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Author Topic: The Key to Big Money Part II: Opportunity cost  (Read 3342 times)

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WanderingWinder

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The Key to Big Money Part II: Opportunity cost
« on: January 21, 2012, 11:08:12 pm »
+3

In a big-money kind of deck, there's really two concepts you need to be aware of; the first is money density, the second is opportunity cost.

At the end of my previous article, we may be left with an interesting little question. The analysis of buying a second smithy shows that it should be good for our deck pretty early on, right? Like, look at this deck: we've got 7 copper, 1 smithy, 3 estates, and 2 silvers. Our effective money density is around $0.917, we've got around a 40% chance of hitting a 7 card hand... adding a second smithy would decrease our effective money density to around $.846, it's true, but significantly increasing the chances at getting two more cards in our hand is worth it, on the analysis, right? Well, if the choice were between buying the second smithy and buying nothing, you'd be right. But it's not. Any time you can buy a smithy, you can buy a silver instead (okay, the silver pile could be run out - extremely unlikely). And if you buy that smithy, that stops you from buying a silver. The correct play here is for the silver, not so much because of the collision problem (though that makes putting a free smithy in your deck barely worth it in the short term), but more because of opportunity cost, i.e. you have to consider what you buy in terms of what else you could have bought, not in a vacuum.

This is actually an important way of looking at all of dominion, not just Big Money, but I think it's easiest to understand in big money, because of the money density being available. So if you're trying to decide whether or not to buy a market, you can't just look and see whether that's good for your deck, you have to see if it's better for your deck than the alternatives.

One nice little way to look at this is with potion-costing cards. Since whenever you buy a potion, you could've gotten a silver, it's generally true that any time you have $PX (where $P means you have a potion in play and X is some coin amount), you could have bought something costing $X+2. For instance, if you buy a possession, that could have almost always been a province if you'd gotten silver instead. Your alchemists could have been laboratories (hey, that actually makes a lot of sense), your familiars could have been witches, etc. Now, whether or not you should go in for potions for these cards has a lot to do with variance and the usefulness of the potion later in the game, but it's a tremendous illustration of opportunity cost in action. The opportunity cost of buying a potion is a silver (or any other $4 or less cost card), and that silver could have gotten you a province; instead you have possession (unless it's very early in the game or there are engine decks at hand shooting for megaturns, you'd rather have the province).

Perhaps the simplest, first way many players need to realize the importance of opportunity cost is with the 'village idiot'. Villages, like any cantrip, can't possibly hurt your deck, since they replace themselves, right (apart from being able to draw them dead)? This is the thought process a lot of people go through early on. This may be true, but that doesn't mean you should just gobble up all the villages you can; if you start of the game buying village after village after village, you'll have a whole bunch of unused actions lying around, with no action cards to use them on, but more importantly, your deck won't have any buying power, because the opportunity cost of buying a village is a silver.

Another great card to look at through the lens of opportunity cost is Hoard. Hoard could have been a gold. So any time you buy a duchy with hoard, you could have bought a gold instead. Now you are gaining that gold as well, it's true, but you have to look at when in the game you are... do you want a 'free duchy' in your deck yet? Maybe so, maybe not. To say nothing of the times where the opportunity cost of going Hoard over gold knocks you down from $8, buying a province, to $7, settling for a duchy and another gold.
Yes, I'm saying that Hoard is overrated and misused.

The concept of opportunity cost extends beyond just once through the deck as well. That silver that your village cost you is going to hurt your buying power now, and on the next reshuffle, and on the next reshuffle.... Furthermore, the buying power reduction that you feel now is going to make you have to buy something worse now, which is going to further hurt you on the next reshuffle, and then that further reduction on that reshuffle will hurt your buying power even more on the next reshuffle... this compounding effect is why the early turns are generally more important than the later ones.

And you can further extend this paradigm to what I call implied opportunity cost. If I buy a chapel on turn one with $3, there are lots of costs to me. I have the $2 that I spent for it, the silver (or other 2- or 3-cost card) I could have bought instead, the cards that will no longer be in my deck once I use it, plus the turns that I'm using it for, on which I probably won't be able to buy things, plus it being a dead card in every hand after a while. Now, the third one of these, getting rid of the coppers and estates you're trashing is probably actually a boon more than a cost. And very often, it's a really big boon. But it does take the turn you're buying the chapel, plus probably two full turns of chapelling things, plus another turn which is partially hampered by trashing, plus all the times you have a worthless chapel in your deck. Which is all to say, chapel, strong as it is, is not all that great for big money.

Of course, this is just the tip of the iceberg, as to a certain extent, the entire game is opportunity cost upon implied opportunity cost, and how they all compound.
« Last Edit: February 16, 2012, 05:42:44 am by theory »
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TheMathProf

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Re: The Key to Big Money Part II: Opporunity cost
« Reply #1 on: January 22, 2012, 12:51:16 am »
0

Very well said.  I can't tell you how much my game improved when I stopped using my 3 for a Village and instead for a Silver on a 4/3 split.
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ecq

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Re: The Key to Big Money Part II: Opporunity cost
« Reply #2 on: January 22, 2012, 01:01:40 pm »
+1

Excellent article.

I'm finding I tend to err on the side of assuming money is better, often to my detriment.  If I see $6, I have a hard time buying a Wharf over a Gold.  Often this means that my BM-X turns into basically just BM because I don't see the right coin totals at the right times, then I lose.

So, I guess my question is how do you know when it is right to buy the Smithy or Wharf or other BM enabler?  Is it a matter of buying whichever card gives you the better average money per turn given your current deck, or is it more complex than that?
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AdamH

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Re: The Key to Big Money Part II: Opporunity cost
« Reply #3 on: January 23, 2012, 12:51:48 pm »
+2

Often times I find myself looking at a board containing a whole bunch of $4 and $5 cost cards that I really want -- weak trashers, labs, etc. I tell myself that I'm going to buy lots of these cards and make an engine out of them, but my turns seem to be producing $3 and $6 (or $8, later on) all of the time. I end up playing BM, maybe with one additional card, when I had intended at the start of the game to do the exact opposite. I also find that my opponent, who has been able to buy lots of the $4/$5-cost cards and build the engine I had originally set out to build, looks successful doing it. I find myself winning these games often, buying my 6th province on turn 15 or so...

There are two ways to look at this:

1. I am still n00bish enough to think that the "engine" I was attempting to build was better then BM, and BM just happened to be the dominant strategy that I stumbled into backwards.

2 (and better for my ego): when you draw exactly $3, $6, or $8 almost every turn whilst playing BM, you are getting extremely lucky, and lucky-BM is a tough strategy to beat. (this is why your post made me think of this)

I would be extremely interested to hear from the more experienced people about what they think of this; I think the closest tangible thing I can come up with that embodies the experience those people have is their understanding of opportunity cost.
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Fabian

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Re: The Key to Big Money Part II: Opporunity cost
« Reply #4 on: January 23, 2012, 01:05:59 pm »
0

AdamH, it's (mostly/in general) 2. What you're describing is imo the easiest to see/most common way of adapting your strategy because of shuffle luck, which imo is a decently important concept I've considered writing a little something about. You're also right that even straight BM is a very strong deck given it gets good opening draws, and while it's (obviously) not a strategy you can/should look for very often, when it happens it's good to capitalize on it instead of buying crappy Bazaars or whatever :)
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Asklepios

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Re: The Key to Big Money Part II: Opporunity cost
« Reply #5 on: January 24, 2012, 03:58:36 am »
0

Often times I find myself looking at a board containing a whole bunch of $4 and $5 cost cards that I really want -- weak trashers, labs, etc. I tell myself that I'm going to buy lots of these cards and make an engine out of them, but my turns seem to be producing $3 and $6 (or $8, later on) all of the time. I end up playing BM, maybe with one additional card, when I had intended at the start of the game to do the exact opposite. I also find that my opponent, who has been able to buy lots of the $4/$5-cost cards and build the engine I had originally set out to build, looks successful doing it. I find myself winning these games often, buying my 6th province on turn 15 or so...

There are two ways to look at this:

1. I am still n00bish enough to think that the "engine" I was attempting to build was better then BM, and BM just happened to be the dominant strategy that I stumbled into backwards.

2 (and better for my ego): when you draw exactly $3, $6, or $8 almost every turn whilst playing BM, you are getting extremely lucky, and lucky-BM is a tough strategy to beat. (this is why your post made me think of this)

I would be extremely interested to hear from the more experienced people about what they think of this; I think the closest tangible thing I can come up with that embodies the experience those people have is their understanding of opportunity cost.

I can empathise with this.

Many times I've opened silver/silver with the goal of getting to $5 first, then hit $6 before $5 and opted for gold, then found myself buying provinces before I've got my first $5.

I personally think we're right to take the gold if the $6 presents itself. This is purely anecdotal, but from broad experience it always seems to me that the player who hits $6 and gets gold almost always does better than the player who hits $6 and takes the strong $5 card (be it Witch, Mountebank, Wharf or whatever). The player who took the gold first gets the chance to pick up the strong $5 card in a couple of turns time anyway, and likely loses out on playing the power card less than once over the course of the game.
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Geronimoo

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Re: The Key to Big Money Part II: Opporunity cost
« Reply #6 on: January 24, 2012, 04:00:49 am »
0

Getting Witch/Mountebank before the reshuffle is more important than getting the Gold.
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