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These include whether a specially marked die (called the Mayhem die) has rolled highest, the lowest number rolled, and whether any two dice show the same number. One other commonly used variant of the 6-sided dice roll is the d3, which is a 6-sided die roll, with the result divided by 2. The average result is 2, and the standard deviation is 0.816.
The probability of dice combinations determine the odds of the payout. There are a total of 36 (6 × 6) possible combinations when rolling two dice. The following chart shows the dice combinations needed to roll each number. The two and twelve are the hardest to roll since only one combination of dice is possible.
As an example, consider the roll 55. There are two rolls ranked above this (21 and 66), and so the probability that any single subsequent roll would beat 55 is the sum of the probability of rolling 21, which is 2 ⁄ 36, or rolling 66, which is 1 ⁄ 36. Therefore the probability of beating 55 outright on a subsequent roll is 3 ⁄ 36 or 8.3%.
Each table has 1 two, 2 threes, 3 fours etc. A standard exercise in elementary combinatorics is to calculate the number of ways of rolling any given value with a pair of fair six-sided dice (by taking the sum of the two rolls). The table shows the number of such ways of rolling a given value :
E.g. a roll of 2-2-4 gives the banker a point of 4. Note that one cannot set a point of 1 or 6, as those would result in an automatic loss or win, respectively (see above). Re-roll: If the dice do not show any of the above combinations, then the banker rolls again and keeps rolling until they get an instant win or an instant loss, or sets a point.
Diceball! is a board game in which two players roll dice to simulate a baseball game, one representing the visiting team and the other the home team. Both players use the dice to throw the baseball from the mound to the plate and field the ball on defense. Diceball! was designed to mirror the statistical reality of baseball.
For example, rolling a single six-sided die yields a uniform distribution, where each number from 1 to 6 has an equal chance of appearing. However, when rolling two dice and summing the results, the probability distribution shifts, as some sums (like 7) become more likely than others (like 2 or 12).
[1]: 169 [2] They throw the dice again: if they roll the chance, they win; if they roll the main, they lose (unlike on the first throw); if they roll neither, they keep throwing until they roll one or the other, winning with the chance and losing with the main. The caster keeps their role until losing three times in succession. [3]