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Author Topic: Is Workshop Garden in more than 2 player games a prisoner's dilemma?  (Read 1042 times)

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Floing

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Hello,

We play casually with 3 to 4 people (only have the basegame) and the last times Workshop+Garden was in the kingdom
it was either only one person going for it and winning or multiple people going for it and placing last and second to last.
Is this a prisoner's dilemma where the options are either someone taking a very likely loss by contesting gardens or allowing the gardens player to win?
I'd appreciate advice on this an I am sorry if there are obvious resources on this I overlooked (most only dealt with 2 player games).
« Last Edit: July 06, 2019, 06:36:35 pm by Floing »
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Titandrake

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #1 on: July 06, 2019, 09:52:18 pm »
+6

Hello,

We play casually with 3 to 4 people (only have the basegame) and the last times Workshop+Garden was in the kingdom
it was either only one person going for it and winning or multiple people going for it and placing last and second to last.
Is this a prisoner's dilemma where the options are either someone taking a very likely loss by contesting gardens or allowing the gardens player to win?
I'd appreciate advice on this an I am sorry if there are obvious resources on this I overlooked (most only dealt with 2 player games).

I'm not sure if Prisoner's Dilemna is the exact right word for it, but multiplayer does have this property.

For example, suppose the kingdom has a deck that supports an engine that beats a simpler treasure-based approach, but only if the engine gets to 7 Villages. In a 2-player game, if one player goes for the engine and the other player doesn't, the engine wins. In a 3-player game, if two players compete on the Villages, the 3rd player who doesn't compete on them gets the win instead.

Because of this, multiplayer tends to involve more posturing: buying cards that could lead into two possible strategies, and delaying which one you commit to until after you see what the other players are doing. The problem is that the later you commit, the worse your deck is.

There is a short series of articles about the difference between 2-player and multiplayer here: https://dominionstrategy.com/2018/05/24/reader-survey-and-intro-to-multiplayer-article-series/

For Workshop Gardens in particular, you really have to commit to it early for it to be good, so it's hard to do this posturing. I'm not sure if it's unbeatable if only 1 player goes for it. If only 1 player goes for it, try not contesting or barely contesting Gardens at all, and force them to empty all the Gardens and Estates on their own. This should give you enough time to get enough points from Provinces to win. This works pretty often in 2-player, the reason I'm not sure it works in 3-player is that the Gardens player gets 12 Gardens instead of 8.

EDIT: well I tried a few quick things in Geronimoo's Sim and in a 3-player game, one Workshop/Gardens vs two Smithy-BigMoneys wins ~75% of the time, even if the Smithy players avoid Estates. And then two Workshop/Gardens vs one Smithy-BigMoney wins almost none of the time. Of course the simulator isn't perfect, but it does suggest Workshop-Gardens is hard to beat if only one player plays it.
« Last Edit: July 06, 2019, 10:00:12 pm by Titandrake »
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JW

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #2 on: July 07, 2019, 01:15:17 am »
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Titandrake, the Smithy-Big Money players may be buying Duchies too early in the simulations. With two of them and one Gardens player, they can probably collectively improve their chances by holding off on Duchies to help empty the Provinces faster. Of course in an actual game they’d find it hard to coordinate in this way.
« Last Edit: July 07, 2019, 01:16:49 am by JW »
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Titandrake

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #3 on: July 07, 2019, 02:37:20 am »
+1

Titandrake, the Smithy-Big Money players may be buying Duchies too early in the simulations. With two of them and one Gardens player, they can probably collectively improve their chances by holding off on Duchies to help empty the Provinces faster. Of course in an actual game they’d find it hard to coordinate in this way.

I tried this a bit and actually found the default rule of "Duchy when Provinces in supply <= 5" did best. Remember that it's a 12 Province game so this corresponds to buying Duchies after the 3rd-4th Province.

I doubt tweaking it is going to flip uncontested Workshop Gardens from 75% down to a fair fight of 33%.
« Last Edit: July 07, 2019, 04:31:05 pm by Titandrake »
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DG

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #4 on: July 08, 2019, 07:37:16 pm »
0

Hello,

We play casually with 3 to 4 people (only have the basegame) and the last times Workshop+Garden was in the kingdom
it was either only one person going for it and winning or multiple people going for it and placing last and second to last.
Is this a prisoner's dilemma where the options are either someone taking a very likely loss by contesting gardens or allowing the gardens player to win?
I'd appreciate advice on this an I am sorry if there are obvious resources on this I overlooked (most only dealt with 2 player games).

There are some prisoner dilemma type kingdoms out there. It can happen with attacks vs defence, slow vs fast, 3 pile jeopardy, splitting of key cards, and plenty of other reasons. In general though, there's some other variation which is competitive. In a kingdom with two players going for gardens, the one who builds up for some duchies as well can often win even if they lose the gardens split. If you put that theory into your kingdom, I'm guessing the scoring and game length could start to vary a bit more.

If you want to look at the bigger picture, Dominion can create many varied player interactions due to the nature of a 10 card random kingdom. It would be surprising if the prisoner's dilemma could never occur. If you want massive kingdom variety then some kingdoms will player better or worse than others.
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popsofctown

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #5 on: July 08, 2019, 07:51:41 pm »
+1

You need to put "prisoner's dilemma" in air quotes.  It is critical to what is novel about prisoner's dilemma that the choices are made simultaneously.  That's never the case in Dominion, a turn based game, unless there's some variant of Messenger where each player secretly makes their own choice and they could all commit to the Workshop or Village path simultaneously, but I cannot think of such a card.
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Jack Rudd

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #6 on: July 09, 2019, 05:08:30 am »
+2

Choices are made simultaneously with Masquerade, but that's the only one I can think of.
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ipofanes

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #7 on: July 09, 2019, 07:42:21 am »
+2

You need to put "prisoner's dilemma" in air quotes.  It is critical to what is novel about prisoner's dilemma that the choices are made simultaneously.  That's never the case in Dominion, a turn based game, unless there's some variant of Messenger where each player secretly makes their own choice and they could all commit to the Workshop or Village path simultaneously, but I cannot think of such a card.

Yes, the dilemma you are talking about is closer to a truel.
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popsofctown

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #8 on: July 09, 2019, 03:21:59 pm »
0

Choices are made simultaneously with Masquerade, but that's the only one I can think of.
I'm not sure we can construct Prisoner's Dilemma with that since passing a card simultaneously decommits you from a strategy but "commits" the recipient to that strategy and at least the Dilemma in OP is based on too people being committed to the same strategy.  But maybe there is a way too.

It's a funny thought experiment.  Like trying to create the Turing machine with Gosper Guns in game of life.
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theorel

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #9 on: July 15, 2019, 09:45:21 am »
+1


EDIT: well I tried a few quick things in Geronimoo's Sim and in a 3-player game, one Workshop/Gardens vs two Smithy-BigMoneys wins ~75% of the time, even if the Smithy players avoid Estates. And then two Workshop/Gardens vs one Smithy-BigMoney wins almost none of the time. Of course the simulator isn't perfect, but it does suggest Workshop-Gardens is hard to beat if only one player plays it.

I played around with this a bit more in Geronimoo's sim, and got some interesting results:
So, as noted, for the baseline if you just compare big money smithy vs workshop/gardens you get:
2 players go Smithy 1 workshop-gardens, then workshop-gardens wins 75% of the time.
2 players go workshop-gardens 1 smithy then smithy wins 100% of the time.

But, interestingly, if you make the workshop-gardens players get Gardens after 2 workshops, then 2 players going for this strategy split the wins 45% each.  (Smithy winning ~2% of the time, with 7% ties).
I believe this is because the game ends quicker with this strategy (looks like it goes about 12 turns), which doesn't give smithy-BM time to get more than about 2-3 provinces, but the workshop players get ~30 cards in their deck.
This might not be the optimal mirror strategy, but getting more workshops does worse, and trying for duchies appears to do worse, so it seems to be at least a little bit stable.
Anyways, it looks like based on that test, 3-player workshop-gardens is not a "prisoner's dilemma", but just a winning strategy the majority of the time, if you go after Gardens strong enough.
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Holger

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #10 on: July 15, 2019, 11:31:45 am »
0

I played around with this a bit more in Geronimoo's sim, and got some interesting results:
So, as noted, for the baseline if you just compare big money smithy vs workshop/gardens you get:
2 players go Smithy 1 workshop-gardens, then workshop-gardens wins 75% of the time.
2 players go workshop-gardens 1 smithy then smithy wins 100% of the time.

But, interestingly, if you make the workshop-gardens players get Gardens after 2 workshops, then 2 players going for this strategy split the wins 45% each.  (Smithy winning ~2% of the time, with 7% ties).
I believe this is because the game ends quicker with this strategy (looks like it goes about 12 turns), which doesn't give smithy-BM time to get more than about 2-3 provinces, but the workshop players get ~30 cards in their deck.
That's a surprisingly drastic change. I would have expected that preferring Gardens over Workshop after only two Workshops would cause the game to last longer, because the Gardens players will have more turns with no Workshop in hand , and Gardens will likely empty before Workshop. For comparison, when does the baseline Workshop/gardens (mirror) strategy start buying Gardens? After 4 Workshops, as suggested by theory's old Gardens article in the Wiki?

Edit: I forgot that there's 12 Gardens in multiplayer. So it's conceivable that the remaining 6 Workshops will still be bought (with exactly $3 in hand) before the 12 Gardens have been gained. Still, there's another 12 Estates to gain before three-piling...


Quote
This might not be the optimal mirror strategy, but getting more workshops does worse, and trying for duchies appears to do worse, so it seems to be at least a little bit stable.

Did you try only one of the two W/G players getting a third Workshop before Gardens? The strategy is only stable if neither W/G player profits from gaining a third Workshop themself, even when the other only gains two Workshops at first.
« Last Edit: July 15, 2019, 11:40:38 am by Holger »
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theorel

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #11 on: July 15, 2019, 03:19:42 pm »
+3

I tried the built-in workshop/gardens strategies and the built-in smithy strategy for the third player.

And, just now, I was playing with it some more and I realized that the buy rule for Gardens being based on number of Workshops in deck is bad...since sometimes workshops run out when being contested, and in those cases they weren't buying ANY gardens.  Fixing the buy rule: Workshop-Gardens just dominates Smithy-BM, even in 3-player regardless of Gardens-preference.

Fixed Buy Rules:
Buy Workshop if < X workshops in deck.
Buy Gardens
Buy Workshop
Buy Estate
Buy Copper
...
Here's the win% for various X values vs each other, given a 3rd player that's going Smithy BM.

P2\P1  1    2     3     4     5     6     7     8     9
1   43\43 36\53 34\56 34\57 35\58 39\54 40\52 42\50 42\49
2   53\36 45\45 42\49 42\50 44\49 47\47 46\48 49\45 50\44
3   34\56 49\42 46\46 46\46 49\45 50\44 51\43 50\44 50\44
4   34\57 42\50 46\46 46\46 50\43 51\42 51\42 51\42 51\42

And if you set X to 10 for each player (i.e. prefer workshop over gardens always) you get ~45% wins for each player with smithy BM getting a paltry 1.4% (7% going to ties)

Interestingly although you want to stop preferring Workshops over Gardens after about 3-4 of them, you don't want to stop getting them entirely. That drops your win-chance to the 30's, splitting your losses between the other workshop-gardens player and the smithy player.  (probably 3-pile doesn't happen as early).

Note that this is still true in a 4-player game.  Even splitting the Gardens 3-ways, the Workshop Gardens players win out over smithy ~30% of the time (vs ~1.4% for the Smithy player)

So, yeah, bad buy rule made it look like Smithy could win...but actually workshop-Gardens just dominates under all circumstances.
« Last Edit: July 15, 2019, 03:22:58 pm by theorel »
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theorel

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #12 on: July 15, 2019, 03:22:06 pm »
0

I chose 2 originally based on the comment in the strategy in the simulator which says:
Quote
The ultimate combo for the basic game.
Surprisingly the optimal number of Workshops to get before starting to gain Gardens is 9.
When two players are going for the same strategy, you only want 2 Workshops before you start gardening.
I think 4 is probably optimal in the 3-player because 12 Gardens gives you more time to get going on the pile.
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theorel

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #13 on: July 15, 2019, 03:37:20 pm »
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So, I wonder what strategies the OP was seeing.  Sims obviously only go so far, and workshop-gardens is super-simple to play once you know the buy-rules (so sim does it well).  But I'm having a tough time coming up with any built-in sim strategies that can beat it.

Coppersmith-Tactician gives a respectable showing.  Rabble-Fishing Village can take it on with a 39% win-rate vs ~28% wins.  But if 2 players go Rabble-Fishing Village the Workshop-Gardens strategy tanks, it doesn't come back to win on its own.

Anyways, maybe the workshop-gardens players were trying to be fancy and giving the province-player time to win, or maybe the province-player was building a good engine that could win vs Gardens?  Or maybe it was just a fluke...
« Last Edit: July 15, 2019, 03:38:22 pm by theorel »
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DG

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #14 on: July 15, 2019, 05:29:01 pm »
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If you some changes to the end game conditions you may get better simulations. I don't think the simulator bots buy a card that loses the game, if I remember correctly, so in this sim when the garden bots have emptied two piles they wait until a winning condition to end the game. Meanwhile, the province player is just buying provinces but the 12 provinces are probably not running out so the province bot is never ending the game. The province bot will not buy a last garden or last workshop unless it is coded to so.
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theorel

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #15 on: July 16, 2019, 01:20:43 pm »
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Making that change helps the Smithy-player a bit.  By making the Smithy-player snipe the last pile, his win-% goes up to ~5%.

My point above was just that I'm not sure what situation might lead to the Gardens player winning alone, but not when splitting piles.
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popsofctown

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #16 on: July 16, 2019, 06:52:09 pm »
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Don't kill my dreams, there must be some way to tweak it till it works.

Envoy vs. Workshop//Silkroad//Island maybe
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theorel

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #17 on: July 18, 2019, 10:33:36 am »
+2

I'm not sure what the hope would be there, or what a reasonable workshop/silkroad/island strategy is....
But I made one up, and it beats envoy whether facing off with 2 or not.

But if we're just looking for 3-player oddities...how about this one:
Ironworks/Island/GH beats IGG/Gardens 87%-13%
If we go 3-players, and 2 people try to go for Ironworks/Island/GH vs a single IGG it's even worse: IGG loses .5% to 45% (for the Ironworks players)
OTOH if that third player goes IGG it wins 33% to 15%, with a good 18% becoming ties (presumably for IGG)

So, it's like the inverse-prisoner's dilemma.

Testing a bunch of different strats...lalalala
Okay, here we go: Witch vs Chapel/Minion

So Witch beats Minion/Chapel all on its own 65%-33%
But, if 2 players try to go Witch, then a third player can do Minion/Chapel and win 40% of the games (vs 28% for Witch)
But then if one of the Witch players decides to switch to Minion/Chapel to get in on the action, the remaining Witch wins 52% of the time (vs 22% for the Minions).

What if the Witch player tries to do an Engine, since they have a Chapel available?  It still goes to the one that picks a different strategy...
1 Witch/Village/Chapel vs 2 Minions/Chapel wins 62% to 18%
But 2 Witch/Village/Chapels vs 1 Minons/Chapel loses 29% to 41%

So, there you go pops...you can still dream. :)
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popsofctown

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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #18 on: July 18, 2019, 11:45:33 am »
0

This makes me happy.  I have noticed weird counter relationships involving minion before in 2p I wonder how much of this is related.


Great Hall is banned if we talk about it theory or rrenaud will come in and ban us.  I'm going to cover for you and say you meant Garrosh Hellscream so that you don't lose your dominionstrategy forum account.  Great Hall is already in my posts words but I will take my site ban like a man.
Ironworks/Island/Garrosh Hellscream/Gardens is a broad enough set of cards that can be kinda good with eachother that I worry the 1st triangle all gets nullified by some dominant mixed strategy but I don't think that's really easy to solve.

Minion/Chapel/Witch is probably just instantly legit because Minion and Witch don't get along very well.  This is different from the other set. 
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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #19 on: July 18, 2019, 06:34:04 pm »
+1

Is there some reason we can't just say Mill instead?
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Re: Is Workshop Garden in more than 2 player games a prisoner's dilemma?
« Reply #20 on: July 23, 2019, 03:44:21 pm »
0

I tried the built-in workshop/gardens strategies and the built-in smithy strategy for the third player.

And, just now, I was playing with it some more and I realized that the buy rule for Gardens being based on number of Workshops in deck is bad...since sometimes workshops run out when being contested, and in those cases they weren't buying ANY gardens.  Fixing the buy rule: Workshop-Gardens just dominates Smithy-BM, even in 3-player regardless of Gardens-preference.

Fixed Buy Rules:
Buy Workshop if < X workshops in deck.
Buy Gardens
Buy Workshop
Buy Estate
Buy Copper
...
Here's the win% for various X values vs each other, given a 3rd player that's going Smithy BM.

P2\P1  1    2     3     4     5     6     7     8     9
1   43\43 36\53 34\56 34\57 35\58 39\54 40\52 42\50 42\49
2   53\36 45\45 42\49 42\50 44\49 47\47 46\48 49\45 50\44
3   34\56 49\42 46\46 46\46 49\45 50\44 51\43 50\44 50\44
4   34\57 42\50 46\46 46\46 50\43 51\42 51\42 51\42 51\42

And if you set X to 10 for each player (i.e. prefer workshop over gardens always) you get ~45% wins for each player with smithy BM getting a paltry 1.4% (7% going to ties)
This seems more reasonable, thanks for the data table! So the optimal strategy is for both (non-cooperating) players to gain 3 or 4 Workshops first, winning 46% of the time each (whether 3 or 4 is slightly better would depend on the unrounded exact win%).

Quote
Interestingly although you want to stop preferring Workshops over Gardens after about 3-4 of them, you don't want to stop getting them entirely. That drops your win-chance to the 30's, splitting your losses between the other workshop-gardens player and the smithy player.  (probably 3-pile doesn't happen as early).
Naturally you always* want to get another Workshop when you can't get Gardens with your buy/gain -the more Workshops you have, the more regularly you can gain a second card per turn, improving your Gardens.

*Except in the end game; but Workshops usually run out long before.
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