You can't just put that 3 player solution with 5 players, because there's more hats. Turns out "guess the opposite color if everyone else has the same hat" is the same as theorel's solution but for 3 players: in both cases, only the person who sees an even amount of hats guesses, and they guess the color they see less. So theorel's solution can be optimal.

I think the idea is that if three of the players ignore the other two, and if those two players never guess, the five player game essentially becomes a three player game. Therefore, the optimal strategy for any number of players must be at least as good as, if not better than, the optimal strategies for all smaller amounts of players.

But also, the logical extension of the three player solution is to use the same strategy for higher numbers of players. "If you see only same-color hats, guess the opposite color, otherwise, don't guess." As the number of players increases, the chances that someone will make a guess decrease exponentially, but the probability that said guess is correct only increases.
I did not consider giving players different strategies...I believe my strategy is correct if all players have to use the same strategy, and the number of hats is 3 mod 4.  There is a different optimal strategy if the number of hats is 1 mod 4.  In fact, with the original strategy the 3-2 case wouldn't get anywhere near a 50% win-rate...because you don't know what to guess.  If you choose randomly, then 3 people are choosing, so first they have to agree which is only a 1/8 chance, then they have to be right, which drops it to 1/16, of the remaining 20.  So, anyways, the total correct cases ends up around 35%
The correct all-same-strategy for 1 mod 4 hats is: if you see an odd number of hats of each color, guess the smaller quantity.  Unless you see all the same color, then guess THAT color.  That strategy hits 22/32 for 5-players.

I'll have to think if you can do better than just let 3 players play the game, maybe by using certain patterns to determine whether they play the game. 
I'm assuming that the abstention is intentional like they have to simultaneously vote White, Red, or Abstain.  If abstention is passive, then you can use timings to do better.
Otherwise, I'm pretty sure 75% is the best you can get.

General Discussion / Re: Maths thread.
« on: January 28, 2020, 03:45:12 pm »
For hat-problem number 2 I don't know the probability, but the strategy that produces better than a 50% chance is:
If you see an even number of hats of each color, guess whichever color you see fewer of. If you see an odd number, don't guess.

And, for hat problem number 1:
Decide ahead of time to always guess odd or always even. Then everyone is guessing the same hat distribution.  This produces a 50% chance of victory, because there's an equal number of even and odd distributions.

I don't see any reason why a combination of 3 sets would be more fun than a combination of 2 sets.  In particular, I think that the recommended sets are probably actually more fun than what someone here is going to haphazardly come up with, although there may be some kingdoms that someone has found fun that they could share, but what's fun for some people that like and have played Dominion for a while may not be fun for your friend that has so far not enjoyed the game.

If you want to do random sets, but not take everything, I'd just take 2 sets with you, shuffle the randomizers together and deal out some random kingdoms.  When restricted to 2 sets, it is unusual for a kingdom to be completely not fun...but if you happen to get a set-up with no +2 action cards, or too many attacks or whatever, just say that looks overly skewed, let's adjust it, and take the next random card that meets your criteria.

I'm a bit confused about their reaction to the previous game, specifically the Workshop-Gardens comment. I think you would have been better served playing workshop-gardens than telling them about it afterwards...and even better served by changing the set as I mentioned in my post in that thread :)

One thing in particular I would like to know, you said "Everyone got Chapel". Did everyone (anyone) trash all their coppers and estates?

I really disliked Dominion when I first played seemed pointless, we were all just buying cards to draw cards to get VPs.  Trashing is what convinced me there was a deeper game there.  If I were trying to convince veteran gamers that there is more to the game I would ask to play 2 games (potentially with the same kingdom, not sure how competitive the strategies are with each other).
The first would include Chapel, Remodel, Village and Smithy.  And I would show off some sort of "Turbo-remodel" where you trash out everything as fast as possible and try to remodel your way into provinces (by remodeling your Golds rather than playing them).  This showcases that trashing can really change the game, and that sometimes you have ways to get provinces besides money, both of which are really key big-picture strategic considerations.

The second would include workshop and Gardens, and you just do the straightforward buy Workshops and Gardens whenever possible, while also buying coppers and other junk.  This in particular shows a significant contrast from the turbo-remodel strategy, and shows off how sometimes Provinces aren't even relevant to the winning strategy.

I'd personally stay away from most attacks and any kind of sloggy games, certainly no Torturer (which is in "the plot thickens").  Bandit's not bad...
Size Distortion replacing Bureaucrat and Witch with Remodel and Smithy looks like a good kingdom for this purpose.

Other Games / Re: Slay the Spire
« on: August 21, 2019, 05:02:41 pm »
Yeah, it's just funny looking at my stats.  Ironclad/Defect are currently Ascension 6, Silent is Ascension 7.
Stats show:
Ironclad: Victories: 6, Deaths: 46
Silent: Victories: 7, Deaths: 24
Defect: Victories: 3, Deaths: 22

So, if you go by beating the act 3 boss, I've got 6 victories as defect vs 19 deaths.  I did 1 extra Silent run pre-ascensions, but mostly, I just barely made it through act 3 with the Silent, where when the Defect was working I managed to grab all the keys each time.

Other Games / Re: Slay the Spire
« on: August 20, 2019, 08:06:55 am »
I don't always acquire all the keys...which is funny because those runs are successes, when the ones where I went on to fight the heart and then died were more "successful" by any reasonable metric, but are marked as failures.
They should have 3 levels of success: Failure=died before end of act 3, Success=defeated act 3 boss, Success+ = defeated the heart.

I've only "Succeeded" twice as the Defect, once before I got access to the Heart, and once when I finally beat it.

I finally beat the heart with the Ironclad, it wasn't an infinite-deck, it was just a fairly quick strength-building deck (Flex+the strength-doubler) which had a couple Heavy Blades, and a lot of block somehow.

Other Games / Re: Slay the Spire
« on: August 08, 2019, 09:31:18 am »
Actually, usually in an infinite-deck you'll have some source of block (vestigial though it may usually be), and since you're infinite, you can generate as much as needed.  At least, that's how my infinite (and near-infinite) deck ran.

The thing that kills infinite decks IME is the 5? status cards, and the damage limit.  They didn't quite stop me, but those are the things that made me sweat. Because I couldn't kill him turn 1, and starting turn 2 I couldn't go infinite any more...also, a significant portion of my cards were useless status effects.

General Discussion / Re: Maths thread.
« on: August 08, 2019, 08:54:58 am »
How would you describe math to a layperson, in such a way as to try to break through their preconceived notions of what it is?

My go-to answer to the question of "what is math?" was "the study of abstractions".
Then, if they actually wanted more information, I would explain how numbers are an abstraction of quantities of things, and arithmetic is an abstraction of counting, and algebra is an abstraction of arithmetic.  (by actually explaining it, y'know, anything you do with 3 and 4 applies to all instances of 3 things and 4 things, etc).

Once I hit algebra, most laypeople would note how they never really understood algebra, and the conversation would move on...but generally this would help those people stop thinking that I did some sort of "advanced arithmetic" or numerology or something.

For the non-maths people that actually understood Calculus, this also offered a nice framework if we continued the discussion with something like, "so what is topology?"

I'm not sure what the hope would be there, or what a reasonable workshop/silkroad/island strategy is....
But I made one up, and it beats envoy whether facing off with 2 or not.

But if we're just looking for 3-player about this one:
Ironworks/Island/GH beats IGG/Gardens 87%-13%
If we go 3-players, and 2 people try to go for Ironworks/Island/GH vs a single IGG it's even worse: IGG loses .5% to 45% (for the Ironworks players)
OTOH if that third player goes IGG it wins 33% to 15%, with a good 18% becoming ties (presumably for IGG)

So, it's like the inverse-prisoner's dilemma.

Testing a bunch of different strats...lalalala
Okay, here we go: Witch vs Chapel/Minion

So Witch beats Minion/Chapel all on its own 65%-33%
But, if 2 players try to go Witch, then a third player can do Minion/Chapel and win 40% of the games (vs 28% for Witch)
But then if one of the Witch players decides to switch to Minion/Chapel to get in on the action, the remaining Witch wins 52% of the time (vs 22% for the Minions).

What if the Witch player tries to do an Engine, since they have a Chapel available?  It still goes to the one that picks a different strategy...
1 Witch/Village/Chapel vs 2 Minions/Chapel wins 62% to 18%
But 2 Witch/Village/Chapels vs 1 Minons/Chapel loses 29% to 41%

So, there you go can still dream. :)

Making that change helps the Smithy-player a bit.  By making the Smithy-player snipe the last pile, his win-% goes up to ~5%.

My point above was just that I'm not sure what situation might lead to the Gardens player winning alone, but not when splitting piles.

So, I wonder what strategies the OP was seeing.  Sims obviously only go so far, and workshop-gardens is super-simple to play once you know the buy-rules (so sim does it well).  But I'm having a tough time coming up with any built-in sim strategies that can beat it.

Coppersmith-Tactician gives a respectable showing.  Rabble-Fishing Village can take it on with a 39% win-rate vs ~28% wins.  But if 2 players go Rabble-Fishing Village the Workshop-Gardens strategy tanks, it doesn't come back to win on its own.

Anyways, maybe the workshop-gardens players were trying to be fancy and giving the province-player time to win, or maybe the province-player was building a good engine that could win vs Gardens?  Or maybe it was just a fluke...

I chose 2 originally based on the comment in the strategy in the simulator which says:
The ultimate combo for the basic game.
Surprisingly the optimal number of Workshops to get before starting to gain Gardens is 9.
When two players are going for the same strategy, you only want 2 Workshops before you start gardening.
I think 4 is probably optimal in the 3-player because 12 Gardens gives you more time to get going on the pile.

I tried the built-in workshop/gardens strategies and the built-in smithy strategy for the third player.

And, just now, I was playing with it some more and I realized that the buy rule for Gardens being based on number of Workshops in deck is bad...since sometimes workshops run out when being contested, and in those cases they weren't buying ANY gardens.  Fixing the buy rule: Workshop-Gardens just dominates Smithy-BM, even in 3-player regardless of Gardens-preference.

Fixed Buy Rules:
Buy Workshop if < X workshops in deck.
Buy Gardens
Buy Workshop
Buy Estate
Buy Copper
Here's the win% for various X values vs each other, given a 3rd player that's going Smithy BM.

P2\P1  1    2     3     4     5     6     7     8     9
1   43\43 36\53 34\56 34\57 35\58 39\54 40\52 42\50 42\49
2   53\36 45\45 42\49 42\50 44\49 47\47 46\48 49\45 50\44
3   34\56 49\42 46\46 46\46 49\45 50\44 51\43 50\44 50\44
4   34\57 42\50 46\46 46\46 50\43 51\42 51\42 51\42 51\42

And if you set X to 10 for each player (i.e. prefer workshop over gardens always) you get ~45% wins for each player with smithy BM getting a paltry 1.4% (7% going to ties)

Interestingly although you want to stop preferring Workshops over Gardens after about 3-4 of them, you don't want to stop getting them entirely. That drops your win-chance to the 30's, splitting your losses between the other workshop-gardens player and the smithy player.  (probably 3-pile doesn't happen as early).

Note that this is still true in a 4-player game.  Even splitting the Gardens 3-ways, the Workshop Gardens players win out over smithy ~30% of the time (vs ~1.4% for the Smithy player)

So, yeah, bad buy rule made it look like Smithy could win...but actually workshop-Gardens just dominates under all circumstances.


EDIT: well I tried a few quick things in Geronimoo's Sim and in a 3-player game, one Workshop/Gardens vs two Smithy-BigMoneys wins ~75% of the time, even if the Smithy players avoid Estates. And then two Workshop/Gardens vs one Smithy-BigMoney wins almost none of the time. Of course the simulator isn't perfect, but it does suggest Workshop-Gardens is hard to beat if only one player plays it.

I played around with this a bit more in Geronimoo's sim, and got some interesting results:
So, as noted, for the baseline if you just compare big money smithy vs workshop/gardens you get:
2 players go Smithy 1 workshop-gardens, then workshop-gardens wins 75% of the time.
2 players go workshop-gardens 1 smithy then smithy wins 100% of the time.

But, interestingly, if you make the workshop-gardens players get Gardens after 2 workshops, then 2 players going for this strategy split the wins 45% each.  (Smithy winning ~2% of the time, with 7% ties).
I believe this is because the game ends quicker with this strategy (looks like it goes about 12 turns), which doesn't give smithy-BM time to get more than about 2-3 provinces, but the workshop players get ~30 cards in their deck.
This might not be the optimal mirror strategy, but getting more workshops does worse, and trying for duchies appears to do worse, so it seems to be at least a little bit stable.
Anyways, it looks like based on that test, 3-player workshop-gardens is not a "prisoner's dilemma", but just a winning strategy the majority of the time, if you go after Gardens strong enough.

General Discussion / Re: Random Stuff Part IV
« on: October 17, 2018, 10:15:02 pm »
Something different I encountered today: check out this sentence. It has both correct grammar and sensible meaning

The complex houses married and single soldiers and their families

this was incredibly confusing to me, I'm not sure if others have an easier time with it. Resolution: [The complex] houses [married and single soldiers and their families]

Somewhat less confusing: The horse raced past the barn fell. Resolution: [the horse (that) raced past the barn] fell. Apperently they're called garden path sentences.
[the house (that was) raced past the barn] fell.  The way you have it has a different meaning than the original sentence.
Now yours doesn't make much sense. How can a house be raced anywhere?

C'mon you've never seen a house-race?  We used to do them all the time out on the farm, past the barns.  Sometimes the barns fell sometimes the house, but it was always exciting.

General Discussion / Re: Random Stuff Part IV
« on: October 17, 2018, 07:42:27 am »
Something different I encountered today: check out this sentence. It has both correct grammar and sensible meaning

The complex houses married and single soldiers and their families

this was incredibly confusing to me, I'm not sure if others have an easier time with it. Resolution: [The complex] houses [married and single soldiers and their families]

Somewhat less confusing: The horse raced past the barn fell. Resolution: [the horse (that) raced past the barn] fell. Apperently they're called garden path sentences.
[the house (that was) raced past the barn] fell.  The way you have it has a different meaning than the original sentence.

General Discussion / Re: Maths thread.
« on: October 16, 2018, 10:28:36 am »
Here's something I've been thinking about again recently

So, a while ago I tried to prove that the derivative of sin is cos using the limit calculation, that's lim h->0 [sin(x + h) - sin(x)] / h. After finishing it, I realized that I used the rule of L'hopital, so I used the fact that sin' = cos in order to prove that sin' = cos. And ofc logically speaking, sin' = cos => sin' = cos is a tautology, so it doesn't prove anything. But then I realized that it's actually still pretty strong evidence certainly it would be strong rational evidence if you didn't know what the derivative of sin was because if you postulate an incorrect derivative, the same calculation will most likely get you a contradiction. For example, if you postulate that sin(x)' cos(x)' = x, then what you prove is that sin'(x) = cos'(x) = x => sin(x) = 0, which is a contradiction, so it does give you a valid proof that sin(x)' or cos(x)' does not equal x.

The other replies are good for the general question, but this specific question seems to have some interesting points in it.
First: note that applying l'Hopital to the general derivative rule produces a tautology:
lim h->0 f(x+h)-f(x)/h=lim h->0 f'(x+h)/1=f'(x).

If you restrict yourself to using the derivative of sin, then you'll get the tautology.  The reason your problem gets wonky is because you're involving the derivative of cos as well, because of the other steps involved in finding the actual solution.
Trying to solve the limit, I assume you used the addition rule for sin, and got to:
sin'(x) = lim h->0 (sin(x)*(cos(h)-1)/h)+ (cos(x)*(sin(h)/h))
Now what's interesting here is that the parts of this equation involving the limit are in fact derivatives at 0.  i.e. lim h->0 (cos(h)-1)/h=cos'(0) and lim h->0 sin(h)/h=sin'(0).
So, applying l'Hopital here is no longer a tautology, it's in fact not changing the equation at all.  So, we have an equation that tells us a relationship between sin'(x) and sin'(0) and cos'(0).  To simplify the form of the relationship let's suppose sin'(x)=f(x) and cos'(x)=g(x) we get:


Now, if we evaluate this at 0 we see that f(0)=g(0)*0+f(0)*1=f(0).  So we can choose any values for f(0) and g(0) and it's valid.  So we get the full set of all solutions:
Note that g(x) does not depend at all on f(x), so it can be whatever you want as long as you choose it first, rather than trying to arbitrarily choose both at the same time.

So, in the end it's funny because using l'Hopital on the derivative rule produces a tautology, but using it on this modified form does not produce a tautology, but actually just expresses what's already true.  The "tautology" element comes from the f(0) evaluation above, but the produced equation is actually a pretty tight constraint on the form of sin'(x).

Dominion General Discussion / Re: Complexity of Dominion
« on: October 08, 2018, 03:04:43 pm »
So, your whole algorithm depends on effects taking place at an instance in time.  Which maybe comes from the Magic layers system, I dunno.

But Quarry's effect isn't written to take place at an instant in's a continuous effect. As is inheritance's effect.  Which is what crj was trying to get at, I believe.  And indeed if you write the 2 effects in a sentence, the order is irrelevant.  i.e. Our gamestate is one where:
-"Estate is an action, and all actions' costs are reduced by 2"
-"All actions' costs are reduced by 2, and Estate is an action"
Now when you dig deep and say how did you decide that the estate's cost was reduced by 2?  We say, because of inheritance.  i.e. Inheritance applies before the cost-reduction...but that's not equivalent to Inheritance applying before Quarry.

When translating such continuous effects into code, or making them instantaneous otherwise, you must add additional constraints, because "we can't go back".  I believe in this case rather than saying it's a "priority" thing (which sounds arbitrary), it should be considered as a "dependency" thing.  Quarry's cost-reduction depends on type, Inheritance effects type, so Quarry depends on Inheritance.  Thus I(Q(G)) evaluated as a single point-effect doesn't make sense, because Q depends on I, and dependencies should always be evaluated first.

A guaranteed triple Lab via Seer after a 5/2 opening looks game-breaking crazy. If there is a junker at $5 you want Seer even more and if there is a trasher at $5 chances are extremly high that you can get it after the first shuffle.
I'm really confused by your comment...Seer only gets cards costing from 2-4.  How is it a guaranteed triple-lab, since it can only draw your opening buy and estates?  How does it help you hit 5?

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