The best trios to have

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ClimateChangeIsReal
Posts: 14
Joined: 01 August 2018, 21:18

The best trios to have

Post by ClimateChangeIsReal » 08 September 2019, 00:49

Clearly the best trio to have is 6,7,8 because that minimizes the chance of you busting. But you will not get 6,7,8 every single time. I simulated each of the near-center trios, as well as a few others, to find the chance of busting. The only-12, only-7, and only-8 are there more for the probability of actually rolling that number. (That is, if a player with 2 claims is one away from claiming 2 or 12, they have about a 13% chance of winning on any given roll.)

The runners-up are 578, 468, and 478.

Not sure how much of a role parity plays in this.

Code: Select all

Scenario           [12]:  171 (bust: 86.81%, expected run: 0)
Scenario            [8]:  727 (bust: 43.90%, expected run: 1)
Scenario            [7]:  834 (bust: 35.65%, expected run: 2)
Scenario         [5, 6]:  949 (bust: 26.77%, expected run: 3)
Scenario     [3, 5, 10]:  983 (bust: 24.15%, expected run: 3)
Scenario         [5, 8]:  997 (bust: 23.07%, expected run: 3)
Scenario     [3, 7, 11]: 1006 (bust: 22.38%, expected run: 3)
Scenario         [5, 7]: 1006 (bust: 22.38%, expected run: 3)
Scenario     [2, 7, 12]: 1012 (bust: 21.91%, expected run: 4)
Scenario     [4, 5, 10]: 1066 (bust: 17.75%, expected run: 5)
Scenario         [6, 8]: 1068 (bust: 17.59%, expected run: 5)
Scenario      [3, 6, 9]: 1071 (bust: 17.36%, expected run: 5)
Scenario         [7, 8]: 1083 (bust: 16.44%, expected run: 5)
Scenario      [4, 5, 8]: 1096 (bust: 15.43%, expected run: 5)
Scenario      [5, 7, 9]: 1106 (bust: 14.66%, expected run: 6)
Scenario      [5, 6, 9]: 1123 (bust: 13.35%, expected run: 6)
Scenario     [4, 7, 10]: 1136 (bust: 12.35%, expected run: 7)
Scenario     [4, 6, 10]: 1145 (bust: 11.65%, expected run: 8)
Scenario      [3, 7, 8]: 1157 (bust: 10.73%, expected run: 8)
Scenario      [4, 7, 9]: 1157 (bust: 10.73%, expected run: 8)
Scenario      [5, 6, 8]: 1160 (bust: 10.49%, expected run: 9)
Scenario      [4, 7, 8]: 1170 (bust:  9.72%, expected run: 9)
Scenario      [4, 6, 8]: 1181 (bust:  8.87%, expected run: 10)
Scenario      [5, 7, 8]: 1185 (bust:  8.56%, expected run: 11)
Scenario      [6, 7, 8]: 1192 (bust:  8.02%, expected run: 11)

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Romain672
Posts: 88
Joined: 05 April 2016, 13:53

Re: The best trios to have

Post by Romain672 » 08 September 2019, 11:34

Your stats just give the best trio to survive, not the best one overall.
Cause advancing a 12 have a lot more value than advancing a 7.

Without maths, I feel that the best one was 6/7/12 (and 2/7/8), or 6/7/8. But I'm not sure at all

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RicardoRix
Posts: 581
Joined: 29 April 2012, 23:43

Re: The best trios to have

Post by RicardoRix » 09 September 2019, 13:24

somebody has published a probability table for this on BGG, but without considering the scoring factor as Romain suggests.

It goes from 52% for 234, to 92% for 678.

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