Playing dice recently we got into a conversation about dice odds. When I first played I figured if the odds of rolling a 1 or a 5 (a scoring number) was 1 in 3 for one die, it had to be about even for three dice. Looking closer, that's not exactly the case.
The odds for one die: 4 of 6 losing combinations, meaning 2 of 6 wins. 1 in 3
The odds for two dice: 4/6 x 4/6 = 16/36 = .444 or 44 of 100 losses, meaning 55.6 of 100 wins. 11 in 20 (roughly)
The odds for three dice: 4/6 x 4/6 x 4/6 = 64/216 = .296 or 30 of 100 losses, meaning 70 of 100 wins. For three dice, we must subtract 4 other scoring combinations of triple digits (222, 333, 444, and 666, as 1s and 5s are already accounted for). So instead of 64/216, the number really is 60/216 = .277 or 28 of 100 losses, meaning 72 of 100 wins. 7.2 in 10
For four dice, it gets more complicated because we must count triple digit scoring rolls (111, 222, 333, etc.) as well as any 1s or 5s...without double-counting 1 and 5 triples. My math ran out of gas at this point. (Anyone good with probability math who can explain the formula to me for figuring scoring probabilities for 4 through 8 dice?)
Maybe it's enough to say that, if my math is correct, the odds look something like this:
# of dice ----- odds of a roll that scores
1 die ----- 33 in 100
2 dice ----- 56 in 100
3 dice ----- 72 in 100
[I described the dice game in the first comment.]
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This is a description of the dice game. It's played with ten dice. I don't know the name of it...I learned it from Doris and Boyd Maag in Glasgow, Montana. Dice count toward your score when they appear in combinations of three of a kind (any number) or 1s and 5s singly, as follows:
1 1 1 = 1000 points
2 2 2 = 200
3 3 3 = 300
4 4 4 = 400
5 5 5 = 500
6 6 6 = 600
1 = 100
5 = 50
Three of a kind must all appear in a single roll (three rolls that each separately roll a 5 don't constitute 500 points, they make up 150 points). Player rolls once, sets aside ALL scoring dice (all triples and any 5s or 1s), and then has the option to roll again or pass the dice and take the score on the table.
A new roller has the option to roll the dice, building on the last roller's score, or start fresh with all 10 dice.
A "rollover" is when all dice score (example: it's your turn, the last person's score is 3300, and you role one die and get a 1). In this example, you get to re-roll ALL the dice, building on your current score of 3400 (3300 + 100 for the 1) plus anything you get in your next roll of ten dice. There is no limit to the number of rollovers.
If on any roll you don't get anything that scores, you "bust" and get 0 points.
Someone tallies the score as the game progresses. Play is to 40K (or 50K if fewer than 6 players).
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