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[AdamH]

DISCLAIMER: I'm well aware that this discussion is largely theoretical in nature. I won't attempt to inject any application of the findings here into actual Dominion strategy -- that's for the reader to you. The purpose of this is simply to calculate an expected draw for your Scrying Pools given a certain deck composition.

Sometimes there's Scrying Pool on a board and there's no trashing. Sometimes it's the only non-terminal source or the best source of draw, enough that if you're going to try and increase your hand size, that's what you're going for. Is it worth it? Say it with me...

Depends on the kingdom.

But how do you tell? I, for one, am no stranger to getting crushed by people who go for Scrying Pool when I've decided it wasn't worth it.

I talked about this in that third link ("crushed") above, but sometimes it's helpful for me to try and calculate one's expected draw with Scrying Pool based on action density, and when I visualize that number in the context of the specific deck I'd try to build, sometimes I can see Scrying Pool's value more clearly. Unfortunately for me this usually happens after the game is over so I'm working on that.

So there are a couple of numbers that I want to talk about computing and maybe I'm close to getting this right. First off, I want to only look at the case where there's no trashing. Let's be generous, though, and say that the only non-Action card you have to buy is a single Potion and everything else is an Action card and not worry about greening, so you have 11 non-Action cards in your deck. I want to know how many Action cards (X) you have to have in your deck to make Scrying Pool's expected draw be E cards.

A simple calculation to make would look like:

Code: [Select]

Expected Draw = 1+(X/11)

and this is what I've been using to get close to this number, but I'm thinking maybe this isn't accurate enough (it doesn't even attempt to take the Spy-effect into account, among some other little things). I want to find either something that's closer and still easy to compute or just find some benchmarks for "E=2 when X=this and E=3 when X=that, etc."

Depending on your deck, you may also want to consider the case that discarding a non-Action card is just as good as drawing it because of the cycling or the nature or your payload (Let's say you're playing Highway/Market Square/Scrying Pool with no other support whatsoever; it doesn't matter if you're drawing your Coppers or not, you just want to find and play as many of your action cards as possible so Scrying Pool gets a boost here).

Here are some of my attempts at refining this calculation:

1. Replace "X" with "X-1" because you can't draw the Scrying Pool you play.
2. Split the formula into two separate cases:

Code: [Select]

E = P(top card was an action)*(Expected draw in that case) + P(top card wasn't an action and you discarded it)*(Expected draw in that case[+1])

-- and you can insert a "+1" where I pointed that out if you're counting the cycling advantage from the card you discarded.

Let me try and come up with expressions for these things

Code: [Select]

P(top card was an action) = (X-1)/(X+10)
P(top card was not an action) = 11/(X+10)

Expected Draw given we saw an action = 2 + (X-2)/11
Expected Draw given we saw a non-action) = 1 + (X-1)/10

The only thing I can think of that this doesn't take into account is the fact that your deck composition changes with each Action card you draw, making it slightly less likely each time that you hit another Action. I can't think of a concise formula for this and I'm terrible with summations so I don't have that formula right away (so far my attempts at coming up with this have just looked wrong to me so I just need to think about this a little more).

This stuff is messy but at least I could plug it into Excel or something and get some numbers and charts that could potentially be useful. I also know there are quite a lot of math people around here that would at least find this intelectually stimulating if nothing else. Help is appreciated, particularly in telling me where I'm wrong.


EDIT 1


Without the spy effect taken into account, but with deck changing taken into account, I believe I'm pretty close with the following formula.

Code: [Select]

Let E = expected draw from playing your Scrying Pool (sans Spy effect)
    X = the number of Action cards in your deck

E(X) = 1 + (X-1)/(X+10) + [(X-1)/(X+10)]*[(X-2)/(X+9)] + [(X-1)/(X+10)]*[(X-2)/(X+9)]*[(X-3)/(X+8)] + ... + [(X-1)/(X+10)]*[(X-2)/(X+9)]*...*[(X-n)/(X+11-n)] + ... + 0 when n eventually reaches X

E(X) = 1 + sum(i=1 up to X-1 (inclusive),
               prod(j=0 up to i-1 (inclusive),
                    (X-1-j)/(X+10-j)
               )
           )

So if that's correct, then we have

Code: [Select]

Let Ea(X) = Expected draw given you saw an Action card
    Eb(X) = Expected draw given you discarded a non-Action card

Ea(X) = 2 + sum(i=1 up to X-2 (inclusive),
                prod(j=0 up to i-1 (inclusive),
                     (X-1-j)/(X+10-j)
                )
            )

Eb(X) = 1 + sum(i=1 up to X-1 (inclusive),
                prod(j=0 up to i-1 (inclusive),
                     (X-1-j)/(X+9-j)
                )
            )

So if we take from above

Code: [Select]

Let Pa(X) = probability that the top card was an action
    Pb(X) = probability that the top card was not an action

Pa(X) = (X-1)/(X+10)
Pb(X) = 11/(X+10)

Then we get

Code: [Select]

E(X) = Ea(X)*Pa(X) + Eb(X)*Pb(X)

I think this is correct, yeah? I'll plug this into Excel when I get a chance and try to make some pretty pictures.


EDIT 2


Using this handy website I'm able to run simple Python code from all kinds of computers; I've written a little bit of Python to compute these formulas. Here's the code, for those interested.

Code: [Select]

#!/usr/local/bin/python2.7

def Ea(X, NA):
  sum = 2.0
  for i in range(1, X-1):
    prod = 1.0
    for j in range(i):
      prod *= (float(X)-2.0-float(j))/(float(X)+NA-2.0-float(j))
    sum += prod
  return sum
     
def Eb(X, NA):
  sum = 1.0
  for i in range(1, X):
    prod = 1.0
    for j in range(i):
      prod *= (float(X)-1.0-float(j))/(float(X)+NA-2.0-float(j))
    sum += prod
  return sum
   
def Pa(X, NA):
  return (float(X)-1.0)/(float(X)+float(NA)-1.0)
 
def Pb(X, NA):
  return (float(NA))/(float(X)+float(NA)-1.0)
 
def EaSimple(X, NA):
  return 2.0 + (float(X)-2.0)/(float(NA))
 
def EbSimple(X, NA):
  return 1.0 + (float(X)-1.0)/(float(NA-1))
 
def Esilly(X, NA):
  return 1.0 + (float(X))/(float(NA))
   
for X in range(2, 31):
  #for NA in range(6, 21):
  for NA in range(11, 12):
    EofX = Ea(X, NA)*Pa(X, NA) + Eb(X, NA)*Pb(X, NA)
    EsimpleofX = EaSimple(X, NA)*Pa(X, NA) + EbSimple(X, NA)*Pb(X, NA)
    print "%2d" % X,
    print "%2d" % NA,
    print "%2.4f" % Esilly(X, NA),
    print "%2.4f" % EsimpleofX,
    print "%2.4f" % EofX

I imported the printed results into Excel and messed around with them until it seemed like it was as visually appealing as I could easily get it. The following are the results from this:



The interesting result here is the difference between the blue and green lines.

So my back-of-the-envelope calculation of E(X) = 1 + (X/11) gives a pessimistic viewpoint of the draw you can expect; the actual expected draw is usually about a half a card more than this calculation gives, or you can get away with having 3-4 less Action cards in your deck than this calculation would imply in order to get the expected draw you're after.

This next picture attempts to show the effect of a different number of non-action cards in your deck on expected draw.



I really don't think any less than 11 non-actions is all *that* relevant to actual Dominion, since if you're trashing your cards and drawing with Scrying Pool the name of the game is minimizing that number and you actually have some power to do so. I wanted to make a 3-D graph with two independent variables but all the Excel options for that look terrible, so I decided to just color-code it. Do with this data what you want, but it seems to me that you probably need to add one extra Action card per non-Action card to your deck in order to make sure your Scrying Pools are expected to draw the same amount. Keep in mind that now you have two extra cards to draw.

[JW]

Sometimes there's Scrying Pool on a board and there's no trashing. Sometimes it's the only non-terminal source or the best source of draw, enough that if you're going to try and increase your hand size, that's what you're going for. Is it worth it? Say it with me...

Seems like you have the correct basic approach.

Edit: Call the average cards drawn by Scrying Pool in a deck of X actions (including Pool) and C non-actions, assuming that you discard non-actions with the self-spy effect, S(X,C).

S(X,C)=  (X^2 + 3*X*C + C^2 - 2*C -1)/ [ (X+C-1) * (C+1)]

See my post below for details.

The self-spy effect is a big part of the card's power. Consider a simple case where the self-spy effect is not trivial but can be included by hand. Assume that your hand consists of 1 Scrying Pool and nothing else. You have 2 other actions (besides the Scrying Pool) and 1 non-action ("Potion") in your deck.

Then the average number of cards that you draw is 2.667: you draw all three cards if the Potion is on top or on bottom (2/3), but only draw two cards if the Potion is second. Without considering the self-spy effect, you average 2 cards (1/3 chance each of 1, 2, and 3 cards).

Here's my calculation, which includes the self-spy effect:
6 actions including Scrying Pool, 11 non-actions: 1.7292 average cards drawn
7 actions including Scrying Pool, 11 non-actions: 1.8529 average cards drawn
8 actions including Scrying Pool, 11 non-actions: 1.9722 average cards drawn
9 actions including Scrying Pool, 11 non-actions: 2.0877 average cards drawn
10 actions including Scrying Pool, 11 non-actions: 2.2 average cards drawn
11 actions including Scrying Pool, 11 non-actions: 2.3095 average cards drawn
12 actions including Scrying Pool, 11 non-actions: 2.4167 average cards drawn
13 actions including Scrying Pool, 11 non-actions: 2.5217 average cards drawn
14 actions including Scrying Pool, 11 non-actions: 2.625 average cards drawn

I realize this would be easier to absorb as a picture, may add that later.

One small point that won't matter for calculations with a lot of stop cards but will matter with few stop cards is that you are typically going to have a 5-card hand that includes Scrying Pool, so if you assume that you already have Scrying Pool + 4 other cards in hand, then the maximum that you can draw off Pool is limited by the number of cards left in your deck.
 

[SCSN]

Sometimes there's Scrying Pool on a board and there's no trashing. Sometimes it's the only non-terminal source or the best source of draw, enough that if you're going to try and increase your hand size, that's what you're going for. Is it worth it? Say it with me...

It is.

[Titandrake]

Pool is a weird card, but in practice every time I think I can skip Pool I lose. I don't think it's as bad as skipping Witch, but it's pretty close.

[amalloy]

Pool is a weird card, but in practice every time I think I can skip Pool I lose. I don't think it's as bad as skipping Witch, but it's pretty close.

Of course Pool is usually a big deal, but exceptions do arise. I skipped it in a league match with ADK, opting to focus on Torturer/FV instead, and in two different casual games to instead try silver-flooding.

Now, obviously I am not the best player in the world, and neither were my opponents in any of those games. Particularly in the Trader/Scheme game I'm not sure I was as far ahead as he thought when he resigned. But there are definitely boards in which the time invested to get Scrying Pool just won't pay off.

[AdamH]

EDIT: THESE NUMBERS ARE NOT CORRECT: SEE OP FOR MOST UP-TO-DATE NUMBERS


Update on numbers:

I wrote some Python code to compute the numbers and I'm going to import it into Excel to make it into pretty pictures. My source code is below (I just did an online portal to execute the Python code since I'm working from a different computer than where my Python is set up)

Code: [Select]

#!/usr/local/bin/python2.7

def Ea(X):
  sum = 2.0
  for i in range(1, X-1):
    prod = 1.0
    for j in range(1, i):
      prod *= (float(X)-1-float(j))/(float(X)+10-float(j))
    sum += prod
  return sum
     
def Eb(X):
  sum = 1.0
  for i in range(1, X):
    prod = 1.0
    for j in range(i):
      prod *= (float(X)-1-float(j))/(float(X)+9-float(j))
    sum += prod
  return sum
   
def Pa(X):
  return (float(X)-1.0)/(float(X)+10.0)
 
def Pb(X):
  return (11.0)/(float(X)+10.0)
 
def EaSimple(X):
  return 2.0 + (float(X)-2.0)/(11.0)
 
def EbSimple(X):
  return 1.0 + (float(X)-1.0)/(10.0)
 
def Esilly(X):
  return 1.0 + (float(X))/(11.0)
   
for X in range(2, 51):
  EofX = Ea(X)*Pa(X) + Eb(X)*Pb(X)
  EsimpleofX = EaSimple(X)*Pa(X) + EbSimple(X)*Pb(X)
  print "%2d" % X,
  print "%2.4f" % EofX,
  print "%2.4f" % EsimpleofX,
  print "%2.4f" % Esilly(X)

It computes all of the intermediate values so I can compare them.

An interesting result (one that makes me question the correctness of my code, actually) is that Eb(X)*Pb(X) was always equal to one. This result seems like it shouldn't be but I can't think of a good reason why and the numbers I get all pass at least a simple sanity check. Did I do something wrong? Is there some reason why this should be the case?

Here's the output of the program:

Code: [Select]

2 1.1667 1.1750 1.1818
 3 1.4615 1.3371 1.2727
 4 1.6758 1.4890 1.3636
 5 1.8659 1.6327 1.4545
 6 2.0414 1.7699 1.5455
 7 2.2058 1.9016 1.6364
 8 2.3611 2.0288 1.7273
 9 2.5088 2.1522 1.8182
10 2.6500 2.2723 1.9091
11 2.7857 2.3896 2.0000
12 2.9167 2.5045 2.0909
13 3.0435 2.6174 2.1818
14 3.1667 2.7284 2.2727
15 3.2867 2.8378 2.3636
16 3.4038 2.9458 2.4545
17 3.5185 3.0525 2.5455
18 3.6310 3.1581 2.6364
19 3.7414 3.2627 2.7273
20 3.8500 3.3664 2.8182
21 3.9570 3.4692 2.9091
22 4.0625 3.5713 3.0000
23 4.1667 3.6727 3.0909
24 4.2696 3.7735 3.1818
25 4.3714 3.8738 3.2727
26 4.4722 3.9735 3.3636
27 4.5721 4.0727 3.4545
28 4.6711 4.1715 3.5455
29 4.7692 4.2699 3.6364
30 4.8667 4.3680 3.7273
31 4.9634 4.4656 3.8182
32 5.0595 4.5630 3.9091
33 5.1550 4.6600 4.0000
34 5.2500 4.7568 4.0909
35 5.3444 4.8533 4.1818
36 5.4384 4.9496 4.2727
37 5.5319 5.0456 4.3636
38 5.6250 5.1415 4.4545
39 5.7177 5.2371 4.5455
40 5.8100 5.3325 4.6364
41 5.9020 5.4278 4.7273
42 5.9936 5.5229 4.8182
43 6.0849 5.6178 4.9091
44 6.1759 5.7126 5.0000
45 6.2667 5.8073 5.0909
46 6.3571 5.9018 5.1818
47 6.4474 5.9962 5.2727
48 6.5374 6.0904 5.3636
49 6.6271 6.1846 5.4545
50 6.7167 6.2786 5.5455

Next up: pretty pictures and results

[AdamH]

EDIT: THESE RESULTS ARE NOT CORRECT: SEE OP FOR MOST UP-TO-DATE RESULTS AND STUFF

RESULTS



Something alarming I see is that I thought taking deck composition into account after drawing actions would actually decrease the expected draw but it seems to have increased it. Not sure if I messed up numbers, but other than that this passes a sanity check.

So the calculation I had been doing gave me an expected draw of a whole card less than what one could actually expect to draw.

"In order to expect to draw X cards, you need at least Y actions in your deck" -- some notable milestones:

2 cards, 6 actions
3 cards, 13 actions
4 cards, 22 actions
5 cards, 32 actions

[Titandrake]

For the Eb(X)*Pb(X) = 1 thing, I have a semi-explanation.

Suppose that your deck is infinite in size, so the odds of revealing a non action card is always the same.

Eb(X) = expected number of draws when you discarded non-action, meaning expected number of draws with no information about top card.

Pb(X) = probability of revealing non-action. (The chance for the top card is the same as the chance for the entire deck, with the assumption made earlier)

Eb(X) = P(draw at least 1 card) + P(draw at least 2 cards) + P(draw at least 3 cards) + ...
(If you draw n cards, it'll get counted in n of the probabilities above. I just discovered this trick last weekend so I'm abusing it wherever I see it.)

So,

Eb(X) = 1 + (1 - Pb(X)) + (1 - Pb(X))^2 + (1 - Pb(X))^3 + ...
= 1 / (1 - (1-Pb(X)) = 1 / Pb(X)

And Eb(X) * Pb(X) = 1.

There might be some trickiness with a deck that actually changes in action proportion, but I think there's a theorem where sifting doesn't affect probability of drawing key cards that I'll cite here. I don't know if it applies, and actually forgot how that theorem goes, but there you go, a semi-explanation.

[AdamH]

Suppose that your deck is infinite in size

This makes that particular issue very clear to me. Thank you. +1

[AdamH]

Sometimes there's Scrying Pool on a board and there's no trashing. Sometimes it's the only non-terminal source or the best source of draw, enough that if you're going to try and increase your hand size, that's what you're going for. Is it worth it? Say it with me...

It is.

SCSN, you know I love you man <3 , but in a 1-card Kingdom with just Scrying Pool you can't tell me I should go for it. OK well you could but I wouldn't believe you. There has to be a line somewhere and I've noticed that finding that line is a weakness in my game. Calculating this expected draw has been really enlightening when looking back on these games so I want to do it.

Yeah people get lots of respect for snarky comments around here, but the fact that a comment that dismisses what I'm trying to talk about gets more respect than what I'm saying leads me to believe that maybe lots of people out there just blindly follow your hyperbole in this case.

If they should then I want to see evidence to back it up. Otherwise I'll just have to be frustrated about that dynamic and try to figure it out for myself; and then one day I'll be a better player than you (and all those people who +1ed you and didn't look at my math) because I put in the work.

<3

[Mic Qsenoch]

This math can not help you play better Dominion at all, I'm sorry.

[DG]

I think you may be better served looking at how the drawing of the scrying pools relates to the non-action cards. The big problem with this maths though, compared even to ventures, is that is built on shifting sand. Adding even one vp card to a scrying pool deck will change the maths. Even weak drawing cards such as mystics can change the viability of scrying pools for drawing.

[AdamH]

Yeah I'm aware of that. The point of this is that my intuition on how much I can expect to draw with a Scrying Pool is off (too low). I did some crude math and it got higher and it's still too low. Now every time I do more precise math it gets better, to the point where it's much higher than I ever expected.

How does it combo with other cards? Well of course math can't tell you that you have to play the game. But when this particular fundamental is off then I'm not getting anywhere.

And when decks green of course that changes. Yeah I can do math on that too and see how it affects things and if that's surprising.

[silverspawn]

This math can not help you play better Dominion at all, I'm sorry.

? why not

[-Stef-]

...
Yeah people get lots of respect for snarky comments around here, but the fact that a comment that dismisses what I'm trying to talk about gets more respect than what I'm saying leads me to believe that maybe lots of people out there just blindly follow your hyperbole in this case.
...

Sorry to read your frustration here (& welcome to the internet).

It's not plain 'upvoting snarky comments' though. You really do over-complicate a question here. Sure you can try to revert to math when your intuition about Scrying Pool fails you, but in this case the required math is very hard to write down. I'd say you're still miles and miles away from getting the math right, whereas a simple rule like "just buy it unless you can explain a rubber duck why you shouldn't" is actually very helpful. At least it is to me. If that rule somehow fails you, I suggest you try SCSN's rule for a while ("just buy it").

[Mic Qsenoch]

This math can not help you play better Dominion at all, I'm sorry.

? why not

Because it focuses on one aspect of SP in an extremely specific case. It says next to nothing about when/how to go about playing an SP deck. The numbers it produces are restricted to a case that doesn't exist in real games of Dominion. How many cards SP can draw isn't even that important, in a real game we want to know roughly how many turns it will take to get the engine going, how many turns will the game last, what can I do once I'm drawing lots of cards etc. The other kingdom cards affect these important questions.

Adam says he has improved his intuition through this exercise, but how? Has he played any more SP games and actually seen the real amount of card draw or effectiveness of the card?

It's also a sophisticated approach to addressing a question of limited strategic importance, which just further enforces the wrong assumption that good Dominion strategy is obtained through analysis and calculation. The analysis and calculation that is popular on this board doesn't help that much with playing Dominion, it's just something to do for fun. It's cool to do things like this, but not helpful for getting better at the game.

Adam wants "evidence" that SCSN's views are correct, he already has it, SCSN is better than him at Dominion. You can't get better evidence that someone's ideas about Dominion are good than them winning lots of Dominion games.

[Davio]

Are we assuming 1 SP and cantrip actions?
Or just multiple SP's and no other actions?

A big part of SP is that it can draw other SPs.

If you want accurate simulations, you should look at multiple SPs and multiple payload or cantrip actions.

[AdamH]

Stef/MQ, thanks for taking the time to write something thoughtful. That's sort of the whole point of this.

I can plug a bunch of numbers into Excel and come up with a pretty picture. Is it helpful? You say probably not but to be honest, if my numbers are correct then I have a very useful conclusion: Take the standard X/11 expected draw, add one to it and you're really close to what the real number is. Knowing that I should have added one to my number in my league match against soulnet would probably have made me go for the Pools.

If I know why I'm going for the card and what benefit I can expect to get from it, then it helps me understand how to build my deck around it appropriately. You're not going to convince me that doing this math has no value because I've already found value in it.

It was SCSN himself who said "If you keep experimenting, keep practicing and keep learning, one year from now you can be better than any player is today." It's also well-known that he's had lots of success with just playing a lot of games with something he thinks he's bad at until he's not bad at it anymore.

Unfortunately, as a result of that second discussion I found out that playing lots of games and trying to get a feel for it works much better for him than it does for me. I played so many games with Familiar and I don't feel like I really got that much better. I felt like I didn't have any direction or purpose.

Don't get me wrong, I plan to play games like this, but I actually want to get something out of it so I'm trying to have some direction when I do this. It's totally OK that SCSN's advice needs a little bit of tweaking before I can make it click in my head; in fact I'd be really surprised if I'm the only person out there that needs a little bit of adjustment.

Am I getting too frustrated that people enjoy snark in the middle of a conversation that I'm taking seriously? Probably. Am I wrong when I say people +1ing a hyperbolic statement means they think my discussion isn't useful and I should just blindly do what SCSN says? Probably. But that is what it looks like sometimes and I've been told many times that it's funny when I get mad.

-----------------------

Davio, Labs can draw other Labs too -- yes this analysis alone won't tell you what you need to draw your deck. I'm just trying to think of SP as "+1 Action, +E(X) Cards", like a Lab variant, to help me better understand its value in a given kingdom -- the rest of the work with understanding how useful it is is something I'm already OK at.

There are other useful numbers to be found here, though. That's for sure.

[AdamH]

[...] the wrong assumption that good Dominion strategy is obtained through analysis and calculation. The analysis and calculation that is popular on this board doesn't help that much with playing Dominion, it's just something to do for fun. It's cool to do things like this, but not helpful for getting better at the game.

Allow me to stone-cold disagree with this statement though. Calculation isn't everything but without it my "intuition" means absolutely nothing. Maybe it doesn't help you but it helps me to be able to compare SP to other non-terminal draw cards using numbers. I know what Lab does and I want to know at what point SP becomes better than Lab -- when does it become the same as having two Labs?

[silverspawn]

...
Yeah people get lots of respect for snarky comments around here, but the fact that a comment that dismisses what I'm trying to talk about gets more respect than what I'm saying leads me to believe that maybe lots of people out there just blindly follow your hyperbole in this case.
...

Sorry to read your frustration here (& welcome to the internet).

It's not plain 'upvoting snarky comments' though. You really do over-complicate a question here. Sure you can try to revert to math when your intuition about Scrying Pool fails you, but in this case the required math is very hard to write down. I'd say you're still miles and miles away from getting the math right, whereas a simple rule like "just buy it unless you can explain a rubber duck why you shouldn't" is actually very helpful. At least it is to me. If that rule somehow fails you, I suggest you try SCSN's rule for a while ("just buy it").

It if was mountebank - fine, but you only go SP on roughly half of all boards, which is why I also thought the comment was stupid. I think it's once again a case where we give the games with scrying pool more weight, because they are more interesting, and take a lot longer to play. But they don't form a vast majority of all games. Maybe - probably - a majority of time playing, but not a majority of games.

Because it focuses on one aspect of SP in an extremely specific case. It says next to nothing about when/how to go about playing an SP deck. The numbers it produces are restricted to a case that doesn't exist in real games of Dominion. How many cards SP can draw isn't even that important, in a real game we want to know roughly how many turns it will take to get the engine going, how many turns will the game last, what can I do once I'm drawing lots of cards etc. The other kingdom cards affect these important questions.

Adam says he has improved his intuition through this exercise, but how? Has he played any more SP games and actually seen the real amount of card draw or effectiveness of the card?

It's also a sophisticated approach to addressing a question of limited strategic importance, which just further enforces the wrong assumption that good Dominion strategy is obtained through analysis and calculation. The analysis and calculation that is popular on this board doesn't help that much with playing Dominion, it's just something to do for fun. It's cool to do things like this, but not helpful for getting better at the game.

Adam wants "evidence" that SCSN's views are correct, he already has it, SCSN is better than him at Dominion. You can't get better evidence that someone's ideas about Dominion are good than them winning lots of Dominion games.

I see. I don't necessarily agree, but it's a good reason.

[silverspawn]

Adam wants "evidence" that SCSN's views are correct, he already has it, SCSN is better than him at Dominion. You can't get better evidence that someone's ideas about Dominion are good than them winning lots of Dominion games.

That's not a proof though. Even if we assume that skill is directly proportional to rating, which isn't true, then skill is not one dimensional. I think it's reasonable to say that skill is roughly identical to "how well can you play an average board", and that demonstrates the problem: every board is different. A lower skill player can always be better at a specific board, or even with a specific card, than a higher level player. I'm not suggesting that SCSN isn't better with SP, he probably is, but I don't like "he has a higher rating, therefore he's right" as a black box argument.

[Mic Qsenoch]

Adam wants "evidence" that SCSN's views are correct, he already has it, SCSN is better than him at Dominion. You can't get better evidence that someone's ideas about Dominion are good than them winning lots of Dominion games.

That's not a proof though. Even if we assume that skill is directly proportional to rating, which isn't true, then skill is not one dimensional. I think it's reasonable to say that skill is roughly identical to "how well can you play an average board", and that demonstrates the problem: every board is different. A lower skill player can always be better at a specific board, or even with a specific card, than a higher level player. I'm not suggesting that SCSN isn't better with SP, he probably is, but I don't like "he has a higher rating, therefore he's right" as a black box argument.

The only proof is playing games of Dominion, words/reasons/arguments are bullshit. So I rely heavily on rating in evaluating strategy advice, simply as a heuristic. I don't have a way of rigorously checking the strategy advice (I can't play enough games). The higher rated player is more likely to be right. It's a probabilistic thing, hey look at that, Dominion has some probabilities too.

[...] the wrong assumption that good Dominion strategy is obtained through analysis and calculation. The analysis and calculation that is popular on this board doesn't help that much with playing Dominion, it's just something to do for fun. It's cool to do things like this, but not helpful for getting better at the game.

Allow me to stone-cold disagree with this statement though. Calculation isn't everything but without it my "intuition" means absolutely nothing. Maybe it doesn't help you but it helps me to be able to compare SP to other non-terminal draw cards using numbers. I know what Lab does and I want to know at what point SP becomes better than Lab -- when does it become the same as having two Labs?

The calculation has no useful information, the number of expected cards drawn doesn't answer even the simple question you propose "when better than Lab?". Cards drawn with SP are more likely to be actions, so there's no straightforward way to compare the two. And this question is barely useful!

Your intuition means everything, your calculation means nothing because it doesn't apply in actual games of Dominion that can be played. Unless you change your calculation to include way more effects, which you won't be able to do as there are just too many. And then you have to update the calculation on each new board! It's hopeless. Almost anyone's hunches are a million times more valuable for playing Dominion than a neutered calculation about SP decks with all junk cards remaining and anonymous action cards without play effects. Certainly yours are!

Here's a comment Adam you can take it or leave it. This is based on your posts and watching your videos. You think too much, you overvalue "understanding", you want things to have reasons so your brain can feel comfortable about the decisions you make in the game.

You agonize over decisions whenever two options seem close. This is the absolute worst time to agonize! It wastes brain power. If two options are close in your mind, flip a coin and pick one. The time to stop and think is when you check the board for interactions, whenever you don't have any ideas at all, when the play order of your actions matters a lot, or when you need to check piles for auto-wins. Don't think the rest of the game. Don't even try to justify what you're doing, just do what immediately seems best.

Dominion games aren't won by playing "optimally". They are won by making reasonable choices and being opportunistic whenever the shuffles go your way, and by not missing chances for wins *right now* (or next turn, or next two turns).

You'll forgive me if I don't write anything else in this discussion, I've already word vomited enough for one day.

[silverspawn]

The only proof is playing games of Dominion, words/reasons/arguments are bullshit. So I rely heavily on rating in evaluating strategy advice, simply as a heuristic. I don't have a way of rigorously checking the strategy advice (I can't play enough games). The higher rated player is more likely to be right. It's a probabilistic thing, hey look at that, Dominion has some probabilities too.

completely agree, I just wanted to make a point that it's not a proof.

[WalrusMcFishSr]

Not meaning any offense to anyone (I find this type of heady discussion quite interesting), but this thread gave me a bad feeling of deja vu as soon as I saw it...

[AdamH]

MQ, you're not understanding how this is helpful because you're just being dismissive. You think I think too much and analyze and understand too much, I consider that a hallmark of my strategy and the reason why I've slowly and steadily improved as a player over the past several years. Maybe it doesn't work for you, and that's OK; I'm not asking you to read this topic or understand it if you don't want to; but I can't tell you how many people have told me that watching me explain things and understand them and break them down on my videos has made things clearer to them and made them a better player. I'm not alone in the way I think about the game and there's value in it. Maybe not for you, but for me and other people out there.

You can't convince me that what I do is wrong. You can't convince me that the way I play or the way I think about the game is wrong. Why would you ever want to do that? Why are you saying that I should think a certain way when you aren't me?! Just because I'm not you or SCSN or in the A division of the Dominion League doesn't mean I can't get there unless I do everything just like you. You aren't perfect. The moment you decide you can't learn more about Dominion is the same moment you'll stop getting better, and I promise you if you stop getting better at Dominion it's only a matter of time before I'm better than you.

Look, I have a lot to learn and that's clear. There's even good advice in your post. Unfortunately what I'm seeing is that I've posted something that's helping me understand a part of the game. You reply and say it's useless because understanding the game is useless, you should just play it. If you've got something helpful to say, can't you just say the helpful thing? If you think this is useless then just don't post in the thread. If you think that talking about Dominion is useless and you should just play more to get better, then why do you even post on the forums? If you think I'm saying something that's incorrect then tell me that, but at least be constructive instead of dismissive.

Or is that too much to ask of people on these forums? Jeez.