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Author Topic: I did some Maths!  (Read 12238 times)

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firefrog

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I did some Maths!
« on: March 23, 2015, 12:03:09 pm »
+7

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.


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HiveMindEmulator

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Re: I did some Maths!
« Reply #1 on: March 23, 2015, 12:11:50 pm »
+1

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

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Re: I did some Maths!
« Reply #2 on: March 23, 2015, 12:26:17 pm »
0

$Power * 5 = Money in a single turn.

I think this can be helpfull in Bot-AI.
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SCSN

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Re: I did some Maths!
« Reply #3 on: March 23, 2015, 01:34:20 pm »
+2

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.
« Last Edit: March 23, 2015, 01:35:21 pm by SheCantSayNo »
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AdamH

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Re: I did some Maths!
« Reply #4 on: March 23, 2015, 04:17:51 pm »
+9

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.
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pubby

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Re: I did some Maths!
« Reply #5 on: March 23, 2015, 04:39:08 pm »
0

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.
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liopoil

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Re: I did some Maths!
« Reply #6 on: March 23, 2015, 04:41:53 pm »
0

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.
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SCSN

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Re: I did some Maths!
« Reply #7 on: March 23, 2015, 04:58:37 pm »
+1

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.
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Witherweaver

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Re: I did some Maths!
« Reply #8 on: March 23, 2015, 05:12:08 pm »
+2

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

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Re: I did some Maths!
« Reply #9 on: March 23, 2015, 07:08:31 pm »
+3

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."
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Joseph2302

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Re: I did some Maths!
« Reply #10 on: March 23, 2015, 07:11:13 pm »
+2

+1 for calling it Maths not Math.
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WanderingWinder

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Re: I did some Maths!
« Reply #11 on: March 23, 2015, 07:11:19 pm »
+9

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.
« Last Edit: March 23, 2015, 07:47:22 pm by WanderingWinder »
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Witherweaver

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Re: I did some Maths!
« Reply #12 on: March 23, 2015, 07:11:25 pm »
+6

You can be wrong without being stupid. 
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pacovf

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Re: I did some Maths!
« Reply #13 on: March 23, 2015, 07:13:00 pm »
+4

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?
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Mic Qsenoch

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Re: I did some Maths!
« Reply #14 on: March 23, 2015, 07:15:11 pm »
0

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.
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Witherweaver

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Re: I did some Maths!
« Reply #15 on: March 23, 2015, 07:15:43 pm »
+1

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

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Re: I did some Maths!
« Reply #16 on: March 23, 2015, 07:17:50 pm »
+3

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.
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SwitchedFromStarcraft

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Re: I did some Maths!
« Reply #17 on: March 23, 2015, 07:53:46 pm »
+5

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.  ;)

« Last Edit: March 23, 2015, 07:56:13 pm by SwitchedFromStarcraft »
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Gherald

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Re: I did some Maths!
« Reply #18 on: March 23, 2015, 08:26:16 pm »
0

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
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Witherweaver

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Re: I did some Maths!
« Reply #19 on: March 23, 2015, 08:28:50 pm »
0

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.
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DG

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Re: I did some Maths!
« Reply #20 on: March 23, 2015, 08:44:17 pm »
0

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.
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AdamH

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Re: I did some Maths!
« Reply #21 on: March 23, 2015, 09:05:08 pm »
+2

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?"
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WanderingWinder

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Re: I did some Maths!
« Reply #22 on: March 23, 2015, 09:09:33 pm »
+5

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

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Re: I did some Maths!
« Reply #23 on: March 23, 2015, 09:11:02 pm »
+1

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.
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XerxesPraelor

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Re: I did some Maths!
« Reply #24 on: March 23, 2015, 09:53:37 pm »
+4

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?
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