- #1
Graff
- 7
- 0
You play against three automated players who’s dice and actions are independent from you.
You start with six randomly rolled dice.
Rules:
-You MUST keep at least one die, but can keep as many as desired.
-A (1) and (4) are qualifiers, without both qualifiers you cannot score. These do not count towards your score.
-Reroll all unchosen dice and repeat.
-Game ends when all six dice are chosen.
-Score is the combined value of the four scoring dice. Ties are considered losses. Wins must beat all three other players.
Pretty simple. A perfect score is 24 with (6,6,6,6,1,4) in no particular order.
Now, can someone help me with proving a best strategy for this game?
Currently I do this:
-No qualifiers or (6) -> Take highest die
-One qualifier and any amount of (6)-> Take qualifier and up to two (6)
- Both qualifiers and one or fewer (6)-> Take (4) and (6) (if (6) is available)
-Both qualifiers and two or more (6)-> Take all (6) and both qualifiers
-(5) will only be kept if it's one of the last 2 dice.
-(4) will only be kept if it's the last die.
Is this strategy significantly better than the default auto players who do what’s listed below?
-Keep any and all qualifiers if needed.
-On any given roll, if you have both qualifiers, it will keep all (6).
-If you have only one of the qualifiers, it will keep a maximum of one (6).
-If you have no qualifiers, it will only keep the highest die roll.
-(5) will only be kept if it's one of the last 2 dice.
-(4) will only be kept if it's the last die.
If you can help me with the math, I would love to figure out the odds here. Thanks!
Please ask any questions!
Examples:
-(6,5,6,6,4,5)
Keep (6,6,4) (roll)
-(2,2,5)
Keep (5) (roll)
-(4,6)
Keep (6) (roll)
-(2)
Does not meet qualifiers, game over. (ex: should I have done only (6,4) to start?)
-(2,3,4,2,4,1)
Keep (4) (roll)
-(1,1,3,1,4)
Keep (1) (roll)
-(5,6,2,1)
Keep (5,6) (roll)
-(3,4)
Keep (4) (roll)
-(4)
Score 19, lose to opponents who have scores of (21,17,20) (ex: should I have done only (6) instead of (5,6)?)
You start with six randomly rolled dice.
Rules:
-You MUST keep at least one die, but can keep as many as desired.
-A (1) and (4) are qualifiers, without both qualifiers you cannot score. These do not count towards your score.
-Reroll all unchosen dice and repeat.
-Game ends when all six dice are chosen.
-Score is the combined value of the four scoring dice. Ties are considered losses. Wins must beat all three other players.
Pretty simple. A perfect score is 24 with (6,6,6,6,1,4) in no particular order.
Now, can someone help me with proving a best strategy for this game?
Currently I do this:
-No qualifiers or (6) -> Take highest die
-One qualifier and any amount of (6)-> Take qualifier and up to two (6)
- Both qualifiers and one or fewer (6)-> Take (4) and (6) (if (6) is available)
-Both qualifiers and two or more (6)-> Take all (6) and both qualifiers
-(5) will only be kept if it's one of the last 2 dice.
-(4) will only be kept if it's the last die.
Is this strategy significantly better than the default auto players who do what’s listed below?
-Keep any and all qualifiers if needed.
-On any given roll, if you have both qualifiers, it will keep all (6).
-If you have only one of the qualifiers, it will keep a maximum of one (6).
-If you have no qualifiers, it will only keep the highest die roll.
-(5) will only be kept if it's one of the last 2 dice.
-(4) will only be kept if it's the last die.
If you can help me with the math, I would love to figure out the odds here. Thanks!
Please ask any questions!
Examples:
-(6,5,6,6,4,5)
Keep (6,6,4) (roll)
-(2,2,5)
Keep (5) (roll)
-(4,6)
Keep (6) (roll)
-(2)
Does not meet qualifiers, game over. (ex: should I have done only (6,4) to start?)
-(2,3,4,2,4,1)
Keep (4) (roll)
-(1,1,3,1,4)
Keep (1) (roll)
-(5,6,2,1)
Keep (5,6) (roll)
-(3,4)
Keep (4) (roll)
-(4)
Score 19, lose to opponents who have scores of (21,17,20) (ex: should I have done only (6) instead of (5,6)?)