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### AuthorTopic: Non transitive challenges - 2nd Edition  (Read 280 times)

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#### NoMoreFun

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##### Non transitive challenges - 2nd Edition
« on: September 15, 2018, 09:37:21 pm »
+4

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)
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#### faust

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##### Re: Non transitive challenges - 2nd Edition
« Reply #1 on: September 24, 2018, 07:24:01 am »
+2

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.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.
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