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[firefrog]

Today I spend some time thinking about a formula to show a deck '$Power'. And I want to show you this:

P = (X+YA)/(S-RA)

P= 1 Card $Power
X= Sumatory of coin values
Y= Sumatory of action $ value.
A= Action Factor (Will explain latter)
S= Deck size
R= Sumatory of draw effects

If we do 5*P we get the average $ we will have in a single turn. Examples:

- Starting hand; P = (7+0)/(10+0) = 0.7
- Starting hand + 3 Silver; P = (13+0)/(13+0)= 1.0

That's easy, but now I will show you the Action Factor:

A = [(S/(5+RA))+O]/N     =>    AARN+A5N-ARO-5O=S

O = Sumatory of +Action effects
N = Action cards in your deck

Some Examples:

- 10 Coppers + 5 Moats; P=10/11.5=0.87
- 10 Coppers + 5 Markets; P=1.5

I'm still having some big problems with the formula(+Action+Draw cards are a pain), but I think the results are really close. Will post again I find something more. Hope you like maths.

[HiveMindEmulator]

Can you explain intuitively what you want "$power" to mean, and in what class of decks this is important?

[firefrog]

$Power * 5 = Money in a single turn.

I think this can be helpfull in Bot-AI.

[SCSN]

I think what he means is the expected $ you will have at the end of your turn when starting from a random 5-card hand at the beginning of a shuffle for a given deck.

$Power is this number divided by 5, which I guess corresponds to the expected pay-off per card in hand, which is a flawed way of looking at things because it presupposes a linear scaling that is absent in reality.

If you want to calculate this for more complicated decks you should just write a Monte-Carlo simulation, because the reason you're having big problems with it isn't because it's hard but because it's extremely cumbersome, like manually counting the number of letters in the Bible.

In any case I think this approach is an exercise in futility because Dominion isn't at all about maximizing your expected coin production, and a Bot utilizing such a mindset should be classified under Artificial Stupidity.

[AdamH]

I think what he means is the expected $ you will have at the end of your turn when starting from a random 5-card hand at the beginning of a shuffle for a given deck.

$Power is this number divided by 5, which I guess corresponds to the expected pay-off per card in hand, which is a flawed way of looking at things because it presupposes a linear scaling that is absent in reality.

I believe this term has been called "money density" around here before. It's been talked about but as SCSN hints at, doesn't apply to most games of Dominion, since it really only applies to Big Money strategies which aren't dominant on most boards. Your formula could potentially be a more accurate calculation of money density than what's been done here before.

Results you can get for this can be useful, you just have to be extremely careful with how you apply them. Simulation and bots that play Big Money seem to be the main applications for this. I'm not an expert at those so I won't say more.

If you want to calculate this for more complicated decks you should just write a Monte-Carlo simulation, because the reason you're having big problems with it isn't because it's hard but because it's extremely cumbersome, like manually counting the number of letters in the Bible.

In any case I think this approach is an exercise in futility because Dominion isn't at all about maximizing your expected coin production, and a Bot utilizing such a mindset should be classified under Artificial Stupidity.

This is completely unnecessary. Just because you're better at Dominion than most people doesn't give you the right to be dismissive like this. Grow up.

I used to think this community was above stuff like this, I used to think we welcomed people and were only critical of their ideas in a constructive way. It seems we're having trouble with that recently.

[pubby]

A greedy simulation/algorithm that tries to maximize the value of this formula each turn would be interesting. The results might not be optimal, but could still be quite reasonable.

[liopoil]

A greedy simulation/algorithm that tries to maximize the value of this formula each turn would be interesting. The results might not be optimal, but could still be quite reasonable.

They would never trash cards or gain cards without buying them. It also would ignore attacks and would trigger shuffles without caring.

[SCSN]

This is completely unnecessary. Just because you're better at Dominion than most people doesn't give you the right to be dismissive like this. Grow up.

Excuse me?

My first two lines explained to HME what this was probably about. Next I explained to the OP why he was having problems with it and what a better approach would be. Only then did I give my personal judgment that this is a waste of time (with the hope of preventing him from wasting his) because it has little to do with good Dominion play, adding a joke/pun on AI.

Your admonishing response is completely uncalled for.

[Witherweaver]

It does sound a little bit like you're calling what he's doing stupid. 

[Mic Qsenoch]

It does sound a little bit like you're calling what he's doing stupid.

What if what he's doing is stupid?

There's no truly nice way to tell someone they're wrong. Wrap it up in whatever niceties you like, but you are still telling them their brain sucks in some way. And this is okay because: who cares? Everybody's brain sucks in some ways some of the time. When people try to soften their criticisms with polite BS I just feel it as a double insult "you're stupid and you're a baby who needs to be talked down to."

[Joseph2302]

+1 for calling it Maths not Math.

[WanderingWinder]

It does sound a little bit like you're calling what he's doing stupid.

What if what he's doing is stupid?

There's no truly nice way to tell someone they're wrong. Wrap it up in whatever niceties you like, but you are still telling them their brain sucks in some way. And this is okay because: who cares? Everybody's brain sucks in some ways some of the time. When people try to soften their criticisms with polite BS I just feel it as a double insult "you're stupid and you're a baby who needs to be talked down to."

That's stupid.

Edit: I should explain better. I don't have a problem with saying that the guy is wrong, saying that what he's doing isn't useful, etc. etc. I really don't have a problem until the very last line of that post, because the 'Artificial Stupidity' comment crosses the line from being substantive disagreement to pointless insult.

[Witherweaver]

You can be wrong without being stupid. 

[pacovf]

Oh hey guys I have an idea! What if we have this discussion in another thread so that whoever wants to discuss firefrog's idea specifically has a place to do so?

[Mic Qsenoch]

You can be wrong without being stupid.

If you're wrong, you're being stupid with regards to whatever thing you're wrong about. But sure, not stupid forever for all things in the whole world.

[Witherweaver]

Is this different than the expected coin value of your hand each turn?

[Witherweaver]

You can be wrong without being stupid.

If you're wrong, you're being stupid with regards to whatever thing you're wrong about. But sure, not stupid forever for all things in the whole world.

This seems a bit of a semantic thing, and I don't really agree with it.  Newton was wrong about Gravity; I wouldn't say that means he was stupid with regards to his theory.  Einstein was wrong, too, but he was kind of clever.

[SwitchedFromStarcraft]

Man I hate seeing this discussion even develop.  I've got other forums where I can watch people get testy with each other.  This one  has been remarkably free of this type of thing for a long time (Mafia situations excluded of course).

Pacovf has the right of it - if this brewing tempest really has to occur, let's move it to another thread.  I personally was thrilled to see the OP.  New guy, new voice, new topic, some enthusiasm (he used a bang, for crying out loud!).  Let's not contaminate that with this.  A good start would be to remember that tone is lost in posting, so what was meant as a joke might not always come off that way.

Especially if you are a drummer that's not really homeless. 

[Gherald]

It's an interesting emo-sensitive world we've arrived at when it's considered rude for a game player to call an AI stupid

[Witherweaver]

It's an interesting emo-sensitive world we've arrived at when it's considered rude for a game player to call an AI stupid

AI have feelings, too.

[DG]

I'll try to give some more substantive feedback.

Formulas might seem reasonable but what decisions are you going to make based on those formulas? A power value on its own is just a statistic. Buying cards to increase power isn't going to win a game. You need to score the most vp and end the game in your favour, but a 'power' deck might not deliver that.

Suppose we use the power level to decide when to buy green cards. We find a problem that the power level changes with each green card bought. Moreover, decks that start with the same power level may see different changes as green cards are added, suggesting they weren't actually equal in the first place. A first thought may be to change the formulas to incorporate this, but actually it is better to realize that calculations change with every card gained and this is always likely to make the process as reliable as building on shifting sand.

[AdamH]

A first thought may be to change the formulas to incorporate this, but actually it is better to realize that calculations change with every card gained and this is always likely to make the process as reliable as building on shifting sand.

This can help with understanding why it's important to be careful how you apply these formulas, but coming up with them can be helpful for some people to see how greening affects different decks. The math here doesn't appear to be wrong, it just has limited application to games of Dominion.

Playing with variables and seeing the results go up and down, or graphing these things, could potentially be a good exercise, it provides a concrete basis with numbers to answer the question "why is my 8th Province more difficult to buy than my 1st?"

[WanderingWinder]

You can be wrong without being stupid.

If you're wrong, you're being stupid with regards to whatever thing you're wrong about. But sure, not stupid forever for all things in the whole world.

That's obviously wrong.

I predict that there will be no major Earthquake anywhere in the world on Thursday. If there is one, I am clearly wrong - does that make my prediction stupid?

It's an interesting emo-sensitive world we've arrived at when it's considered rude for a game player to call an AI stupid

The problem is that the statement has a clear implication behind it. If I say that everything you have ever said is completely idiotic, I could claim that I'm not insulting you - technically, I would only be talking about your statements. But the way that the language is being used makes it quite clear that I would in fact be insulting your intelligence.

[Witherweaver]

You can be wrong without being stupid.

If you're wrong, you're being stupid with regards to whatever thing you're wrong about. But sure, not stupid forever for all things in the whole world.

That's stupid

Fixed that for you.

[XerxesPraelor]

You can be wrong without being stupid.

If you're wrong, you're being stupid with regards to whatever thing you're wrong about. But sure, not stupid forever for all things in the whole world.

That's stupid

Fixed that for you.

Can't you just edit your own post?

[Titandrake]

To original post: This is kind of neat as an exercise, but it's not that helpful for actually playing Dominion. Your distribution of money each turn is much more important - even in decks with 1 Smithy + treasures, it's not important that you hit a certain money density, it's important how often you spike $8 from either Golds or Smithies, because that spike is what gets you to $8 while cycling your deck. (Which is also why 1 Smithy + treasures loses to 1 Smithy + 2nd or 3rd bought at the right time + treasures, but wins against too-many-Smithies + treasures.) If you want to do more, I'd definitely recommend doing simulations instead of trying to work out the probabilities by hand, unless you're doing this for personal math fulfillment in which case do what you want.

To, like, everything else: There is a line between criticism and constructive criticism, except it's not a line, it's a sliding scale, and this whole debacle is about where people think this falls on that scale, yada yada etc.

Addressing SCSN's comment in particular:

Improperly explained complaints are basically worthless - if that person doesn't know why something is bad, how is telling them "this is useless" and not explaining WHY going to actually change anything? You did make some earlier constructive comments about it, but I think they're too succinct. Shorter comments are better if you can get away with it, but only if you can get away with it. In this scenario of a clearly new poster making a post that indirectly displays some misconceptions about the useful points of Dominion, your post reads like a brick wall. I don't think I would have been able to identify where you point out why this heuristic is bad if I hadn't had the same point explained to me a while ago, on this very forum, but in more detail and with more explanation. Even then, I still missed the tail end of that sentence the first time through because surprise - assuming someone is going to catch every word of your sentence in a post on an internet forum is highly optimistic. My overall feeling is that it's well-intentioned, but misguided, and it reads badly from a newcomer perspective.

---

In the extreme, badly explained or unexplained criticism leads to very tight communities that are incredibly difficult to get into without lurking for months, in hopes that you don't make a fool of yourself when you finally make a post about strategy instead of random stuff. I'd rather avoid that.

[theory]

Let's move on.  I will assume SCSN was making a ill-advised pun and had no particularly mean intentions.  I will also assume we all know that we should be treating people who present new ideas nicely, so as not to discourage people from presenting new ideas. 

==

I think that there is potential in firefrog's approach though it's obviously a little simplistic.  If you wanted to model something more sophisticated I suggest you start with considering cards like Market, which are basically an invisible "+$1" to your hand.

[Witherweaver]

So, yeah, welcome to the forum!

Forum games, etc. etc.

[market squire]

The topic that firefrog raises is quite interesting imo.
I wouldn't calculate my exact money power, but I think it is important to have a feeling about it. I also have thought about the money strength of a deck quite similarly.
For example, it is helpful to know how much +$ you can expect to get from a Smithy.
It should be good in gameplay to think like "every card that I add to my deck makes my average money approach that value".

I don't understand the Action part of your formula.
How can you define the variable A by using itself in that term?

To be able to make more situational conclusions, you may add a formula for average deviation.
Like, in a deck with many Silvers, you'll have a smaller deviation than in a deck with Golds and Curses.
Also there could be another formula that counts your Actions as Curses (for terminal draw).

[Witherweaver]

Well, more statistics than average value would be important, like variance.  Also, deck tracking is probably more important in many cases.  It's not so helpful that the average card value of your deck is $1.9 or whatever if all your Golds are in your discard pile and you're not going to get a Shuffle from  your Smithy. 

Edit: Oh,  you brought up the point of deviation.

[firefrog]

Is this different than the expected coin value of your hand each turn?

You can use this to get the expected coin value. Just take in account that the formula always work with 5 cards in hand. If you do 5*P you will get the avarage value even if you only have coins and draw cards.

I think you can include every single card in the game bassed on this formula. But we need to add a "benefit over time" condition. Something like:

bot = ("Power your deck will get each time yo play this card"/"Amount of turns it takes to replay the card") - "Turns left to end"

And it may not be difficult to get an easy aproximation of the turns left to end. Using "Average deck power of each player" and "Amount of green cards left". (Adding something more for the 3 piles end)

[werothegreat]

To British people: why is "maths" plural, but "sport" singular?

[qmech]

Maths isn't plural: it just has an "s" on the end.  If sport were short for sportematics I'm sure we'd also call it sports.

[Deadlock39]

[WanderingWinder]

The biggest problem with looking at things formulaically like this is that it really starts coming apart when you deal with draw-your-deck engines. There, the math is way more about getting yourself to consistently-draw-my-deck-land AFAP (as fast as possible). Once you ARE there, it then becomes about increasing the total economic output of your deck, without damaging your ability to draw the thing. And once you're talking about the economic output of your whole deck, you can just count it - the formula is going to have a problem with running out of cards anyway (yes, you can fix that, but it's really more trouble than it is worth).

[pacovf]

Maths are singular!?!?

Who allowed this!?

[Witherweaver]

Maths are singular!?!?

Who allowed this!?

Maths is*

[pacovf]

[Witherweaver]

We don't joke about grammar around here, sir.

[eHalcyon]

Video

The first time I heard "maths" was in this video, Look Around You: Maths.  Anybody who has never heard of the Look Around You Series should check it out!

I thought they were adding the -s to make it sound sillier.  I can't remember when I learned that it was just the British way.

[Gherald]

Sounding sillier is just the British way. (Eh chaps?)

I have two ways to make a thread about maths and grammars more fun:

[Kirian]

Sounding sillier is just the British way. (Eh chaps?)

I have two ways to make a thread about maths and grammars more fun:

<3 Klein Four... even if they really only have one song.  Also, annotated for non-math majors here:  http://en.wikipedia.org/wiki/User:Nobi/Finite_Simple_Group_of_Order_Two