Dominion Strategy Forum

Dominion => Dominion General Discussion => Topic started by: WanderingWinder on September 22, 2011, 12:07:24 pm

Title: Can there be a second-player Advantage?
Post by: WanderingWinder on September 22, 2011, 12:07:24 pm
This has come up in several other places, and I think it deserves its own thread. Is there any board with dominion cards currently in print that lead to a second-player advantage? We've yet to find one, but I think one exists.
I think the most likely thing is that there's some Rock-Paper-Scissors scenario out there that is big enough that taking a wait-and-see approach is bad and making a fist commitment is also bad. We haven't found one yet.

My first best guess: Minion/Horse Traders/BM
Title: Re: Can there be a second-player Advantage?
Post by: DStu on September 22, 2011, 12:14:07 pm
From the last thread, as I think it is good to know where you have to look (or especially where not)

The first logical consideration is that the first player can possibly either (1) buy nothing or (2) buy a silver just to pass any "first player penalty" onto the next player. Any solution kingdom needs to prevent this by making every available supply card a game losing purchase but still not as bad as buying nothing at all. While this might seem like a minor point, it may restrict the solution kingdoms to such a degree that any second player advantage has negligable effect.

I don't think it's a minor point, it greatly limits the search space...
Assume for simplicity that we would reshuffle after each turn and the winning condition would be symmetric (i.e. not differntiate if you where first or second player), which are I think the only things that prefend this from being a proof.
Then buying nothing at all would just swap the positions. By buying nothing the second player is in exactly the same position as you where before. By assumption every move he can make is a winning move for you (including, by assumption, doing nothing), which contradicts the assumption.

So under the simplifications such a board can not exist, that means that, if such a board exists the second player advantage must either involve the shuffling or is limited by the "second player compensation".
Title: Re: Can there be a second-player Advantage?
Post by: DStu on September 22, 2011, 12:15:52 pm
My first best guess: Minion/Horse Traders/BM

You think that "wait-and-see" on BM is not possible here to switch to HT if the other guys goes Minion?
Title: Re: Can there be a second-player Advantage?
Post by: Empathy on September 22, 2011, 09:31:10 pm
From the last thread, as I think it is good to know where you have to look (or especially where not)

The first logical consideration is that the first player can possibly either (1) buy nothing or (2) buy a silver just to pass any "first player penalty" onto the next player. Any solution kingdom needs to prevent this by making every available supply card a game losing purchase but still not as bad as buying nothing at all. While this might seem like a minor point, it may restrict the solution kingdoms to such a degree that any second player advantage has negligable effect.

I don't think it's a minor point, it greatly limits the search space...
Assume for simplicity that we would reshuffle after each turn and the winning condition would be symmetric (i.e. not differntiate if you where first or second player), which are I think the only things that prefend this from being a proof.
Then buying nothing at all would just swap the positions. By buying nothing the second player is in exactly the same position as you where before. By assumption every move he can make is a winning move for you (including, by assumption, doing nothing), which contradicts the assumption.

So under the simplifications such a board can not exist, that means that, if such a board exists the second player advantage must either involve the shuffling or is limited by the "second player compensation".

The thing that makes the reasoning break down (in a very limited number of cases, granted) is the fact that you don't reshuffle on your first turn. There is an incentive to break the "see and wait" depending on how many turns you have until the reshuffle. I'm not sure however if you want to maximize your "powerful" cards present after the first reshuffle or minimize the ability of your opponent to counter your strategy due to reshuffle.

To give an example, if p1 skips his first turn, so can p2. Then p1 skips again, and p2 can buy a card on his t2. p1 cannot counter whatever strategy p2 chose until his next reshuffle (giving p2 a whole cycle as a head start).

Still, I believe this is a very niche scenario. In most cases, p1 just has a big advantage over p2.
Title: Re: Can there be a second-player Advantage?
Post by: ehunt on September 22, 2011, 09:51:14 pm
I was very happy not too long ago to go second in a set with familiar, remake, and fishing village/wharf/talisman/treasuremap, which had a similar rock-paper-scissors like feel in terms of the opening 4 buy.

Similar feelings in young witch games with bad or mediocre bane cards.
Title: Re: Can there be a second-player Advantage?
Post by: Davio on September 23, 2011, 03:48:05 am
I was very happy not too long ago to go second in a set with familiar, remake, and fishing village/wharf/talisman/treasuremap, which had a similar rock-paper-scissors like feel in terms of the opening 4 buy.

Similar feelings in young witch games with bad or mediocre bane cards.
When I go second and have 4/3 and I only want a $3-costing card (Masquerade, Steward, Ambassador, that sort of thing), I often use my first buy (whether $4 or $3) for a Silver to keep my opponent guessing about my second purchase.

Obviously, this doesn't work with 5/2 or when you want a $4-card.
Title: Re: Can there be a second-player Advantage?
Post by: Empathy on September 23, 2011, 09:30:08 am
You could also just play 2 coppers to make the other player believe you have a 5 hand?

He might catch the fact that you are playing your coppers one by one, however.

I'm too lazy to do this systematically, but I thought it might be an unfair mind trick.
Title: Re: Can there be a second-player Advantage?
Post by: barsooma on September 23, 2011, 09:41:16 am
You could also just play 2 coppers to make the other player believe you have a 5 hand?

He might catch the fact that you are playing your coppers one by one, however.

I'm too lazy to do this systematically, but I thought it might be an unfair mind trick.

This is dead obvious on isotropic, but it would be fun to have a "play selected money" option for bluffs like that.
Not sure it is useful enough to be worth programming / gumming up the UI though.
Title: Re: Can there be a second-player Advantage?
Post by: Geronimoo on September 23, 2011, 09:52:35 am
When the difference between your isotropic level and your opponent's is big (say 15+ points), it's very likely your lower level opponent will just follow your lead, thereby constructing the same, likely close to optimal, deck reducing the better player's win rate. If the better player is in second position, the worse player has an opportunity to make a sub-optimal first buy and stick with his sub-optimal plan thereby greatly increasing the better player's win rate despite being in second position.
Title: Re: Can there be a second-player Advantage?
Post by: Captain_Frisk on September 23, 2011, 12:12:43 pm
Situations I can think of where being second player might have an advantage:

Embargo + alchemy - if your opponent goes potion you can slap down an embargo on that alchemist... and if your opponent doesn't buy embargo, you might decide to go alchemist instead.  Embargo wouldn't stop me from going familiar though.

The previously mentioned young witch / bane card.  If the bane card is sub-optimal you can use the "2nd player advantage" to know whether or not its utility has increased.

I'm not certain that either of those actually make up for the possibility of having one less turn than your opponent, although I suspect that there exists some set of 10 for which a 2nd player advantage truly exists.
Title: Re: Can there be a second-player Advantage?
Post by: danshep on September 24, 2011, 12:46:54 am
When the difference between your isotropic level and your opponent's is big (say 15+ points), it's very likely your lower level opponent will just follow your lead, thereby constructing the same, likely close to optimal, deck reducing the better player's win rate. If the better player is in second position, the worse player has an opportunity to make a sub-optimal first buy and stick with his sub-optimal plan thereby greatly increasing the better player's win rate despite being in second position.

I believe that this is correct - When I was lower ranked (not that I'm a star now), I would win most often in second place due to seeing my opponent's strategy, following him into it and then managing to pull it off better (or have better luck).
Title: Re: Can there be a second-player Advantage?
Post by: PSUmvp on September 24, 2011, 08:37:35 am
I think there is a huge advantage to going second with ambassador and marginal $4 cards.  If you can get out of the first two turns and take two ambassadors while your opponent only takes one, you can almost definitely overload their deck.  It becomes even more pronounced if there is a +action card, which ultimately lets you reduce your entire deck, take a curse and give all of them to your opponent.

If you go first in an ambassador game and take one on each of your first two turns, it is a lock that your opponent will as well.  They likely will anyways on turns 3 or 4 in reaction to your doubling up.  But if the shuffle is right, it may be too late for them.
Title: Re: Can there be a second-player Advantage?
Post by: DG on September 24, 2011, 11:00:47 am
Quote
I think there is a huge advantage to going second with ambassador and marginal $4 cards.

There is actually a very large disadvantage to going second with ambassadors in the set. If your ambassador is drawn on turn 4, your opponent could already have shuffled up a small deck before you give them your cards. The same problem could hit the next shuffle, or the one after that. If you simulate a kingdom with just ambassadors and labs (a good basic strategy) you'll find that it gives one of the strongest first player starts.

Quote
If you can get out of the first two turns and take two ambassadors while your opponent only takes one, you can almost definitely overload their deck.

This comes across as "if the first player buys the wrong cards then the second player can buy the right cards and has an advantage". Did you mean something else?
Title: Re: Can there be a second-player Advantage?
Post by: DG on September 24, 2011, 12:13:29 pm
In fact, if I remember correctly there were once some statistics collected about the success of cards as first and second seat openings. It was quite a weird collection of cards that fared better in second seat. Some could be explained as being a good response to an opponent's buy (secret chamber), some were never fully explained (navigator), and then there was also the bishop. The bishop appears to give a lot of information to an opponent that could help second player decisions (single bishop vs single smithy should be a win for smithy).

Perhaps however there is also an intrinsic second player advantage for the bishop when trashing cards on turn 4. A card trashed by the first player due to a second player's bishop will already have been included in the reshuffle. This minor speed advantage for the second player may mitigate first player advantage, especially repeated over a number of a shuffles. Unfortunately since victory point scoring can change end game strategies, it might be difficult to clearly analyse the subtleties of the bishop.
Title: Re: Can there be a second-player Advantage?
Post by: PSUmvp on September 24, 2011, 01:44:07 pm
I stand by it...  Buying 1 ambassador isn't necessarily the wrong move, until your opponent has 2.  Going in the second position allows you to take the second one even if they don't.  If you take two from the first position, there is no way your opponent doesnt also take 2.  As with anything it is all about the first shuffle, but if I can go into turn 3 up 2 ambassadors to 1, I think it is an advantage.  That isn't possible from the first position.
Title: Re: Can there be a second-player Advantage?
Post by: ackack on September 24, 2011, 01:47:10 pm
I stand by it...  Buying 1 ambassador isn't necessarily the wrong move, until your opponent has 2.  Going in the second position allows you to take the second one even if they don't. If you take two from the first position, there is no way your opponent doesnt also take 2.  As with anything it is all about the first shuffle, but if I can go into turn 3 up 2 ambassadors to 1, I think it is an advantage.  That isn't possible from the first position.

It only isn't possible if your bolded assumption is correct. I really don't think it is, and I don't think the "second Ambassador before turn 3 or after?" question has ever been settled.
Title: Re: Can there be a second-player Advantage?
Post by: guided on September 25, 2011, 10:30:16 pm
As a general rule, I will happily open Ambassador/Silver (or Ambassador/something else) while my opponent opens Ambassador/Ambassador, then get another Ambassador at turn 3 or 4.

Actually forget I told you that! Feel free to open double Ambassador against me any time.
Title: Re: Can there be a second-player Advantage?
Post by: Empathy on September 26, 2011, 06:04:25 am
Double trasher (without benefit) is indeed a bad opening. There is such a thing as tempo, and having some buying power helps. Double ambassador sounds like a chapel+island opening to me. Looks cool in theory but loses empirically. *pokes guided*
Title: Re: Can there be a second-player Advantage?
Post by: AJD on September 26, 2011, 08:39:27 am
How do you feel about double Ambassador opening against Sea Hag? If your opponent opens Sea Hag there's less of a comparative tempo loss and greater importance to fast trashing.
Title: Re: Can there be a second-player Advantage?
Post by: Empathy on September 26, 2011, 08:59:04 am
I agree. I don't know what to answer though, because the whole seahag ambassador business seems like one of those games where whoever actually manages to get himself out of the money lock will probably win.

It's like when I open 5/2 in second position on a board with sea hag and no 2 drop.

If I follow sea-hag + silver by sea hag (which might be in vacuum the best choice if there is no cursing or trashing card at 5), then I will be a silver and a turn behind. Given that I will be getting curses + the sea hag won't give me $, I could stay locked away from money for potentially a long time...

So I always feel queezy about locking myself away from money without seeing a clear exit out. Now if there is a feast and a decent 5$ money card, that's a different story.

I'll try to find an old game on mine again where the board was essentially sea-hag/tactician/bank (and some non-descript card). I opened 5/2 on second turn and decided to give tact+bank a chance, knowing that I would definitely lose the sea hag race (no source of money at 5).
Title: Re: Can there be a second-player Advantage?
Post by: DG on September 26, 2011, 09:00:54 am
Timing and number of ambassadors depends upon the rest of the kingdom, always, since the ambassadors don't buy you provinces. You need other cards to do that.

Since we're not getting far with the second player kingdom, I'll suggest this one (without any testing) and maybe someone can improve on it.

Warehouse, Smithy, Coppersmith, Pirate Ship, Conspirator, Spy, Counting House, Harem, Grand Market, Bank
Title: Re: Can there be a second-player Advantage?
Post by: WanderingWinder on September 26, 2011, 09:23:14 am
Double Ambassador opening is something I go with if you've got some kind of village on the board, not otherwise. But its not entirely clear from anything I've seen, either way.
Title: Re: Can there be a second-player Advantage?
Post by: chwhite on September 26, 2011, 09:32:04 am
My default assumption is to open double Ambassador rather than Ambassador/Silver, and it's served me quite well.  If the two Ambassadors clash, then yes there's a good chance you're sunk, but if you can hit on both Turns 3 and 4 (and that's more likely) it's a huge advantage.

Obviously, there are cards I will pick up instead of the second Ambassador: Tournament, Caravan, Potion (if Apothecary is around), probably Lighthouse and Fishing Village...

...

I suspect a board with Ambassador, Horse Traders, and Gardens might have a second-player advantage, as Horse Traders/Gardens is strong when your opponent is Ambassadoring and weak otherwise.
Title: Re: Can there be a second-player Advantage?
Post by: WanderingWinder on September 26, 2011, 09:47:51 am
My default assumption is to open double Ambassador rather than Ambassador/Silver, and it's served me quite well.  If the two Ambassadors clash, then yes there's a good chance you're sunk, but if you can hit on both Turns 3 and 4 (and that's more likely) it's a huge advantage.

Obviously, there are cards I will pick up instead of the second Ambassador: Tournament, Caravan, Potion (if Apothecary is around), probably Lighthouse and Fishing Village...

...

I suspect a board with Ambassador, Horse Traders, and Gardens might have a second-player advantage, as Horse Traders/Gardens is strong when your opponent is Ambassadoring and weak otherwise.

Well, I'm not so sure this is weak otherwise with nothing else around - you need something of the right strength to make it powerful enough to beat HT/Gardens, but not too strong to make one of the other options unplayable against it. Maybe just bishop is enough.
Title: Re: Can there be a second-player Advantage?
Post by: rinkworks on September 26, 2011, 10:26:33 am
I really think Ambassador/Ambassador vs. Ambassador/Silver is, generally speaking, so close in power level that the variance in shuffle luck dwarfs whatever modest mathematical advantage there might be one way or the other.

Regardless of which might be preferable, both are elite openings.  Ambassador/Ambassador is not at all weak, and the councilroom opening stats bear this out.

Although "don't open double trasher" is a good maxim, it's not an iron-clad rule.  Ambassador/Ambassador works because on Ambassador boards you probably have a lot more to trash, as you're getting junk cards passed back to you.  (There are also exceptions like Chapel/Bishop, too.)
Title: Re: Can there be a second-player Advantage?
Post by: DG on September 26, 2011, 10:46:37 am
Quote
Although "don't open double trasher" is a good maxim, it's not an iron-clad rule.


Is it even a good maxim once you look beyond chapels?
Title: Re: Can there be a second-player Advantage?
Post by: Empathy on September 26, 2011, 10:48:56 am
Maybe I went a bit overboard with trashing the double trashing argument.

My maxim is more around the lines "make sure you get a source of money at some reasonable point". Ambassador and chapel both have this weakness of basically making you skip your turn when they are most effective (double/quadruple trash). It's a powerful turn, but you can get royally screwed if you're not careful (or get disrupted: militia hurts a hand with ambassador + 1 estate +1 silver +2 coppers).

Trash for benefit are great as secondary trashers: apprentice, bishop, remake, remodel and salvager all work really well with chapel/ambassador as your main trasher. Bishop is probably the best because you're really using the fact that the other guy is probably also trashing like mad and not getting the benefit from your bishop. Though salvager/remodel have something to say about getting you out of the money trap.

I'll happily get a salvager to complement my first ambassador rather than a second ambassador. I'll only ambassador coppers, and salvage estates. If the other guy ambassador's his coppers, he's not going to lift off the ground any time soon, and if he just ships me an estate a turn, I'm completely fine with that.

It's a very specific example, I agree.It's just that for newer players, reading lines like "open double ambassador" can be misleading. They will not play it out properly, even when it is the right call to make.
Title: Re: Can there be a second-player Advantage?
Post by: rinkworks on September 26, 2011, 11:00:39 am
Ah, I see what you're getting at.  Makes sense.

It's  certainly easy to mistakeningly trash too heavily in the first few turns.  I've played enough to watch out for that, and I still occasionally find myself wondering where my third-to-last Copper went.
Title: Re: Can there be a second-player Advantage?
Post by: rod- on September 26, 2011, 12:06:25 pm
I suspect a board with Ambassador, Horse Traders, and Gardens might have a second-player advantage, as Horse Traders/Gardens is strong when your opponent is Ambassadoring and weak otherwise.
But is the following line really an advantage to the 2nd player?
1) ambassador
2) horse traders
3) silver
4) (silver?)
5-6) ambassador 2 estates, buy silver (or lucky 2 silvers),(2p:buy 2 horse traders)
7+) stop ambassadoring due to horse traders, steal 1 gardens and just go big money because you know you can get 4provinces and presumably a tiebreaker duchy before they empty estates/ht/gardens (that's 23 more buys because you added 1 estate to the pile - 12 more turns if the gardens player is lucky enough to draw horse traders every turn despite buying tons of estates early on - not to mention how hard it is to come across 6$ hands with only 1 silver in your deck)

Turn 19 is a bit slow, and i can't seem to make it work any faster for mr. gardens...am i off?  I understand that ambassador doesnt always(or really all that often) hit 2 estates, but 18 turns for 4 provinces is still pretty easy even with the normal 3 dead cards in deck.

I suppose i'm assuming that this gardener doesn't hit 40 cards, which may be inaccurate.  (12 estates, 7 coppers, 10 horse traders, 7 gardens, and 4 random coppers?)
Title: Re: Can there be a second-player Advantage?
Post by: Captain_Frisk on September 26, 2011, 01:04:59 pm
This is a long long long shot, but what about Jester?

A 2nd player's jester played played on turn 4 (in most normal situations) 4 cards out of 14 that you could potentially want, while player 1 can only hit 2 cards.

I seriously doubt if that is enough to make up for the fewer turns issue, and of course the 1st player has a chance to Jester 2p's jester before he can even play it... but i figured i'd throw it out there.
Title: Re: Can there be a second-player Advantage?
Post by: Empathy on September 26, 2011, 01:08:24 pm
On a similar note, how does smuggler fare depending on table position?

I know it's an ok counter as p1 when the other person opens with 2 coppers. (because of the random chance of stealing his 5 on t3).
Title: Re: Can there be a second-player Advantage?
Post by: chwhite on September 26, 2011, 01:19:17 pm
I suspect a board with Ambassador, Horse Traders, and Gardens might have a second-player advantage, as Horse Traders/Gardens is strong when your opponent is Ambassadoring and weak otherwise.
But is the following line really an advantage to the 2nd player?
1) ambassador
2) horse traders
3) silver
4) (silver?)
5-6) ambassador 2 estates, buy silver (or lucky 2 silvers),(2p:buy 2 horse traders)
7+) stop ambassadoring due to horse traders, steal 1 gardens and just go big money because you know you can get 4provinces and presumably a tiebreaker duchy before they empty estates/ht/gardens (that's 23 more buys because you added 1 estate to the pile - 12 more turns if the gardens player is lucky enough to draw horse traders every turn despite buying tons of estates early on - not to mention how hard it is to come across 6$ hands with only 1 silver in your deck)

Turn 19 is a bit slow, and i can't seem to make it work any faster for mr. gardens...am i off?  I understand that ambassador doesnt always(or really all that often) hit 2 estates, but 18 turns for 4 provinces is still pretty easy even with the normal 3 dead cards in deck.

I suppose i'm assuming that this gardener doesn't hit 40 cards, which may be inaccurate.  (12 estates, 7 coppers, 10 horse traders, 7 gardens, and 4 random coppers?)

I tend to think of Horse Traders/Gardens as more of a hybrid strategy that takes its time to grab Duchies too and doesn't just rush the Estates.  And if you only play Ambassador once or twice, then go BM and stop using it out of fear of HT, then you've more or less wasted your opening buy, and are going to be really slow.