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Author Topic: Generalisation of the Penultimate Province Rule (PPR) (edit)  (Read 1205 times)

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vsiewnar

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Generalisation of the Penultimate Province Rule (PPR) (edit)
« on: October 25, 2017, 11:01:57 pm »
+15

To begin, let us recall what the PPR states:

If you are trailing, do not buy the second-to-last Province if you can instead purchase lesser Victory card(s) to take the lead (taken from the blog in an article dated 2011)

While concise, the PPR is only applicable in a few circumstances and can result in sub-optimal choices when used outside of those circumstances. Consequently, let us look at the idea or the motivation behind the PPR with the intention of developing a greater understanding and a more general statement about endgames.

At its heart, the PPR is really warning you against putting the game in a position that allows your opponent to win i.e. meet a condition to end the game and have a victory point (VP) lead on their next turn(s). Note that in addition to an empty Province/Colony pile or an empty third supply pile, getting more than 50% of the VP (on finite VP kingdoms) is another effective end condition.

To determine whether your opponent can end the game, you should look at their ‘pile-emptying power’. ‘Pile-emptying power’ refers to their ability to move cards out of the supply i.e. empty piles which can be done by some combination of buying, gaining and trashing out of the supply. Accurately determining your opponent’s ‘pile-emptying power’ is not always easy but often manageable.

Another drawback of the PPR is that it encourages a defensive mindset for the endgame since you may end up mostly thinking about how to not lose the game. However, thinking about how to win the game is (at least) equally important. Thinking about how to win the game can start from turn 1 but let us concentrate on the endgame here. How to win may involve assessing your own ‘pile-emptying power’ and how to increase it so that you can win in the next turn(s) without allowing your opponent to win.

Another important aspect of how to win is knowing when you must take a risk to give yourself a winning chance. The risk here refers to giving your opponent some non-zero chance of winning on their next turn based on the decisions you make on your turn. The idea is that you should always give yourself the best chance of winning, regardless of how small, if a 100% win is not possible. Sometimes your best chance of winning is tiny and sometimes it is large; in both cases, you should make the appropriate decision(s) to achieve this. This decision is affected by numerous factors such as number of cards in play (especially Duration and Reserve cards), tracking the position of critical (maybe pile-emptying) cards and understanding how decks deteriorate while greening to name a few.

To summarise, perhaps a more general and more widely applicable statement of the PPR is to not put the game in a position that allows your opponent to win unless doing so gives you the best chance of winning.
« Last Edit: October 30, 2017, 03:49:20 pm by vsiewnar »
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #1 on: October 25, 2017, 11:17:46 pm »
+3

I think PPR is a great springboard to begin analyzing the state of the game as the end approaches. Basically, PPR is the "basic deck types" of how to play the endgame. In itself it falls short of giving the whole picture of what you should analyze at endgame, but it starts the discussion and piques our interest into examining how to close out a game in a way that gives you the greatest chance of winning.
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #2 on: October 25, 2017, 11:18:45 pm »
+1

Finally, the ideas here were focused on the Province pile because that has traditionally been the pile that ends the game. However, there are other piles that do this: the Colony pile and the third empty pile from the supply. The ideas here are easily transferable to the Colonies while only some of the ideas here might be applicable to the third empty pile.

Similar ideas apply when two piles are already empty but only a non-Province/Colony victory card pile is close enough to empty that a player can do it in one turn.  "Penultimate Duchy rule" or the like. 

General advice about endgames is very difficult. But you should point out that if a third pile is near empty (or one pile is empty, and other are low, etc.), you may need to get points to avoid losing to a 3-pile. How many points? Enough that your opponent can't empty the third pile and take a points lead.
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #3 on: October 25, 2017, 11:48:02 pm »
+5

Just be a man and buy that Province, you know you want to! Death or Glory!
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DG

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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #4 on: October 26, 2017, 12:14:19 am »
+1

I think there are a number of ways a player can improve their PPR decisions by knowing the quality of each deck, how the decks deteriorate when adding green cards, the possible variance of each hand and how each might generate 8 coins, tracking important cards for yourself and your opponent, thinking about shuffles, effect of attacks, changing your card play based on what you want to buy, watching the size of secondary piles like duchies, and so on. I'd like to say these are all good training for engine based endgames but a player will probably learn more from engine endgames and then take the skills back to the simpler PPR situations.
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #5 on: October 26, 2017, 12:25:41 am »
+11

I think the PPR can be generalized to the following statement: Do not put the game in a state such that your opponent can win next turn.  It's as simple as that.  I would say that this rule should be broken sometimes, but I think that in BM games the PPR should be broken sometimes too.
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #6 on: October 26, 2017, 12:33:13 am »
+8

The active approach here is sometimes underutilized in difficult positions. Sometimes you just have to threaten a win and hope that they dud.
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #7 on: October 26, 2017, 01:58:15 am »
+1

The way I've been thinking about endgames recently is that you need to think about "pile emptying power", which comes from either getting lots of money and buys, playing cards that gain other cards, or in rare cases trashing directly from the Supply (Lurker, Salt the Earth.) On a separate axis is "VP gaining power", which is how many points they can threaten to gain on their turn. The two are pretty correlated but they have their differences. For 3-pile endings in particular, the more cards you leave in the pile, the less flexibility they have in gaining VP if they want to end the game. (Unless the VP is from a VP token giving card like Goons, in which case you're just screwed.)

A good rule of thumb is that if you're behind, you should break PPR more often - that way you need to get lucky fewer times in order to win.
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #8 on: October 26, 2017, 06:17:47 am »
+2

I think the PPR can be generalized to the following statement: Do not put the game in a state such that your opponent can win next turn.  It's as simple as that.

This.
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #9 on: October 26, 2017, 10:47:53 am »
+2

I think the PPR can be generalized to the following statement: Do not put the game in a state such that your opponent can win next turn.  It's as simple as that.
The simplest statement is surely "do things that increase your chance of winning and avoid things that reduce it".

The endgame problem is complicated by the lack of certainty about what your opponent will be able to do on their turn. If you're 100% sure they'll buy exactly one Province and do nothing else, fine. But what if there's, say, a 30% chance they'll be able to buy a Province?
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #10 on: October 26, 2017, 11:13:25 am »
+2

I think the PPR can be generalized to the following statement: Do not put the game in a state such that your opponent can win next turn.  It's as simple as that.  I would say that this rule should be broken sometimes, but I think that in BM games the PPR should be broken sometimes too.

The biggest caveat to emphasize is that this is only a hard rule if you are reasonably certain they will end it next turn. There are plenty of situations where you should buy the second to last Province if their chances of dudding are bigger than your chances of coming back if you get a Duchy etc
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #11 on: October 26, 2017, 11:33:47 am »
+2

For the record, here's how I worded the PPR a while ago:

the idea of paying attention to what your opponent's deck can do and making sure you don't accidentally leave the supply in a state where the opponent can end the game and win on their turn (and knowing when you have to do that on purpose and just hope for the best)
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #12 on: October 26, 2017, 04:17:16 pm »
+5

I think the PPR can be generalized to the following statement: Do not put the game in a state such that your opponent can win next turn.  It's as simple as that.  I would say that this rule should be broken sometimes, but I think that in BM games the PPR should be broken sometimes too.

What is great about the concept of PPR as initially described (literally second to last Province) is that it is a concrete example of this principle in action. It's a scenario that is easy to identify when it happens (especially thanks to the VP counter), and a clear course of action is proposed ("Duchy dancing").

You can take a look at any "forced win" puzzles to understand that not putting the game in a state where your opponent can win is not always easy. Identifying these scenarios is not enough on its own to win the game though, because sometimes you have a better chance of winning by breaking the rule and "getting the Penultimate Province", hoping that your opponent doesn't draw the win.

Sometimes the "PPR" actually relates to the kingdom supply pile when there are lots of gains available but no one has a lot of points. In these cases, you might get a "Province Dancing" scenario. Maybe this is familiar to you as well.

In fact, preparing for the Province Dancing scenario in advance can be what gives you the win. A player could have a way to get a lot of cards from the supply, but cannot do so while gaining a Province due to lack of economy or whatnot. The other player having a similar gain potential, maybe a bit less, but having a bit more economy to buy a Province or other VP card could have a real advantage in these games.
« Last Edit: October 26, 2017, 04:20:50 pm by markusin »
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #13 on: March 18, 2018, 06:09:16 pm »
+2

Sometimes you just have to threaten a win and hope that they dud.

In addition, sometimes you know if you're opponent has a dud; reveal-their-hand, they caused a shuffle when they shouldn't have, etc.
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Re: Generalisations of the Penultimate Province Rule (PPR)
« Reply #14 on: March 22, 2018, 03:01:47 pm »
0

The active approach here is sometimes underutilized in difficult positions. Sometimes you just have to threaten a win and hope that they dud.

I had this happen just the other night. There were 2 Colonies left. I was down 4 Colonies to 2. I could have bought a Colony and a  Province, but went with 2 Provinces instead hoping she would only be able to buy one Colony the next turn. (She only had one card in her hand with +buy.) Instead, she hit that card and was able to buy both Colonies. She only won by 5. I believe she still would have won, but barely, and if her hand had only given enough for a Colony and Duchy, I would have won. So I have decided to try being more aggressive in those PPR situations and see what happens.
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