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WanderingWinder

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An Endgame Primer
« on: August 05, 2011, 09:23:22 pm »
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Endgames

First of all, read this (http://dominionstrategy.com/2011/03/28/the-penultimate-province-rule/). Next, knkow that most of the rest of this article is devoted to two-player games. Once you hit multiplayer, things change a bit, and I'll address that towards the end, but I'm not much of an expert at all in multiplayer.

Okay, so the PPR is the third fundametal rule of endgame play. The first is to always end the game in a win immediately if you can (this requires point tracking, something you should be doing if you don't have software to do it for you. The second is to never end the game with yourself behind. PPR is, as I said, third, but this is a rule which you should sometimes break. More on that later.

The PPR itself, however, is merely indicative of a core principle of endgame play: depriving your opponent of the opportunity to favorably end things. This most obviously extends to not coming close to emptying that third pile. But it comes into effect in other places as well - when to start buying out things with those goons buys, when to start bishopping your golds to stay that tick ahead of the pace, etc.

Now to when breaking the PPR is correct. If you both have decks which have been very clogged, say by mountebank wars, then breaking PPR can be the right move. Also if your deck is less resilient to clogging than your opponent's, you should more often take the chance. What do I mean by this? Well, if you've played a chapel/money deck against a bureaucrat deck, say, and you're slightly behind on VP, it could well be worth it to go ahead and grab that penultimate province. The logic behind this is that the extra green of waging a duchy war is going to hurt your deck a lot more than his, and so when that duchy war ends, you will have a very difficult time hitting 8 again, while he'll have fewer problems. Alternately, after a few rounds of the PPR-fueled duchy war, it might be time to vary and buy the province. Why? Well, youe decks are both getting ever more clogged, and it's getting ever less likely for you to get back to 8.

Generally, there are two factors to consider when deciding whether or not to break the PPR. One is the likelihood of making it back to 8 of either deck. The more likely it is, the more you should follow PPR. An important factor to look at here is duration cards, which increase the chances almost always, often significantly, of making that magic 8 number. The second is resiliency to clog. This often has a lot to do with how fat your deck is - a deck beefy with money is resilient; a thin, action-fueled deck is often not, as it's more likely to gum up. But these are really deck specific.

Now let's look at some of the finer mathematical points of the various situations. The clearest is the case with only Province, Duchy, and Estate. The thing to note here is that it takes a four duchy interval to overcome the standard minimum two province deficit. This means that, without a lot of help, trying to fight provinces with duchies is a pretty big longshot. That doesn't mean it's impossible though.
If you throw Colonies in, the province is a little better at fighting against them than duchies are at fighting provinces - but not a ton. A 2-point VP card (island, nobles, harem) is a good tiebreaker which, since they give you other benefits, you can spam a bit more. A big lead in these can actually fight an extra province off better than duchies in most cases (though often it's a combination of these AND duchies), and they're great in the tiebreaking aspects. Four Point VPs (either gardens or fairgrounds typically) can actually really start to fight against those provinces, as you only need three to match out two. Curses help for sure, but their impact is actually not so big on the VP end as it is on the deck's buying power - compare to estate.

But the biggest way (Duke will get its own article) to fight those extra provinces is with VP chips. Goons is ridiculous, of course, Bishop can give you a decent cushion, and the extremely underrated monument can pump up quite a lot over the course of a game. 12 points isn't so hard to get, and you can almost always get 10 and a duchy or 7 and two. And since these are all long-term cards anyway, you want to go for those duchies a lot earlier and really dig in.

And here's my biggest obvious secret of all. Rating estates. Your first estate above your opponent is, (without extra buys), almost entirely as good as a duchy. This is simply because a one-point lead and a three-point lead aren't all that different, but they're both leads. so you should be quicker than you think to snap up that first extra estate than you'd think. But the second extra is next to worthless, so you should be more hesitant to grab it. Always important though, is to watch your reshuffle and buying power. The less likely you are to see the next reshuffle, the more likely it is that you should be buying the best VP cards you can (obviously if you need to three pile or avoid three piles, this changes stuff a little). But still know the score situation - look at the case where you're basically playing big money, there are two provinces left, and you've just run the duchies out, with you being up 5-3 on duchies and even on provinces. It's the first hand of your reshuffle, and you have $6.  Nothing's happened to estates or curses since the game began. The blindly-following-rules-without-thinking player is going to buy estate here, because with only 2 provinces left, it's time to munch up estates. But that's only a rule of thumb, and it's a big mistake here - you need to grab the gold. Why? Well, if you split the provinces, you're up 6. It takes a net of 6 estates to overcome that, which means winning the race for estates 7-1 or better. That's extremely unlikely, and at any rate, you're almost assured of being able to get 2 estates later if you really need to. But the gold will really help you get that province split you need - if they 2-0 you on the last provinces, YOU need that 7-1 or better split. It's the same story if you're behind the two duchies, except that you end up needing more luck.

Of course everything changes with the cards are on the board, particularly trash-for-benefit cards like apprentice and the king endgame monkey-wrench, salvager. But that's a more complex article than this one.

Edit: fixed a typo; thanks Razzishi
« Last Edit: August 06, 2011, 08:07:16 pm by WanderingWinder »
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ARTjoMS

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Re: An Endgame Primer
« Reply #1 on: August 06, 2011, 11:48:25 am »
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A lot of obvious and trivial stuff.

I will just add that in common case where your buying power consists of money your last two shuffles probably have bigger impact on outcome than your 2nd shuffle, getting early gold might help you to accelerate advantage, but it won't do much if your money per turns in endgame are: (13 4 4) or (7 7 7) and your opponent hits (8 8 5). Or when you reshuffle your ~25 card deck and it matters in which turn you get your 8 coin, especially this is true as to who will get his savager, remodel, forge, expand, smithy, envoy etc in his hand first. What i wanted to say that there is a lot of luck involved in endgame. Really, everyone can do envoy+BM and better players don't have that much of advantage there.

WanderingWinder, i think it is more interesting as to when start buying provinces. As i remember from simulations for smithy+money tactics is better to wait until you have gold or two rather than buy province on 3/4/5 turn. With vault this probably isn't true.

Another interesting thing is what to do with 2 buys (wharves, council room) and 6-7 coin, go for gold or 2 silvers? -- gold will probably be better if your average money per card in your deck is greater than one, but this might change when we start to go green.
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WanderingWinder

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Re: An Endgame Primer
« Reply #2 on: August 06, 2011, 02:50:45 pm »
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A lot of obvious and trivial stuff.

I will just add that in common case where your buying power consists of money your last two shuffles probably have bigger impact on outcome than your 2nd shuffle, getting early gold might help you to accelerate advantage, but it won't do much if your money per turns in endgame are: (13 4 4) or (7 7 7) and your opponent hits (8 8 5). Or when you reshuffle your ~25 card deck and it matters in which turn you get your 8 coin, especially this is true as to who will get his savager, remodel, forge, expand, smithy, envoy etc in his hand first. What i wanted to say that there is a lot of luck involved in endgame. Really, everyone can do envoy+BM and better players don't have that much of advantage there.

WanderingWinder, i think it is more interesting as to when start buying provinces. As i remember from simulations for smithy+money tactics is better to wait until you have gold or two rather than buy province on 3/4/5 turn. With vault this probably isn't true.

Another interesting thing is what to do with 2 buys (wharves, council room) and 6-7 coin, go for gold or 2 silvers? -- gold will probably be better if your average money per card in your deck is greater than one, but this might change when we start to go green.

That's why it's a primer. But we've had people asking for basic stuff, so I decided to give some basic advice, especially since  I've seen a lot of people mess this stuff up, and it generally has more impact than your 'more interesting' questions.

Excellent point about the order of the last reshuffle having huge luck impact though.
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