Whenever we're bored, we play a dice game we uncreatively call "The
Dice Game". If there's an actual name for this game, I haven't found
it. The rules are:
Everyone 'antes' a set amount (usually $1).
First shooter rolls six dice. The shooter must remove at least 1 die
and set aside. Shooter rerolls remaining dice until all the dice are
set aside. The shooter must set aside a rolled 1 and a 2 to "qualify"
his score. If the shooter fails to roll a 1 and a 2, he is out and
must pay another ante. If he does roll a 1 and 2, the total of the
remaining 4 dice is his score. The best possible roll is 1 and 2 with
6, 6, 6, 6, for 24 points.
For example, shooter rolls six dice to start. Rolls are 1, 3, 4, 4, 5,
6. Shooter elects to set aside 1 and 6. Rolls 4 remaining dice: 2, 2,
4, 5. Shooter elects to set aside 2 to "qualify" his turn. Rolls 3
remaining dice: 3, 4, 4. Must remove one, selects a 4. Rolls again:
2, 6. Sets aside the 6. Rolls the last die: 3. Dice set aside: 1, 2,
6, 6, 4, 3, for a final score of 19.
The next shooter repeats the process. When the last person has
completed their turn, the highest score wins the pot for that round.
Note a person may be unable to beat the high score, but may still have
to roll to qualify his turn; i.e., a person has to beat a score of 23,
but has so far set aside: 1, 5, 5, 6. The person can only score a max
of 22, but must still continue rolling and hope to get a 2 to avoid
having to pay another ante into the pot.
My question is, is there an optimal strategy for this game...
especially regarding when to save a 5? I know that a later turn is
obviously better, since you know the score to beat. Often one may
elect to discard a 5 (or even a 6?) if one hasn't yet qualifed... to
give a higher chance of rolling a needed 1 or 2 on the next roll. For
example, a person rolls 6, 6, 3, 3, 4, 5 on the first roll. Elects to
save both of the sixes. Rolls 6, 6, 4, 5 on the next roll. Pulling
out both sixes means he must next roll two dice, and hope to get a) a 1
and a 2, b) a 1 on one die, and a 2 on the next roll, or c) a 2 on one
die, then a 1 on the next roll. The person may elect to remove only 1
six, so that he may roll three dice with his next turn, which seemingly
makes it easier to qualify his turn. The person in this example has
chosen to risk not making the highest score on this turn (thus
forfeiting his $1) for a chance at not having to forfeit $2... is this
a profitable long term strategy?
I haven't found any discussions of strategy for this game, if anyone
has leads I'd appreciate it.
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