Basic Dice Probabilities

[Phoxtrot]

D8
Chance that the minimum out of 3 rolls is exactly:
-- Chance of obtaining at least 1 roll out of 3 that is inferior or equal to that value

• 1: 33,0% -- 33,0%
• 2: 24,8% -- 57,8%
• 3: 17,8% -- 75,6%
• 4: 11,9% -- 87,5%
• 5: 7,2% -- 94,7%
• 6: 3,7% -- 98,4%
• 7: 1,4% -- 99,8%
• 8: 0,2% -- 100%

D12
Chance that the minimum out of 3 rolls is exactly:
-- Chance of obtaining at least 1 roll out of 3 that is inferior or equal to that value

• 1: 23,0% -- 23,0%
• 2: 19,2% -- 42,1%
• 3: 15,7% -- 57,8%
• 4: 12,6% -- 70,4%
• 5: 9,8% -- 80,2%
• 6: 7,3% -- 87,5%
• 7: 5,3% -- 92,8%
• 8: 3,5% -- 96,3%
• 9: 2,1% -- 98,4%
• 10: 1,1% -- 99,5%
• 11: 0,4% -- 99,9%
• 12: 0,1% -- 100%

[Phoxtrot]

Now, if you want to roll a high number, you can easily convert the tables above by doing the following transformation:

D8:
Chance of the maximum being exactly N = Chance of the minimum being exactly 9-N
Chances of at least 1 roll >= N = Chances of at least one roll <= (9-N)

D12:
Chance of the maximum being exactly N = Chance of the minimum being exactly 13-N
Chances of at least 1 roll >= N = Chances of at least one roll <= (13-N)

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Another way that you can elaborate on the tables above is as follow:

If you roll for low and want to know say what are your chances of ending with a 1 if your strategy is to stop as soon as you roll a 3 or below then the chance of ending with a 1 is 1/3 of the chance of rolling at least one die less or equal to 3. Because the table gives you the chance of rolling at least one die less or equal to 3 and if that happen, that "stop" die has an equal chance of being a 1, a 2 or a 3.

[atticus_mech]

I made this nice chart showing all dice probability calculations if you're interested. Give it a like on BGG at this link: https://boardgamegeek.com/image/6859143/feast-odin