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#### NoMoreFun

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##### Challenge: Rock/Paper/Scissors
« on: September 05, 2014, 06:40:18 am »
+5

Challenge: Find 3 strategies (A, B, C), all of which beat Big Money, that have a rock/paper/scissors relationship (i.e. A beats B, B beats C, C beats A).

In addition, all 3 strategies must be playable in the same kingdom (so only 10 cards total can be referenced between the 3 strategies except for the cases of Young Witch and Black Market).

There will be 3 win loss ratios between the strategies. The winner will be the triad with the highest win loss ratio in the triads closest matchup (so a triad with 99/1, 99/1, 51/49 is not as good as a triad with 70/30, 70/30, 65/35)
« Last Edit: September 05, 2014, 06:44:38 am by NoMoreFun »
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#### DG

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #1 on: September 05, 2014, 10:01:14 am »
+1

Essentially these A>B>C>A strategies are not uncommon, but you change your strategy based on what you are playing against. The simplest example is smithy+treasure vs workshop+gardens. If the smithy player buys some gardens it becomes harder for the workshop player to win, but buying gardens would not part of any normal smithy+treasure strategy. You could compare families of strategies but then the challenge becomes quite wooly.

This challenge is actually similar to finding a kingdom where the second player has a winning advantage. In this sort of kingdom you would assume there to be this A>B>C>A strategy relationship, so that if player 1 starts with strategy A then player chooses strategy C to win. The problem again is that player 1 can buy into strategy B on turn three, leaving the A>B>C>A relationship quite meaningless.
« Last Edit: September 05, 2014, 10:06:00 am by DG »
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#### NoMoreFun

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #2 on: September 05, 2014, 11:07:01 am »
0

One thing you can do is avoid revealing the strategy until it's too late for the opponent to counter it. In the case of gardens it's normally hard to hide what you're doing so the fact that you can be undercut is part of the strategy.
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#### SCSN

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #3 on: September 05, 2014, 12:31:24 pm »
+2

Nontransitivity alone doesn't make something RPS-like, the far more restrictive requirement is that of a mixed Nash equilibrium (in the case of RPS: throw R, P or S each with a probability of 1/3).

Quote
The simplest example is smithy+treasure vs workshop+gardens. If the smithy player buys some gardens it becomes harder for the workshop player to win, but buying gardens would not part of any normal smithy+treasure strategy.

So this does not qualify as a RPS-like dynamic, as "Smithy+Treasure, deny Gardens if opponent goes for it" is a pure equilibrium.
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#### soulnet

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #4 on: September 05, 2014, 01:44:57 pm »
+2

Nontransitivity alone doesn't make something RPS-like, the far more restrictive requirement is that of a mixed Nash equilibrium (in the case of RPS: throw R, P or S each with a probability of 1/3).

Assuming R/P/S are the only strategies, non-transitivity implies a mixed equilibrium. So I guess you mean a restriction of "no strategy is better than all three of those" should be added? The problem is that, for challenges, you want to only consider "programmable" strategies (programmable not in the computability sense, but in the "I would program it and not feel annoyed about having to do so" sense). Maybe a rule that another person giving a strategy that beats all three in a submission invalidates it.
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#### luser

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #5 on: September 07, 2014, 09:29:11 am »
+3

Nontransitivity alone doesn't make something RPS-like, the far more restrictive requirement is that of a mixed Nash equilibrium (in the case of RPS: throw R, P or S each with a probability of 1/3).

Assuming R/P/S are the only strategies, non-transitivity implies a mixed equilibrium. So I guess you mean a restriction of "no strategy is better than all three of those" should be added? The problem is that, for challenges, you want to only consider "programmable" strategies (programmable not in the computability sense, but in the "I would program it and not feel annoyed about having to do so" sense). Maybe a rule that another person giving a strategy that beats all three in a submission invalidates it.
Here you have problem that you have universal counterexample if opponent does A do B, if he does B do C, if he does C do A that should beat all of A, B, C

Second problem is that its ill defined what is strategy, my answer would be

then

A: First turn buy duchess and proceed with pin until you have woodcutter in hand, then buy curses
B: First turn buy woodcutter and proceed with pin until you have chancellor  in hand, then buy curses
C: First turn buy chancellor and proceed with pin until you have duchess in hand, then buy curses
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#### Holger

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #6 on: September 07, 2014, 03:38:55 pm »
0

This challenge is actually similar to finding a kingdom where the second player has a winning advantage. In this sort of kingdom you would assume there to be this A>B>C>A strategy relationship, so that if player 1 starts with strategy A then player chooses strategy C to win. The problem again is that player 1 can buy into strategy B on turn three, leaving the A>B>C>A relationship quite meaningless.

Yes, player 1 could always do nothing on his first turn and thus effectively make the second player "starting player" (except for the tiebreak and ignoring shuffle luck and shuffle timing), or he could do something that helps all three strategies (e.g. buy a Silver in many cases).

Finding a kingdom where the second player has a winning advantage is probably much more difficult, and would be worthy of a challenge of its own. I don't think it's ever been rigorously done, and I'm not even sure if such a kingdom exists. (I think Last Footnote once claimed that Noble Brigand-BM has a second-player advantage, but he didn't give an explicit strategy or proved that it was optimal for both players.)
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#### ephesos

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #7 on: September 09, 2014, 10:50:20 am »
+12

Strategy A: Beggar Gardens
Strategy B: Double Mountebank

Obviously, A beats B because you're only helping Gardens with Mountebank. B beats C by preventing the pin from taking place. C beats A because Beggar Gardens doesn't stop the pin and takes a long time to 3 pile with Copper/Gardens/Silver. If it can't get all of the Gardens by the time the pin is on, Beggar Gardens has no way to end and will lose to infinite Goons scaling.

Testing:
A beats B: 99.8% (that's a lot...)
B beats C: 82.6%
C beats A: 68.7% (could probably be improved with optimization of the Pin strategy)

Tested using Dominate with the default Beggar Gardens and Double Mountebank, and luser's implementation of Quarry Pin(http://forum.dominionstrategy.com/index.php?topic=9781.25) with the Chapel in case of Mountebank removed.
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#### NoMoreFun

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #8 on: September 09, 2014, 01:50:31 pm »
0

Strategy A: Beggar Gardens
Strategy B: Double Mountebank

Obviously, A beats B because you're only helping Gardens with Mountebank. B beats C by preventing the pin from taking place. C beats A because Beggar Gardens doesn't stop the pin and takes a long time to 3 pile with Copper/Gardens/Silver. If it can't get all of the Gardens by the time the pin is on, Beggar Gardens has no way to end and will lose to infinite Goons scaling.

Testing:
A beats B: 99.8% (that's a lot...)
B beats C: 82.6%
C beats A: 68.7% (could probably be improved with optimization of the Pin strategy)

Tested using Dominate with the default Beggar Gardens and Double Mountebank, and luser's implementation of Quarry Pin(http://forum.dominionstrategy.com/index.php?topic=9781.25) with the Chapel in case of Mountebank removed.

Well done. That's already higher than I was expecting, and I wouldn't be surprised if there's a way to get C beats A into the 80s or higher (and it may involve slowing A down even more somehow). Suboptimal bots are fine, they just all have to beat big money.
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#### ephesos

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #9 on: September 10, 2014, 01:47:10 am »
0

Alright, 99.6 win rate can be obtained by Pin against Beggar Gardens, but only by hurting Beggar Gardens. In order to achieve this win rate, I made Beggar Gardens never want to buy the last Copper or the last Beggar. Thus, it can't 3 pile against Pin. I'm sure I could achieve 100% win rate by not having it buy the last Estate, but that might hurt its odds against Double Mountebank.

I feel like it's starting to get to luser's scenario, though. By intentionally handicapping one strategy specifically when facing another, we can always obtain an RPS relationship. Still, even with the best optimization I can come up with, I can't boost Pin's rates above 80% against Beggar Gardens, since it's so fast and Beggar is a soft counter to the Pin.
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#### silverspawn

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #10 on: September 10, 2014, 08:19:28 am »
0

shouldn't the pin have a flat 100% against beggar/gardens when played correctly? how do you want to lose with it? even with the worst draws, you gotta have it going eventually
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#### Holger

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #11 on: September 10, 2014, 08:32:54 am »
+1

shouldn't the pin have a flat 100% against beggar/gardens when played correctly? how do you want to lose with it? even with the worst draws, you gotta have it going eventually

"Eventually" may be after Beggar/Gardens has finished the game.   It's not that slow...

Alright, 99.6 win rate can be obtained by Pin against Beggar Gardens, but only by hurting Beggar Gardens. In order to achieve this win rate, I made Beggar Gardens never want to buy the last Copper or the last Beggar. Thus, it can't 3 pile against Pin. I'm sure I could achieve 100% win rate by not having it buy the last Estate, but that might hurt its odds against Double Mountebank.

Even by intentionally preventing 3-piling, B/G can once in a blue moon win by gaining all Provinces in time.

I feel like it's starting to get to luser's scenario, though. By intentionally handicapping one strategy specifically when facing another, we can always obtain an RPS relationship.

But you get a RPS relationship even without handicapping. There may well be no single optimal strategy on this board...
(You could try Double Mountebank into B/G, maybe?)
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#### silverspawn

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #12 on: September 10, 2014, 08:43:15 am »
0

I'm not so sure about that. I find it hard to believe that a good player can ever take longer to get the pin going than a beggar player needs to pile out... copper, gardens, and beggars? if i understand the simulation correctly, it should be within the rules to provide the pin player with any support he needs to get his components together, as long as it stays within a 10 card kingdom. that should probably include cards like chapel, baker, maybe butcher, hermit. were even some of those included in the simulation?
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#### Holger

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #13 on: September 10, 2014, 09:25:37 am »
+1

I'm not so sure about that. I find it hard to believe that a good player can ever take longer to get the pin going than a beggar player needs to pile out... copper, gardens, and beggars? if i understand the simulation correctly, it should be within the rules to provide the pin player with any support he needs to get his components together, as long as it stays within a 10 card kingdom. that should probably include cards like chapel, baker, maybe butcher, hermit. were even some of those included in the simulation?

As I understand his above post, ephesos only used Quarry and a single Chapel as pin support. As he said, it "could probably be improved with optimization of the Pin strategy"; but it's hard to make a pin simulation a "good player". Obviously, B/G and DM could also be improved by adding support cards, but you only have two empty kingdom spaces left for all three strategies together. The OP's rules don't require any strategy to be "unimprovable"...
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#### DG

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #14 on: September 10, 2014, 09:28:15 am »
+4

The goons attack will allow beggars to be discarded to gain silvers. This means that beggars are never lost to the pin and the silver pile will empty. Remember that a 5 beggar hand can be completely discarded to gain 10 silvers.

I'm sure there will be a 100% solution to this problem with a 5 card deck (monument/bishop), a strategy with strong saboteur/pirate attack, and a basic money deck with masquerades/militia. You can also put strange conditions into the strategies, such as only buying provinces after the opponent does, that will defeat big money but ensure failure against non-province strategies.
« Last Edit: September 10, 2014, 09:30:20 am by DG »
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#### Holger

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #15 on: September 10, 2014, 10:04:29 am »
0

The goons attack will allow beggars to be discarded to gain silvers. This means that beggars are never lost to the pin and the silver pile will empty. Remember that a 5 beggar hand can be completely discarded to gain 10 silvers.

Right you are. By always discarding Beggar to attacks, BeggarGardens wins >50% of games against QuarryPin. BG would win or tie 100%, if QuarryPin wasn't programmed to break the Pin "too early" (after 50 turns, even before all Coppers are trashed from BG's deck).
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#### ephesos

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #16 on: September 10, 2014, 10:45:29 am »
+1

Okay, I see, the default Beggar Gardens always keeps a Beggar in hand, so it can gain 3 coppers. Changing it to reveal all the time still only gives it a 40% win rate in my simulation, though.

The loss situation for the Pin is when a 3 pile happens while B/G has a deck still containing Gardens. Pretty much, that's when B/G buys out Copper and has already bought out two of Beggar, Gardens, Duchy. B/G always gets "pinned" before the 3 pile happens, but still manages in some situations to buy out Copper.

The version of Quarry Pin I used has Chapel removed. Otherwise, it can beat Double Mountebank(this was why Chapel was added to the original)

I'm starting to lose track while testing, but another change was having Pin buy a Copper when it has exactly 6 cards in deck. This counters a specific side case where we draw KC/KC/Masq with Goons in deck and decide to triple Masq, defaulting to trashing everything since the Pin is "on", and passing the last card in the deck, Goons.
I'm sure the better way is just to put a condition on trashing/passing with Masq i.e. don't do it when Goons is in hand, KC/KC/Masq is in play, and there's only one card in hand other than Goons. But for some reason, I can't get the wording right.

Also, I've upped Double Mountebank's odds against the pin by turning it into Always Mountebank(no restriction on the number of Mountebanks). Wins about 92% of the time against Pin, and loses... I think it's pretty safe to say 100% of the time against Beggar Gardens. 12407 games and it still hasn't won even one.
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#### Holger

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #17 on: September 10, 2014, 11:37:30 am »
0

Okay, I see, the default Beggar Gardens always keeps a Beggar in hand, so it can gain 3 coppers. Changing it to reveal all the time still only gives it a 40% win rate in my simulation, though.
You could be right, I could only simulate ~100 games (with 56% BG win rate) before some broken script stopped Dominiate from working, so 40% is probably in my margin of error. (OTOH, I kept QP's Chapel improvement in place.)

The loss situation for the Pin is when a 3 pile happens while B/G has a deck still containing Gardens. Pretty much, that's when B/G buys out Copper and has already bought out two of Beggar, Gardens, Duchy. B/G always gets "pinned" before the 3 pile happens, but still manages in some situations to buy out Copper.

BG may never three-pile before the pinning starts, but it still has plenty of time to three-pile before its deck is destroyed. Quite often, QuarryPin doesn't manage to destroy all of BG's VP cards within 50 turns; by this time, BG will often be able to three-pile. In fact, in two out of three BG-winning game logs I looked at, BG still has >40 points around turn 50 and wins by three-piling Beggar, Gardens and Silver (the latter with QP's help; but without playing Goons QP is lost anyway).
« Last Edit: September 10, 2014, 11:48:21 am by Holger »
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#### luser

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #18 on: September 10, 2014, 12:16:23 pm »
0

Okay, I see, the default Beggar Gardens always keeps a Beggar in hand, so it can gain 3 coppers. Changing it to reveal all the time still only gives it a 40% win rate in my simulation, though.

The loss situation for the Pin is when a 3 pile happens while B/G has a deck still containing Gardens. Pretty much, that's when B/G buys out Copper and has already bought out two of Beggar, Gardens, Duchy. B/G always gets "pinned" before the 3 pile happens, but still manages in some situations to buy out Copper.

The version of Quarry Pin I used has Chapel removed. Otherwise, it can beat Double Mountebank(this was why Chapel was added to the original)

I'm starting to lose track while testing, but another change was having Pin buy a Copper when it has exactly 6 cards in deck. This counters a specific side case where we draw KC/KC/Masq with Goons in deck and decide to triple Masq, defaulting to trashing everything since the Pin is "on", and passing the last card in the deck, Goons.
I'm sure the better way is just to put a condition on trashing/passing with Masq i.e. don't do it when Goons is in hand, KC/KC/Masq is in play, and there's only one card in hand other than Goons. But for some reason, I can't get the wording right.

Also, I've upped Double Mountebank's odds against the pin by turning it into Always Mountebank(no restriction on the number of Mountebanks). Wins about 92% of the time against Pin, and loses... I think it's pretty safe to say 100% of the time against Beggar Gardens. 12407 games and it still hasn't won even one.

Yes, the pin executes pin suboptimally for simplicity. It does not get second masq for start. Also due to no special-casing a hand of kc, goons, masq, junk, junk it plays kc-goons instead kc-masq.

Second improvement would be get monument once pin starts to generate additional 90 vp.

Okay, I see, the default Beggar Gardens always keeps a Beggar in hand, so it can gain 3 coppers. Changing it to reveal all the time still only gives it a 40% win rate in my simulation, though.
You could be right, I could only simulate ~100 games (with 56% BG win rate) before some broken script stopped Dominiate from working, so 40% is probably in my margin of error. (OTOH, I kept QP's Chapel improvement in place.)

That does not make difference as chapel is bought only when you have curse in deck.
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#### ephesos

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #19 on: September 11, 2014, 10:28:59 am »
0

You can't get a second Masq. I've tried it, and you have to get rid of it somehow. So, you pass it to Beggar Gardens, who plays it, and kills the Pin.

Adding Monument seems to help a lot, you can outscale the Gardens before the 3 pile happens.
Wins something like 95% against B/G that always reveals, but I can't test enough cause Dominate keeps crashing. Loses 80% against All The Mountebanks.

Current version, with no Chapel, fixed KC/Masq priority over KC/Goons, Monument added.
Code: [Select]
`#Ruthlessly executes unsuspecting bots with the KC/Goons/Masquerade pin{  name: 'QuarryPin'  requires: ["Monument", "King's Court", "Masquerade", "Goons", "Quarry"]  gainPriority: (state, my) -> [    "King's Court" if my.countInDeck("King's Court") < 2    "Goons" if my.countInDeck("Goons") == 0    "Masquerade" if my.countInDeck("Masquerade") == 0    "Quarry" if my.countInDeck("King's Court") < 2 && my.countInDeck("Quarry") < 4       "Gold" if my.turnsTaken >= 50 #MAKE IT STOP    "Duchy" if my.turnsTaken >= 70    "Estate" if my.turnsTaken >= 90    "Copper" if my.numCardsInDeck() == 6    "Monument" if my.countInPlay("King's Court") == 2 and my.countInPlay("Goons") == 1 and my.countInPlay("Masquerade") == 1 and my.numCardsInDeck() == 4  ]  trashPriority: (state, my) -> [    "Curse"    "Estate"    "Copper" if my.countInHand("Goons") == 0 or my.countInHand("Copper") > 1    "Silver" if my.countInDeck("King's Court") == 2 and my.countInDeck('Goons') == 1    #kill anything once the pin starts    "Gold"    "Province"    "Duchy"    "King's Court" if my.countInDeck("King's Court") > 2 and my.countInDeck('Goons') == 1    "Goons" if my.countInDeck("King's Court") == 2 and my.countInDeck('Goons') > 1    "Masquerade" if my.countInDeck("King's Court") == 2 and my.countInDeck('Goons') == 1    "Beggar"    "Gardens"    "Quarry" if my.countInDeck("King's Court") == 2 and my.countInDeck("Goons") == 1 and (my.countInHand("Goons") == 0 or my.countInHand("Copper") > 1)    "Mountebank"  ]   wantsToRebuild: (state, my) ->    return 0   wantsToJM: (state, my) ->    false   multipliedPriority: (state, my) -> [    "King's Court"    "Masquerade" if my.countInPlay("King's Court") == 1    "Goons"    "Monument"    "Masquerade"    "Chapel"  ]}   `
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#### JW

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #20 on: September 11, 2014, 10:41:02 am »
0

You can't get a second Masq. I've tried it, and you have to get rid of it somehow. So, you pass it to Beggar Gardens, who plays it, and kills

Trash the second masq to the first masq? In general the pin strategy should usually beat a money mountebank deck if played well, which as soulnet pointed out above means the resulting strategies don't reflect any actual strategic ambiguity in this kingdom.
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#### Holger

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #21 on: September 11, 2014, 11:22:59 am »
0

You can't get a second Masq. I've tried it, and you have to get rid of it somehow. So, you pass it to Beggar Gardens, who plays it, and kills the Pin.

Adding Monument seems to help a lot, you can outscale the Gardens before the 3 pile happens.
Wins something like 95% against B/G that always reveals, but I can't test enough cause Dominate keeps crashing. Loses 80% against All The Mountebanks.

Current version, with no Chapel, fixed KC/Masq priority over KC/Goons, Monument added.
[...]

If you want to make it optimal, the bot should also buy Quarries if he doesn't have a Goons yet - I've seen a game log where the bot trashed itself down to KC, KC, Masq, never acquiring a Goons. (The game went on for 20,000 turns (!) without ever reaching a pin.)
Also, I don't see why one would try and end the game by buying Golds first - these would help the opponent thanks to Masq. Better to buy VP cards and Curses to three-pile instead.

In general the pin strategy should usually beat a money mountebank deck if played well, which as soulnet pointed out above means the resulting strategies don't reflect any actual strategic ambiguity in this kingdom.

With Chapel added to the kingdom, yes. But if you disallow it (and any other strong pin support like Monument), there's still a RPS situation unless you can improve the pin strategy substantially.
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#### JW

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #22 on: September 11, 2014, 11:31:24 am »
+1

In general the pin strategy should usually beat a money mountebank deck if played well, which as soulnet pointed out above means the resulting strategies don't reflect any actual strategic ambiguity in this kingdom.

With Chapel added to the kingdom, yes. But if you disallow it (and any other strong pin support like Monument), there's still a RPS situation unless you can improve the pin strategy substantially.

I don't know if I could improve the programming of the pin but I expect that on a board of quarry, masquerade, goons, mountebank and KC, someone like SCSN could win most of the games with the pin against All the Mountebanks. Get a number of masquerades, at least two quarries, don't pass curses so you can block MB, then get KCs, thin your deck drastically, add Goons and win.
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#### Holger

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #23 on: September 11, 2014, 11:45:08 am »
0

In general the pin strategy should usually beat a money mountebank deck if played well, which as soulnet pointed out above means the resulting strategies don't reflect any actual strategic ambiguity in this kingdom.

With Chapel added to the kingdom, yes. But if you disallow it (and any other strong pin support like Monument), there's still a RPS situation unless you can improve the pin strategy substantially.

I don't know if I could improve the programming of the pin but I expect that on a board of quarry, masquerade, goons, mountebank and KC, someone like SCSN could win most of the games with the pin against All the Mountebanks. Get a number of masquerades, at least two quarries, don't pass curses so you can block MB, then get KCs, thin your deck drastically, add Goons and win.

That's not unlikely, but SCSN might also win against an average pin player by playing Mountebanks, adding some support from Masq and other cards. That's why NMF allowed suboptimal strategies.

In case a perfectly implemented QuarryPin does beat Multi-Mountebank, we may still get a board strategically ambiguous also to humans by disallowing Quarry as well...
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#### sudgy

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##### Re: Challenge: Rock/Paper/Scissors
« Reply #24 on: September 11, 2014, 03:13:04 pm »
0

The pin can be set up pretty quickly.  KC-Masquerade can trash your deck pretty quickly.
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