Dominion > Simulation

Non transitive challenges - 2nd Edition

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NoMoreFun:
I posted 2 challenges in 2014 to try and find non transitive strategies. With Landmarks it may be easier, and the winning strategies the first time around involved Masquerade pins, so I'm posting them again.

Challenge 1: 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).

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)

Challenge 2: Find 3 strategies, A, B and C such that in a 3 player game, when it comes to the percentage of wins

Strategy A>Strategy B>Big Money
AND
Strategy B>Strategy C>Strategy A
(Or B>A>C, or C>B>A)
Strategy C also must beat 2 Big Money bots in 3 player (so it's a real strategy that can win games).

The winner is the strategy that demonstrates the most decisive shift in the balance; the highest possible score is 200 (which would be a 100:0 changing to a 0:100).

Common Rules

* 2nd edition cards only: No 1st edition only cards from Base and Intrigue, and cards that function differently (like Masquerade) function as they do in the 2nd edition
* Every Card/Event/Landmark referenced in all 3 strategies must fit into a single kingdom (10 cards and maximum 2 Events/Landmarks with exceptions like Young Witch)

faust:
I feel that there should be some rule that disqualifies a triple (A,B,C) if there is a strategy D that beats all of A, B, C on the same board.

ahyangyi:
Yep, I would assume that all dominated strategies would be iteratively removed before we find the intransitivity in the remaining strategies.

https://en.wikipedia.org/wiki/Strategic_dominance

And yes, thread necromancy but we don't have new posts in this board. And... I'm kinda thinking about writing my own simulator to design a few tailored kingdoms. Needed that thing to get people into Dominion. And intransitivity is obviously a nice trait for this kind of tailored kingdoms.

People look at Dominion and say "well this game's power lies in the randomization but each of the actual game is very shallow" or "this game is mostly multiplayer solitaire", neither of which is very true, but it's good to have a prepared example where you have to pay attention to what your opponent is doing and counteract accordingly and the best strategy is still not clear after playing the same kingdom three times.

ephesos:
Oh geez, it has been over 7 years since that post. Good times.

I'm tempted to follow the same line as before: strategy A is robust to attacks, but slow to end the game, strategy B is all about disruptive attacks, and strategy C is a slow combo that's weak to attacks, but wins if uncontested. Maybe something like Pursue Patron Travelling Fair, with a slow trasher like Counterfeit that can't get rid of Curses. Once you build up some Coffers, you can start to multiply them by revealing Patrons with Pursue. Add in Mission to double the growth rate so that it has a better chance of beating A, and maybe City Gate for a little more consistency (topdecking a Patron from your hand).

ahyangyi:
I'm thinking about how "apart" the strategies are. Sometimes we can have A,B,C on paper, but in reality, one of them can be easily transformed to another as they observe their opponents' purchases. For example, A beat B, B beat C, C beat A, but A can change halfway into B when they see their opponents do C. Then the "hybrid A" might still just dominate the game.

Having combos seems like a good starting point, since they usually have a higher sinking cost than other strategies, and switching is hard. Not sure about the Pursue Patron Travelling Fair/Mission combo though, Patron sounds like too compatible with other strategies.

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