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Author Topic: Rats?  (Read 23367 times)

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Mic Qsenoch

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Re: Rats?
« Reply #25 on: January 27, 2015, 10:30:25 am »
+5

A lot of this could slide into the sort of Tunnel case of "yes this makes the card do SOMETHING but it's not actually worth doing".

The Doctor/Journeyman idea has got to be even farther into that class than most wacky Tunnel things. In fact I think even "buy Rats just to trash Curses" is already in that camp.
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Re: Rats?
« Reply #26 on: January 27, 2015, 12:57:33 pm »
0

rats are great with ambassador because they have the same name as the other rats. this is true even though ambassador doesnt let you incur the +1 card benefit.

Are you sure just ambassadoring the junk itself isn't better?
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

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Re: Rats?
« Reply #27 on: January 27, 2015, 03:14:26 pm »
0

A lot of this could slide into the sort of Tunnel case of "yes this makes the card do SOMETHING but it's not actually worth doing".

The Doctor/Journeyman idea has got to be even farther into that class than most wacky Tunnel things. In fact I think even "buy Rats just to trash Curses" is already in that camp.

+1 for this. I've only ever bought Rats to trash Curses in super-heavy junking games, and I've only ever been happy with that buy once.
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jomini

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Re: Rats?
« Reply #28 on: January 27, 2015, 05:12:56 pm »
0

A lot of this could slide into the sort of Tunnel case of "yes this makes the card do SOMETHING but it's not actually worth doing".

The Doctor/Journeyman idea has got to be even farther into that class than most wacky Tunnel things. In fact I think even "buy Rats just to trash Curses" is already in that camp.

It isn't that wacky, you add one dead card to your deck in exchange for say gaining 6VP (6 curses -> Rats). That is exactly what you do when you buy a province. Except of course that Rats costs $4 less and isn't dead if you draw it with a curse. Sure better trashing means this isn't your first option, but seriously its "wacky" to say "if you have no other curse trashing"? If you have 6 curses in 20 cards it is pretty much impossible not have Rats beat a duchy before game end which is not exactly a bad buy in a lot of slog setups. If you'd buy duchy over silver you are likely getting close to where you want Rats over silver as well when you have Curses.



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Re: Rats?
« Reply #29 on: January 27, 2015, 09:01:48 pm »
+1

The difference is you can wait to buy a Province and forfeit a gold buy when it's the appropriate time to green.  If you buy Rats with the same timing as when you would buy a Province, you're not going to have time to trash six curses. 

It's kinda like opening Great Hall/Great Hall in terms of the timing issue.
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Re: Rats?
« Reply #30 on: January 27, 2015, 09:59:52 pm »
0

rats are great with ambassador because they have the same name as the other rats. this is true even though ambassador doesnt let you incur the +1 card benefit.

Are you sure just ambassadoring the junk itself isn't better?

Yeah, I don't understand the concept of Ambassadoring Rats at all.
Even though Rats do help consolidate Ruins, I just think there's way too much opportunity cost to make it worth it.

I think there's also this wrong-headed notion that putting a Rats in your opponents deck means that your opponent will soon be drowning in Rats.
Well, yeah, that works if your opponent is a poorly programmed bot or a naive new player, but against an experienced opponent it is less harmful than just sending in a Curse, and maybe even helpful in some cases.
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Re: Rats?
« Reply #31 on: January 28, 2015, 01:46:06 am »
0

I could see Rats being worth it with Ambassador on a Shelters board where you really need that thinning. The downside is that then your opponent can do the same and he doesn't have to waste a $4 buy on Rats.
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Re: Rats?
« Reply #32 on: January 28, 2015, 06:57:09 am »
0

rats are great with ambassador because they have the same name as the other rats. this is true even though ambassador doesnt let you incur the +1 card benefit.

Are you sure just ambassadoring the junk itself isn't better?

you start by ambassadoring the junk and then shift to ambassadoring the rats when you draw two rats and not two junk. I'm not sure, but I think it's better than amb/amb, say. More so if there's shelters.
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Re: Rats?
« Reply #33 on: January 28, 2015, 07:18:34 am »
+1

Buying rats as a "better duchy" is usually a losing proposition. You need to line up rats with curses 3 times; this isn't all that likely to happen on your first three shuffles, but even if it does, if your deck is so clogged, you aren't going to get through it very fast, in which case, you probably aren't likely to even get through 3 more reshuffles. Moreover, when you do, it may be better than duchy, but you would never want to buy duchy in that case - the game isn't ending soon enough.

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Re: Rats?
« Reply #34 on: January 28, 2015, 09:17:18 am »
+1

A lot of this could slide into the sort of Tunnel case of "yes this makes the card do SOMETHING but it's not actually worth doing".

The Doctor/Journeyman idea has got to be even farther into that class than most wacky Tunnel things. In fact I think even "buy Rats just to trash Curses" is already in that camp.

It isn't that wacky, you add one dead card to your deck in exchange for say gaining 6VP (6 curses -> Rats). That is exactly what you do when you buy a province. Except of course that Rats costs $4 less and isn't dead if you draw it with a curse. Sure better trashing means this isn't your first option, but seriously its "wacky" to say "if you have no other curse trashing"? If you have 6 curses in 20 cards it is pretty much impossible not have Rats beat a duchy before game end which is not exactly a bad buy in a lot of slog setups. If you'd buy duchy over silver you are likely getting close to where you want Rats over silver as well when you have Curses.

Errrmm, that scenario you described will never happpen. 6 curses in 20 cards when there's no other trashing = somehow gaining 6 curses by turn 4. If the game is as sloggy and trashless as you suggest, that's not going to happen until about turn 10.

To Wandering Winder's point: statistically speaking, on average it's going to take you about 15 turns just to clear out three curses*. $4 for a Duchy that takes 15 turns to realize its value does not seem like a good value proposition.

*based on a 1,000,000 game naive Monte Carlo simulation, assuming no trashing or additional cycling.


« Last Edit: January 28, 2015, 09:26:51 am by TheExpressicist »
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Re: Rats?
« Reply #35 on: January 28, 2015, 06:09:38 pm »
0

Errrmm, that scenario you described will never happpen. 6 curses in 20 cards when there's no other trashing = somehow gaining 6 curses by turn 4. If the game is as sloggy and trashless as you suggest, that's not going to happen until about turn 10.

To Wandering Winder's point: statistically speaking, on average it's going to take you about 15 turns just to clear out three curses*. $4 for a Duchy that takes 15 turns to realize its value does not seem like a good value proposition.

*based on a 1,000,000 game naive Monte Carlo simulation, assuming no trashing or additional cycling.

Ugg. As I noted, this works best in a setup where you have some trashing (e.g. Spice Merchant) and preferably some draw. In the situation where you are drawing your deck, in 3 turns you can trash a total of 7 Curses for one dead card. 6:4 is the second most common split for curses. Going light trashing -> cursing -> engine is good. So the question then becomes would you ever buy a duchy with 3 or more turns left to play? Absolutely. It can be the correct move to buy the duchies before ever grabbing a province.

So what about non-engine setups? Well there are a number of cards that allow for a dramatic increase in pairing odds e.g Courtyard, Haven; and even there a simple search isn't going to tell you a lot unless you account for gaining additional rats.  I grant these do take a long time to beat out duchy, but they are also boards where you have a lot more turns. For instance, I ran a very simple Dominionate matchup of Double Witch vs Double Witch; duchies were being bought 15 turns before game end on a few of the spot check (~12 turns before game end appeared to be the average point to start buying duchies).

The difference is you can wait to buy a Province and forfeit a gold buy when it's the appropriate time to green.  If you buy Rats with the same timing as when you would buy a Province, you're not going to have time to trash six curses. 

It's kinda like opening Great Hall/Great Hall in terms of the timing issue.
So let me make sure I understand this. We are playing gainer (e.g. Workshop), draw (e.g. Smithy), village (e.g. Walled Village), copper trashing (e.g. Moneylender), Rats, and Young Witch. We both go Young Witch/Engine (the bane is something horrid like Chancellor). You lose the curse split 6:4 (sorry, you were P2). You won't workshop a Rats anytime to kill the curses? After all with deck drawing, you will hit clear all 6 in just three turns. You will instead grab another village or draw card so I can three pile that much easier?

I get, you don't want to buy Rats to kill curses too late in the game - you won't see your Rats often enough. You don't want to buy them too early - the extra card is not yet worth the VP. You may face too high of an opportunity cost (Rats vs Wandering Minstrel is likely a lose); but I really just don't see the numbers working out. Do you really expect to always buy your provinces within the last 3 turns of the game? That seems highly sub-optimal.
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TheExpressicist

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Re: Rats?
« Reply #36 on: January 29, 2015, 06:49:27 am »
+1

Okay, that's fair - I didn't notice the "no curse trashing" distinction. And also, I agree that it certainly makes sense to buy Duchies earlier than 3 turns before end-of-game. But let's be clear that what you are talking about is an extreme edge case. For your scenario to happen you need 1. Rats. 2. Non-curse trashing (AKA: Counterfeit, Loan or Spice Merchant).  3. Viable curse attack (Young Witch, Mountebank, Sea Hag, Witch). 4. No other curse trashers.  You're looking at about a 1 in 10000 chance of getting a board with those four components.

But to make matters more difficult, you're looking at 10 dead cards in your deck at minimum: 6 curses (soon to become 7 rats), 3 estates. And then you still need your light-trasher, and at minimum $4 worth of coin. So that's really somewhere between 12 and 13 dead cards in your deck. You need a seriously beefy engine to be able to plow through all of that. Now, to be fair to Rats: if you want to speak of best case scenarios - if you're drawing your entire deck, you can actually clear out all your curses in one turn.

Re: non-engine setups, if you lose the Province split, those extra VP aren't actually going to help you all that much because you will still be forced to buy 6 Duchies in order to win. (5 province + 3 duchies + curses still beats out 3 province + 5 duchies + no curses). Even with cards like Haven or Courtyard, it will still take 3 reshuffles on average to equal a Duchy. And until it does, you've added an extra dead card to your deck; a dead card which you will see a minimum of 3 times. Which makes it a lot more likely you'll lose the Province split.

 
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jomini

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Re: Rats?
« Reply #37 on: January 29, 2015, 02:57:57 pm »
0

Okay, that's fair - I didn't notice the "no curse trashing" distinction. And also, I agree that it certainly makes sense to buy Duchies earlier than 3 turns before end-of-game. But let's be clear that what you are talking about is an extreme edge case. For your scenario to happen you need 1. Rats. 2. Non-curse trashing (AKA: Counterfeit, Loan or Spice Merchant).  3. Viable curse attack (Young Witch, Mountebank, Sea Hag, Witch). 4. No other curse trashers.  You're looking at about a 1 in 10000 chance of getting a board with those four components.

But to make matters more difficult, you're looking at 10 dead cards in your deck at minimum: 6 curses (soon to become 7 rats), 3 estates. And then you still need your light-trasher, and at minimum $4 worth of coin. So that's really somewhere between 12 and 13 dead cards in your deck. You need a seriously beefy engine to be able to plow through all of that. Now, to be fair to Rats: if you want to speak of best case scenarios - if you're drawing your entire deck, you can actually clear out all your curses in one turn.

Re: non-engine setups, if you lose the Province split, those extra VP aren't actually going to help you all that much because you will still be forced to buy 6 Duchies in order to win. (5 province + 3 duchies + curses still beats out 3 province + 5 duchies + no curses). Even with cards like Haven or Courtyard, it will still take 3 reshuffles on average to equal a Duchy. And until it does, you've added an extra dead card to your deck; a dead card which you will see a minimum of 3 times. Which makes it a lot more likely you'll lose the Province split.
Let's be really clear. Of the copper trashers you've neglected to include Moneylender and  Mint as well as possible psuedo-trashing in Island and Native Village that don't eliminate the -1 VP (e.g. Turn Curse into Rats -> Courtyard -> Nv allows your to both clear a dead card from the deck and not score -1 VP).

Let's also remember that a "viable cursing attack" includes Familiar (where your Pot may also be a dead card mid game), Swindler, Jester, Soothesayer, Torturer (if you don't forefeit as soon as the other guy reliably hits his Torturer chain), and Followers. Also you can get some situations where buying through an Embargo token is viable with the curse (e.g. your opponent embargos Province after they've bought the first one).

And let's not forget the fun of the Black Market deck. Your opponent may get both the trasher and the curser that was in the Bm, so yet another possible option.

But you have to draw 10 dead cards? So what. That is just barely more than 3 Hunting Grounds/Village pairs. Or maybe 4 Border villages/Smithies. Wharf, Envoy, Adviser, Embassy, etc. all work for quickly pushing through a big stack of dead cards. Drawing 20 cards (curses, estates, and coins) is perfectly viable on a lot of boards (like say anything that can do a normal Engine and then add Warehouse as a kingdom card.)

So let's quit with this garbage. The single biggest restraint isn't needing light trashing (that's one possible option), sifting (e.g. Warehouse, which is a second) - it is having a board where you don't have another trasher (even Trade Route is better than Rats for this barring more rare setups) and you have a viable setup for fast cycling. The odds of having Rats + cursers + no curse trashing + engine is just a bit more common than any specific 2 card combo (e.g. Hermit/Market Square or Nv/Bridge or Pstone/Herbalist).

In non-engine setups you are assuming 2 player, this is not always the case (granted it the game tends to end more quickly in 3er) and no possible alt-VP or VP tokens from Goons/Monument. I'm not saying that these setups are common, but that they are possible. More importantly, you are ignoring the possibility of 3-piling. Curses typically exhaust so we have just two more piles. Depending on what else gets bought down (e.g. Haven), I may well expect to clear enough curses and pile out long before we even care who wins the province split. Remember in near mirrors you should expect at least a third of games to end on three piles (e.g. if we both follow the PPR we can stall on 6 provinces), optimized Big money variants should end a LOT of times on piles.

But even that isn't the biggest thing. All the arguments about losing the province split also apply to duchy, except that with Rats you non-zero odds of them NOT being a dead card (play them to trash a curse). Of course Rats may not find itself competing against Duchy, but Silver or Estate. Which drops our shuffle count lower before payback. Again, neither of these are common, but in aggregate, using Rats to get rid of curses is likely a good move more often than playing Pstone/Herbalist simply because Rats/Curser is so much more common than Pstone/Herbalist.
« Last Edit: January 29, 2015, 03:01:59 pm by jomini »
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TheExpressicist

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Re: Rats?
« Reply #38 on: January 29, 2015, 05:17:09 pm »
+4

My point was never to say that Rats is never good as a curse trasher. It was to say that it's very rarely good. You can introduce edge cases all day long. But each additional constraint you add just lowers the odds even further that it will actually happen in real life. 

Remember, according to you, you need: 1. Rats, 2. Curse attack, 3. No curse trashing, 4. Light trashing, and 5. Strong engine components. Even if you count all of your additions (most of which I personally consider to be real stretches) among the possibilities, you're still looking at about a 1 in 1200 chance of all those pieces coming together. The notion that it's "just as likely as any two card combo" (which is 1 in 400) is just patently false.
 





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werothegreat

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Re: Rats?
« Reply #39 on: January 29, 2015, 11:38:34 pm »
+2

My point was never to say that Rats is never good as a curse trasher. It was to say that it's very rarely good. You can introduce edge cases all day long. But each additional constraint you add just lowers the odds even further that it will actually happen in real life. 

Remember, according to you, you need: 1. Rats, 2. Curse attack, 3. No curse trashing, 4. Light trashing, and 5. Strong engine components. Even if you count all of your additions (most of which I personally consider to be real stretches) among the possibilities, you're still looking at about a 1 in 1200 chance of all those pieces coming together. The notion that it's "just as likely as any two card combo" (which is 1 in 400) is just patently false.
 

I blame you for the half hour I just spent figuring out the formula required to find the probability of getting a d-sized combo in a k-sized sample from an n-sized set.  For your information, it's k!(n-d)!/(n!(k-d)!) .  Which, for a 2-card combo in a 10-card kingdom (ignoring Banes because fuck that) from a set of 206 kingdom cards is exactly 9/4223.  Which rounds to 1/400.

EDIT: Fun fact!  With the release of Adventures (30 kingdom cards), this will decrease to ~1/550 !!!  :D :D :D ALL OF OUR TIME HERE IS WORTHLESS
« Last Edit: January 29, 2015, 11:41:39 pm by werothegreat »
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Re: Rats?
« Reply #40 on: January 30, 2015, 12:33:44 am »
+1

My point was never to say that Rats is never good as a curse trasher. It was to say that it's very rarely good. You can introduce edge cases all day long. But each additional constraint you add just lowers the odds even further that it will actually happen in real life. 

Remember, according to you, you need: 1. Rats, 2. Curse attack, 3. No curse trashing, 4. Light trashing, and 5. Strong engine components. Even if you count all of your additions (most of which I personally consider to be real stretches) among the possibilities, you're still looking at about a 1 in 1200 chance of all those pieces coming together. The notion that it's "just as likely as any two card combo" (which is 1 in 400) is just patently false.
 

I blame you for the half hour I just spent figuring out the formula required to find the probability of getting a d-sized combo in a k-sized sample from an n-sized set.  For your information, it's k!(n-d)!/(n!(k-d)!) .  Which, for a 2-card combo in a 10-card kingdom (ignoring Banes because fuck that) from a set of 206 kingdom cards is exactly 9/4223.  Which rounds to 1/400.

EDIT: Fun fact!  With the release of Adventures (30 kingdom cards), this will decrease to ~1/550 !!!  :D :D :D ALL OF OUR TIME HERE IS WORTHLESS

This is why I computer science:

Code: [Select]
import random

cards = range(206)
count = 0
trials = 1000000

for i in xrange(trials):
kingdom = random.sample(cards, 10)
if (1 in kingdom) and (2 in kingdom):
count += 1

print float(count)/float(trials)

0.002133

off by <0.1% :P
« Last Edit: January 30, 2015, 12:35:47 am by GeoLib »
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Re: Rats?
« Reply #41 on: January 30, 2015, 12:41:12 am »
+9

Yes, well, *I* have an elegant answer derived from a theoretical understanding of the material.
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Re: Rats?
« Reply #42 on: January 30, 2015, 01:35:46 am »
+1

I blame you for the half hour I just spent figuring out the formula required to find the probability of getting a d-sized combo in a k-sized sample from an n-sized set.  For your information, it's k!(n-d)!/(n!(k-d)!) .  Which, for a 2-card combo in a 10-card kingdom (ignoring Banes because f*** that) from a set of 206 kingdom cards is exactly 9/4223.  Which rounds to 1/400.

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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

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Re: Rats?
« Reply #43 on: January 30, 2015, 05:33:49 am »
+2

My point was never to say that Rats is never good as a curse trasher. It was to say that it's very rarely good. You can introduce edge cases all day long. But each additional constraint you add just lowers the odds even further that it will actually happen in real life. 

Remember, according to you, you need: 1. Rats, 2. Curse attack, 3. No curse trashing, 4. Light trashing, and 5. Strong engine components. Even if you count all of your additions (most of which I personally consider to be real stretches) among the possibilities, you're still looking at about a 1 in 1200 chance of all those pieces coming together. The notion that it's "just as likely as any two card combo" (which is 1 in 400) is just patently false.
 

I blame you for the half hour I just spent figuring out the formula required to find the probability of getting a d-sized combo in a k-sized sample from an n-sized set.  For your information, it's k!(n-d)!/(n!(k-d)!) .  Which, for a 2-card combo in a 10-card kingdom (ignoring Banes because fuck that) from a set of 206 kingdom cards is exactly 9/4223.  Which rounds to 1/400.

EDIT: Fun fact!  With the release of Adventures (30 kingdom cards), this will decrease to ~1/550 !!!  :D :D :D ALL OF OUR TIME HERE IS WORTHLESS

Prepare to have your life ruined:

What is the probability of a d-sized combo where each card is interchangeable with x different equivalents in a k-sized sample from an n-sized set?
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Re: Rats?
« Reply #44 on: January 30, 2015, 07:47:07 am »
0

My point was never to say that Rats is never good as a curse trasher. It was to say that it's very rarely good. You can introduce edge cases all day long. But each additional constraint you add just lowers the odds even further that it will actually happen in real life. 

Remember, according to you, you need: 1. Rats, 2. Curse attack, 3. No curse trashing, 4. Light trashing, and 5. Strong engine components. Even if you count all of your additions (most of which I personally consider to be real stretches) among the possibilities, you're still looking at about a 1 in 1200 chance of all those pieces coming together. The notion that it's "just as likely as any two card combo" (which is 1 in 400) is just patently false.
 

Oh please. I have said you need light trashing or some other method to make the engine viable excluding things that trash curses. This can be any the many light trashers. It can also be a lot of sifters (e.g. Warehouse, Embassy, Cellar, Storeroom, etc.). It can also be some Alt-VP enablers for a really slow build (e.g. Fairgrounds, Vineyards). It can also be some attack that slows the end game heavily (e.g. Ghost Ship, Rabble). Yes you need engine enablers, but something simple like Rats/University/Familiar/Rabble would work. But also you could have a lot of other things.

I've been using strong card examples to illustrate the point. Quite often it will be a mix of things say you have Inn for sifting/setting up big draw turns early, Fairgrounds to make the game last longer, and Rabble to slow the other guy from piling out. Or it could be Kc/Inn/Oracle

Basically, according to you, any time you get cursed it is rare to build an engine unless you can trash. Yeah 5-6 extra cards to draw sucks; but on the other hand once you have an engine you get a lot more bang for your buck.


Even if we grant your laughably poor numbers of 1/1200 to 1/400; that means that Rats killing curses is potentially a thing 1/3rd of the time that Herbalist/P.Stone is. Of course, with the new expansion we should expect another curser or two and likely another light trasher and several sifters so even with your current numbers, the odds are going to change dramatically again.

I don't understand this on a board talking about dominion strategy, everyone wants to stop talking about dominion strategy. That's an edge case. Well yes, every single game of dominion is an edge case at this point. There are 3.5 EE 11 possible kingdoms. ANYTHING is going be an edge case. Even the collective play of everyone on the forum isn't going to hit 1% of the possible game states.

Now I know that there is degeneracy - Chancellor/Stash and Scavenger/Stash play fairly similarly. But whatever degree of degeneracy we allow is completely arbitrary. You may not think of Mint of as a light trasher, but Opening Smithy/Silver and hitting all 7 starting coppers makes it decent. Quibbling over probabilities that are within an order of magnitude is pathetic. EVERYTHING is an edge case these days.
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WanderingWinder

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Re: Rats?
« Reply #45 on: January 30, 2015, 08:52:51 am »
+1

The point is, Rats trashing curses is an AWFUL plan. It has nothing to do with probabilities of how likely it is to come up.

So, you say, you have a game where the only trashing is rats and some treasure trashing, and there's pretty heavy cursing, and there's card-draw pieces. Ok, I will give you that. Yeah, it won't come up often, but I don't really care, that is not my point, and I agree that it being a rare board isn't really relevant. So let's just assume we're on that board. Great.

You're saying there's a point where the correct move would be to buy rats. You're saying that some point after the curses are gone (I'll give you some flexibility to say, just before they're all gone, only most of them are gone). First of all, this is the exact kind of game where, most of the time, you shouldn't be building an engine, because just going for money will be both faster and, because of the high amount of junk (and lack of trashing), more reliable in the long-run. But ok, for some strange reason, you actually want to build the engine. But in this case, where you're drawing your deck pretty much every turn (somehow), you should have enough money to be buying provinces every turn. Or if you don't have that much money, you should be getting money to do that, rather than rats. Or if you don't have the reliability, that first of all will hurt rats, and moreover, you should be getting the engine components to give you that reliability. Or if you're to the point where piles would be an issue from doing that for you, you should be getting the points now now now. At best, there is some situation where you have something like 7 curses, but you're somehow overdrawing your deck anyway, reliably (this already isn't super possible, since you have at least 10 junk/stop cards,but ok, it's vaguely reliable say), and you buy a rats right at the end, or better, you gain one midturn, so you can play it, then draw the new one, and set it up to play and draw all of them in the same turn, netting you some points. But not only is this scenario absurdly contrived, not only are you probably still losing this game anyway, given your opponent has done, you know, something, with a lot fewer junk floating around, not only all that, but there, it's really more of a one-off tactical play than something to keep in your mind and watch out for.

Except, of course, if you're also going vineyards. But that's more about vineyards, and it's already been covered.

werothegreat

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Re: Rats?
« Reply #46 on: January 30, 2015, 09:21:37 am »
+1

My point was never to say that Rats is never good as a curse trasher. It was to say that it's very rarely good. You can introduce edge cases all day long. But each additional constraint you add just lowers the odds even further that it will actually happen in real life. 

Remember, according to you, you need: 1. Rats, 2. Curse attack, 3. No curse trashing, 4. Light trashing, and 5. Strong engine components. Even if you count all of your additions (most of which I personally consider to be real stretches) among the possibilities, you're still looking at about a 1 in 1200 chance of all those pieces coming together. The notion that it's "just as likely as any two card combo" (which is 1 in 400) is just patently false.
 

I blame you for the half hour I just spent figuring out the formula required to find the probability of getting a d-sized combo in a k-sized sample from an n-sized set.  For your information, it's k!(n-d)!/(n!(k-d)!) .  Which, for a 2-card combo in a 10-card kingdom (ignoring Banes because fuck that) from a set of 206 kingdom cards is exactly 9/4223.  Which rounds to 1/400.

EDIT: Fun fact!  With the release of Adventures (30 kingdom cards), this will decrease to ~1/550 !!!  :D :D :D ALL OF OUR TIME HERE IS WORTHLESS

Prepare to have your life ruined:

What is the probability of a d-sized combo where each card is interchangeable with x different equivalents in a k-sized sample from an n-sized set?

I was thinking about that, and then I got lazy.  Also, this still doesn't incorporate Young Witch.  What is the probability if one of the events selected allows you to select an 11th event from a smaller subset?  This would involved tracking whether or not the other events already selected are from that subset.
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TheExpressicist

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Re: Rats?
« Reply #47 on: January 30, 2015, 10:12:21 am »
0

I don't understand this on a board talking about dominion strategy, everyone wants to stop talking about dominion strategy. That's an edge case. Well yes, every single game of dominion is an edge case at this point. There are 3.5 EE 11 possible kingdoms. ANYTHING is going be an edge case. Even the collective play of everyone on the forum isn't going to hit 1% of the possible game states

I don't mind talking about edge cases. I don't even mind talking about fairly unlikely edge cases, because they do come up. What I do mind is talking about an extreme edge case and pretending it's a common scenario. That's my issue. That's it. If you had simply owned it and prefaced it with, "This is a ridiculously uncommon edge case, but...", I would have no problem.

Wandering Winder did a solid job of explaining how, even in an 'absurdly contrived scenario', using Rats as a curse trasher is 'more of a one-off tactical play than something to keep in your mind and watch out for.' Now, that said, I am quite certain you could build a kingdom where that's not the case.

But you simply cannot equivocate between that contrived, tailor-made kingdom, and a kingdom containing a two-card combo. Saying "ANY situation is an edge case" doesn't make them equivalent. Unless you think my theory that pink unicorns live at the end of the rainbow deserves equal consideration as the theory of gravity, because, well, ANY scientific theory has a degree of uncertainness to it!
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jomini

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Re: Rats?
« Reply #48 on: January 31, 2015, 10:06:55 am »
0

The point is, Rats trashing curses is an AWFUL plan. It has nothing to do with probabilities of how likely it is to come up.

So, you say, you have a game where the only trashing is rats and some treasure trashing, and there's pretty heavy cursing, and there's card-draw pieces. Ok, I will give you that. Yeah, it won't come up often, but I don't really care, that is not my point, and I agree that it being a rare board isn't really relevant. So let's just assume we're on that board. Great.

You're saying there's a point where the correct move would be to buy rats. You're saying that some point after the curses are gone (I'll give you some flexibility to say, just before they're all gone, only most of them are gone). First of all, this is the exact kind of game where, most of the time, you shouldn't be building an engine, because just going for money will be both faster and, because of the high amount of junk (and lack of trashing), more reliable in the long-run.
Granted, hence why I have said repeatedly that you need things to push you toward engines. A non-exhaustive list includes things like: Colonies, gainers (e.g. Iw, Armory, Haggler), anti-money deck attacks (e.g. Noble Brigand, Cutpurse, Rabble), power engine cards (e.g. Kc, Tr, Border village/$5 draw), engine favoring sifting (e.g. Inn, Cellar, Farming Village). I have stated from the beginning that the criteria of when to go Rats over duchy is when you will see them often enough to trash three curses. Engines, while not common, make this conceptually easy to estimate. Two turns with a perfect deck drawing engine is the obvious case for Rats being equal to Duchy. 

Quote
But ok, for some strange reason, you actually want to build the engine. But in this case, where you're drawing your deck pretty much every turn (somehow), you should have enough money to be buying provinces every turn. Or if you don't have that much money, you should be getting money to do that, rather than rats. Or if you don't have the reliability, that first of all will hurt rats, and moreover, you should be getting the engine components to give you that reliability. Or if you're to the point where piles would be an issue from doing that for you, you should be getting the points now now now. At best, there is some situation where you have something like 7 curses, but you're somehow overdrawing your deck anyway, reliably (this already isn't super possible, since you have at least 10 junk/stop cards,but ok, it's vaguely reliable say), and you buy a rats right at the end, or better, you gain one midturn, so you can play it, then draw the new one, and set it up to play and draw all of them in the same turn, netting you some points.
I've built for a colony engine off Iw/Smithy/Farming Village. I spent my first (two?) $5 on Counterfeit and have been going Rabble/Bazaar with $5 sinces (or grabbing doubles of Fv/Smithy). We are out of Farming villages and I draw an Iw. I have 4 Smithies, 4 Rabble (net draw +16) against 6 curses, 3 estates, of course I should expect to skip 2 or 3 with the Fv each draw so that leaves me with 11 draw slots, with a single Bazaar in play I need 4 Plats, one Counterfeit for double Colonies. Presumably my opponent is either trying to pile down Smithy/Fv with me (and hence going engine-ish at least) or he is going to have a hellavu time making a dent in the provinces or 3 pile when he gets repetitively Rabbled.

I draw deck with 1 action and Iw/Rabble outstanding. My Iw is otherwise useless, so I get the Rats. I expect to have three turns (buying 4 colonies over the next two turns, then either more Colonies for an easy win or some form of end game dancing).

Oh my a blindingly obvious example where Rats has low opportunity cost (it is actually competing with estate, not duchy) and there is a nice confluence of gaining, sifting, attacks, and extra VP to make it farcical.

But we can look at a lot of other options. I'm setting up the engine exactly as you outline (say I have Familiar/University/Pool with decent $5's, say I'm just playing with Alchemy, Base, Prosperity and Dark Ages). But it is starting to fail and I want the Duchies "now, now, now". I'm down 6:4 on curses. I draw a Green, a Curse, a Market, a Gold, and dead draw (e.g. something like Moat). I play the Market, draw a curse, I elect not to play the dead draw because I've been deck tracking and know I have low odds of hitting more coin, but good odds of kicking off my engine next turn. I have $4, I'm down by 2 VP - what do I buy?

Another component (e.g. something like Oasis)? Well maybe that will let me win the province split. But that has to take into account 3 piles and the fact that I'm going to give my opponent a free shot at VP - a duchy gets him up by $5 so then I can no longer win with a 4:4 province split and a bonus duchy. Highly situational odds if a component works. Okay well what about estate? It is 1 VP now, now, now. But it literally does nothing for me unless I get a second estate later; which is rare without a +buy. Rats? Okay I might be able to play it for 1 VP and then draw the gained Rats with a Pool for another VP. Well that is actually useful. Going Rats may well be a tactical choice that ends up working well just because you get a busted hand with $4. Its another path to victory, so why not think about it when analyzing the board?

Quote
it's really more of a one-off tactical play than something to keep in your mind and watch out for.
Funny, I whole heartedly concur. It is a tactical play that can work well. I have never said otherwise.


The times when you need to keep the tactical possibility in mind are about as common as any specific two card combo. E.g. maybe 1 in 500 games. So you approach a board that has cursing. You quickly see that cursing with no curse trushing means this is going to be a cursing game. Now you have to make a decision - what am I going to do when the cursing is done? You should obviously NOT plan around Rats nibbling away the curses. But if you have an engine setup that looks promising - say other attacks to make the game longer still (note, not discarding attacks that are relatively weak against cursed decks), strong engine cards (e.g. Kc, gainers), and perhaps some more VP so the money player has to take more provinces to secure the win (e.g. Colonies, Fairgrounds, Island) then when you do your calculations for how many points you can score via engine you should keep in mind that Rats can be a pretty nice extra 3-4 on the engine side if you are worried about slipping below 50%+1 before your engine works.

Will this be common? No, as I already said the biggest sieve is the need for other trashing to not be there. What typically makes engines viable after cursing is the trashing.  But there are a large constellation of things that move you toward engine besides trashing. Sifting. Gainers. Colonies. Shelters. Other attacks. Power engine cards. Some Alt-VP. Some pseudo-trashing. Goons/Bish. Light trashing. The exact point at which any combination of these works out into a pattern that says "go engine" is highly board dependent, and I'm tired of having people nitpick where exactly the marginal line is drawn. Clearly I can make illustrative cases where the thread isn't derailed, but somehow people who I've beaten every single time I've played them (which I grant is a huge amount of luck beyond what little skill I have) will go gonzo that my marginal cases are too weak. Rats killing curses is a tactical thing. It isn't common but then no specific card interactions are either. What is it, only 5% of games will even have Rats at all?


I don't mind talking about edge cases. I don't even mind talking about fairly unlikely edge cases, because they do come up. What I do mind is talking about an extreme edge case and pretending it's a common scenario. That's my issue. That's it. If you had simply owned it and prefaced it with, "This is a ridiculously uncommon edge case, but...", I would have no problem.

Oh get off it. I have never said it was common. Your back of the envelope is 1 in 1200, mine is around 1 in 400. I laid out my specific criteria in the very first post - you have be in a place where you'd consider gaining Duchy and the game has to last long enough to eat the curses (seeing the original Rats 3 times is pretty decent as Rats is a bit less harsh on an engine than Duchy, but Duchy is assured points now).

You then proceeded to pretend that I somehow said this was common. I put it on par with any specific two card combo (because there is a LOT of degeneracy between cursers and between engine enablers). Further, there are a lot of common play scenarios that totally warp the odds. E.g. When I play IRL it is not uncommon for me to bring just a few expansions, so we might just have Base, Dark Ages, and Prosperity - which massively inflates the numbers when Rats/Curse killing can be a thing.

"Edge case" has become ludicrous on this forum, we may as well close the forum down to any discussion of specific card interactions - they are all edge cases. I mean do you knwo the odds are that you will Young Witch, Tunnel, and scaling TfB are? Or how about Forager, 2 kingdom treasures, no villages, and cantrip +draw, and a gainer? Or perhaps Chancellor/Stash/Pillage/Alt-VP? Those are my last three games. In the first, the Bane was Tunnel, the TfB was Butcher and it was totally engineless game because Butchering Golds was easy. The second I went Forager/Pot, grabbed 6 Alchemists (bought a second Pot the turn before grabbing #5&6), then I stocked up on Foragers, then grabbed Loan/Contraband/Gold and quickly went to town with $6 Foragers for a triple province turn followed by a double. In the last I completely ignored the Chancellor/Stash because we also had Rogue and I went engine and buried his Chancellor while stocking up on Islands/Duchies. Each of these were "contrived edge cases".

But then most games are. The average game has: no significant trashing (e.g. excluding Death Cart, Prssn, etc.), has no draw, and has no villages (includes Golem, Tr, etc.), has no +buy, has no cursing, has no discard, has no gainers and has no Alt-VP.

Every game is a statistical fluke. Yet we hit them. Sure, saying I need these 3 specific cards is pretty rare. But saying I need a number of confluences (one of these 7 cards, one of these cards that is in 40% of games, etc.) is not the same as edge casing.

Frankly, unless you want to give me a statistically robust definition for "edge case" you are just pissing around with a No-True-Scotsman fallacy.
« Last Edit: January 31, 2015, 10:08:24 am by jomini »
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TheExpressicist

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Re: Rats?
« Reply #49 on: January 31, 2015, 12:09:11 pm »
0

Firstly, let's stay civil. No need to get all worked up over a card game.

Secondly, I'm all for getting specific about what constitutes an "edge case"*.
The "There's No Point Even Discussing This" Edge Case: Something so unlikely, the average player never has and never will encounter it. (1 in 300,000 chance)
The "Extreme" Edge Case: Something so unlikely, the average player has only encountered it once. (1 in 2000 chance).
The "Normal" Edge Case: Something that the average player will see 9 or 10 times throughout the course of their play. (1 in 500 chance)
The "Not Actually An..." Edge Case: Something that really isn't an edge case, because the average player will actually probably see once or twice a week. (1 in 20ish chance)

I have no problem discussing "normal" edge cases. And I agree that people are far too quick to apply the "edge case" label to things that are actually fairly likely. But I take issue with equivocating between the "Extreme" edge case and the "Normal" edge case. They may be within an order of magnitude of each other but the real world impact is huge. And that's what you continue to do when you insist that the "Rats is a good curse trasher" scenario is equally as likely as a two-card combo.

The entire point of my back-of-the-napkin calculations was to show that, even when you're being extremely generous and giving 1 in 1200 odds that such-and-such components are in play, it's still rarely a good play because there are so many situational factors you have to take into account as well: are you losing the Curse split? Will the game last long enough to trash all the curses? Are you going to lose the game anyway? etc. etc.. Granted, I didn't go into detail as to why it's not a good play, but that's because WW is already doing that. What I was pointing out is that you have to add even more qualifiers to those 1 in 1200 odds to get a scenario where what you're saying makes sense.  Which makes it even more unlikely.

*Note: I've rounded off the numbers slightly, but these are pretty close to accurate. If you really want me to explain the statistics behind it, I will.
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