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Dominion Articles / Estimating Basic Engines
« on: November 08, 2014, 12:05:57 pm »
I found myself wondering how effective a very basic engine could be, i.e. one that uses only three different cards. Since engines usually require 4 things, namely trashing, villages, draw and payload, there need to be cards that can do several of these things. Cards such as Steward.
On a very basic version it would only desire any village to be an engine on it's own. Yet, this would be a very bad engine since it needs to gain at leats 10 cards before greening and it can't green very well. It also needs 5 turns of trashing your 10 starting cards, so you could maybe hope to be ready around turn 11 or 12 to pick up one Province per turn. Too late for many other strategies. You could, of course, add attack cards to slow down your opponent. However, I wondered if some simple gaining like workshop would be enough to catch up.
It's pretty obvious that every card potentially strengthens this engine, but I wonder wether the bsic version consisting only of Steward, Village and Workshop would be good enough to compete against Big Money strategies. Maybe you need to exchange village and replace it by farming village (you don't want to draw green cards once you start greening).
Is there any estimation of what can be worth it or how much it takes to be worth going for the engine - especially without +buy?
On a very basic version it would only desire any village to be an engine on it's own. Yet, this would be a very bad engine since it needs to gain at leats 10 cards before greening and it can't green very well. It also needs 5 turns of trashing your 10 starting cards, so you could maybe hope to be ready around turn 11 or 12 to pick up one Province per turn. Too late for many other strategies. You could, of course, add attack cards to slow down your opponent. However, I wondered if some simple gaining like workshop would be enough to catch up.
It's pretty obvious that every card potentially strengthens this engine, but I wonder wether the bsic version consisting only of Steward, Village and Workshop would be good enough to compete against Big Money strategies. Maybe you need to exchange village and replace it by farming village (you don't want to draw green cards once you start greening).
Is there any estimation of what can be worth it or how much it takes to be worth going for the engine - especially without +buy?
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Dominion General Discussion / How to play a with mirror as P2
« on: April 28, 2014, 10:33:45 am »
The discussion about T1 M ountebank opening in this thread has made me think about the odds of player 2 in a mirror match with $5 power cards such as Witch.
Of course, it matters a lot which other cards are available. Let's first assume there are only non-drawing $2 cards (and no Cellar).
Let player 1 open witch and an arbitrary $2 card. I'm going to invest the odds of cursing before the second shuffle.
a) You mirror P1 and open Witch/$2-card.
- There is a 2/12 cahnce for your witch to miss the first shuffle. P1 can play his Witch either n T3 or T4 and still curse you before your shuffle.
- There is a 5/12 chance your Witch appears on T4. In this case you curse after the reshuffle of P1 and P1 still has the chance to curse you on T3 or T4.
- There is a 5/12 chance your Witch appears on T3. In this case you curse P1 before his shuffle and he has still the chance to curse you on T3 or on T4.
--> odds of getting a curse before your reshuffle: 10/12 = 83% (P1 Witch doesn't miss the shuffle)
--> odds of dealing a curse before his reshuffle: 5/12 + 5/12*2/12 = 49%
b) You open Witch/nothing
- 1/11 chance for your Witch to miss the shuffle.
- 5/11 chance for your Witch to appear on T3. P1 now only has T3 left to deal his curse before your reshuffle. There is a ~1/9 chance for your Witch to appear again on T4 (top card of your shuffle).
- 5/11 chance for your witch to appear on T4. P1 has both, T3 and T4 for his cursing AND you Witch misses the shuffle. At least, you will deal the curse before his shuffle with a probability of 2/12.
--> odds of getting a curse before the shuffle: 6/11*10/12 + 5/11*5/12 = 85/132 = 64%
--> odds of dealing a curse before the shuffle: 5/11 + 5/11*2/12 = 35/66 = 53%
--> odds of your witch missing the next (9-card) shuffle: 6/11*10/12 = 10/22 = 45%
Actually this can be good if you hit $5 with your T4 Witch, so you can safely buy another Witch or another $4 terminal that is worth getting.
c) You open Witch/Cantrip
- There is a ~1/12 + 1/12*1/11 = 1/11 chance for your Witch to miss the shuffle (exceptions below).
- If you play your Cantrip before the Witch, you are sure to reshuffle before T5. Whether this is good really depends on when you play your Witch. With a Witch/Cantrip hand on T3 you should play the Cantrip, same hand on T4 and you probably shouldn't because it would make your Witch miss the shuffle. Only Cantrip on T3 is a tough call. You can decrease the odds for your Witch to miss T4, but you greatly increase the chance for your Witch to miss the next shuffle.
- There also is a slight chance to draw your Cantrip dead (Should be around 2/12). Drawing it dead on T3 is bad, but drawing it dead on T4 is mostly good.
All in all, I'd say that a Cantrip is mostly a clever buy, because you can chose to activate it - or not to.
Special $2 cards:
Pearl Diver - guarantees to play your Witch until T4 unless both cards are at the bottom of your shuffle or Witch is your bottom card and Pearl Diver doesn't appear on T3. [corrected]
Vagrant - has the potential to draw two cards - one of which is a bad one. Very good, as it gets those curses out of your sight.
Haven - helps you getting $5 if your Witch appears on T4 (~5/12).
Cellar - must-buy unless there is...
Chapel - must-buy
Pawn - worth buying, maybe worth trying $ and card just to get $5.
Lighthouse - maybe Witch isn't that great anymore...
Hamlet - doesn't provide direct benefit other than being a Cantrip at first. Very good, if your going to build an engine later on.
Crossroads - potential to draw up to three cards. Can be tricky and gets less useful later on unless your going to slog (silk raod or gardens) or need a village for an engine.
Fool's Gold - very likely a must-buy. Yet, less great with all these curses.
Beggar - Anti-cycling on opponent's attack, but provides economy. Great for slogs, otherwise pretty awful. At least, it let's you spike a second witch almost certainly - at the cost of 3 more Coppers. Again, great in Slogs, bad otherwise.
Candlestick Maker - helps you get $5 or $6
Duchess - Only useful for P2. Discard anything but your witch. Also helps your opponent a bit.
Of course, it matters a lot which other cards are available. Let's first assume there are only non-drawing $2 cards (and no Cellar).
Let player 1 open witch and an arbitrary $2 card. I'm going to invest the odds of cursing before the second shuffle.
a) You mirror P1 and open Witch/$2-card.
- There is a 2/12 cahnce for your witch to miss the first shuffle. P1 can play his Witch either n T3 or T4 and still curse you before your shuffle.
- There is a 5/12 chance your Witch appears on T4. In this case you curse after the reshuffle of P1 and P1 still has the chance to curse you on T3 or T4.
- There is a 5/12 chance your Witch appears on T3. In this case you curse P1 before his shuffle and he has still the chance to curse you on T3 or on T4.
--> odds of getting a curse before your reshuffle: 10/12 = 83% (P1 Witch doesn't miss the shuffle)
--> odds of dealing a curse before his reshuffle: 5/12 + 5/12*2/12 = 49%
b) You open Witch/nothing
- 1/11 chance for your Witch to miss the shuffle.
- 5/11 chance for your Witch to appear on T3. P1 now only has T3 left to deal his curse before your reshuffle. There is a ~1/9 chance for your Witch to appear again on T4 (top card of your shuffle).
- 5/11 chance for your witch to appear on T4. P1 has both, T3 and T4 for his cursing AND you Witch misses the shuffle. At least, you will deal the curse before his shuffle with a probability of 2/12.
--> odds of getting a curse before the shuffle: 6/11*10/12 + 5/11*5/12 = 85/132 = 64%
--> odds of dealing a curse before the shuffle: 5/11 + 5/11*2/12 = 35/66 = 53%
--> odds of your witch missing the next (9-card) shuffle: 6/11*10/12 = 10/22 = 45%
Actually this can be good if you hit $5 with your T4 Witch, so you can safely buy another Witch or another $4 terminal that is worth getting.
c) You open Witch/Cantrip
- There is a ~1/12 + 1/12*1/11 = 1/11 chance for your Witch to miss the shuffle (exceptions below).
- If you play your Cantrip before the Witch, you are sure to reshuffle before T5. Whether this is good really depends on when you play your Witch. With a Witch/Cantrip hand on T3 you should play the Cantrip, same hand on T4 and you probably shouldn't because it would make your Witch miss the shuffle. Only Cantrip on T3 is a tough call. You can decrease the odds for your Witch to miss T4, but you greatly increase the chance for your Witch to miss the next shuffle.
- There also is a slight chance to draw your Cantrip dead (Should be around 2/12). Drawing it dead on T3 is bad, but drawing it dead on T4 is mostly good.
All in all, I'd say that a Cantrip is mostly a clever buy, because you can chose to activate it - or not to.
Special $2 cards:
Pearl Diver - guarantees to play your Witch until T4 unless both cards are at the bottom of your shuffle or Witch is your bottom card and Pearl Diver doesn't appear on T3. [corrected]
Vagrant - has the potential to draw two cards - one of which is a bad one. Very good, as it gets those curses out of your sight.
Haven - helps you getting $5 if your Witch appears on T4 (~5/12).
Cellar - must-buy unless there is...
Chapel - must-buy
Pawn - worth buying, maybe worth trying $ and card just to get $5.
Lighthouse - maybe Witch isn't that great anymore...
Hamlet - doesn't provide direct benefit other than being a Cantrip at first. Very good, if your going to build an engine later on.
Crossroads - potential to draw up to three cards. Can be tricky and gets less useful later on unless your going to slog (silk raod or gardens) or need a village for an engine.
Fool's Gold - very likely a must-buy. Yet, less great with all these curses.
Beggar - Anti-cycling on opponent's attack, but provides economy. Great for slogs, otherwise pretty awful. At least, it let's you spike a second witch almost certainly - at the cost of 3 more Coppers. Again, great in Slogs, bad otherwise.
Candlestick Maker - helps you get $5 or $6
Duchess - Only useful for P2. Discard anything but your witch. Also helps your opponent a bit.
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Dominion General Discussion / How important is cycling?
« on: February 05, 2014, 07:41:58 am »
First of all, hello to everybody, as I'm new to this forum.
Lately, I've thought about cellar being one of these cards, players tend to ignore (except for tunnel/cellar combo). This also applies to the qvist ranking, where cellar takes a rather boring place (10th-13th). The card description on dominionstrategy talks a bit about synergies with non-terminal card drawers like laboratories.
Figuring out whether these cases are the only ones where cellar can shine, I generalized the question to: "How much does it help to cycle through your deck?" or rather "In which cases..."
I ended up thinking, that cycling helps you to play your action cards more often wihtout the risk of collisions.
So, generally speaking, cycling cards like cellar, inn, warehouse and so on help strategies with terminals you want to play as often (or as soon) as possible. Such terminals would especially be cursers, but also stuff like monument or bishop.
I guess one big letdown is, that engine decks allow you to play these cards even more than once per turn. Still, if I am planning any engine, say around bishop, is it then a mistake to open bishop/cellar? Is it worth to cycle through your deck, just to play that card more often?
In a 2-player-match you can take about 15-20 turns. In any non-enginge-deck you would play a card no more than 6 times, I guess. With cellars, you could play your favorite card about nearly every turn, at least 12 times, I guess. Is this worth the investment (i.e. the opportunity cost of not buying a silver)?
Lately, I've thought about cellar being one of these cards, players tend to ignore (except for tunnel/cellar combo). This also applies to the qvist ranking, where cellar takes a rather boring place (10th-13th). The card description on dominionstrategy talks a bit about synergies with non-terminal card drawers like laboratories.
Figuring out whether these cases are the only ones where cellar can shine, I generalized the question to: "How much does it help to cycle through your deck?" or rather "In which cases..."
I ended up thinking, that cycling helps you to play your action cards more often wihtout the risk of collisions.
So, generally speaking, cycling cards like cellar, inn, warehouse and so on help strategies with terminals you want to play as often (or as soon) as possible. Such terminals would especially be cursers, but also stuff like monument or bishop.
I guess one big letdown is, that engine decks allow you to play these cards even more than once per turn. Still, if I am planning any engine, say around bishop, is it then a mistake to open bishop/cellar? Is it worth to cycle through your deck, just to play that card more often?
In a 2-player-match you can take about 15-20 turns. In any non-enginge-deck you would play a card no more than 6 times, I guess. With cellars, you could play your favorite card about nearly every turn, at least 12 times, I guess. Is this worth the investment (i.e. the opportunity cost of not buying a silver)?
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