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For example, if two fair six-sided dice are thrown to generate two uniformly distributed integers, and , each in the range from 1 to 6, inclusive, the 36 possible ordered pairs of outcomes (,) constitute a sample space of equally likely events. In this case, the above formula applies, such as calculating the probability of a particular sum of ...
The players alternate rolling the dice and, if possible, moving. On each die, the 1 represents a pawn, 2 a knight, 3 a bishop, 4 a rook, 5 a queen, and 6 a king. The player may move either of the pieces indicated on the two dice. For example, a player rolling a 1 and a 2 may move either a pawn or a knight. A player who rolls doubles (the same ...
A set of dice is intransitive (or nontransitive) if it contains X>2 dice, X1, X2, and X3... with the property that X1 rolls higher than X2 more than half the time, and X2 rolls higher than X3 etc... more than half the time, but where it is not true that X1 rolls higher than Xn more than half the time.
Another example of events being collectively exhaustive and mutually exclusive at same time are, event "even" (2,4 or 6) and event "odd" (1,3 or 5) in a random experiment of rolling a six-sided die. These both events are mutually exclusive because even and odd outcome can never occur at same time.
These two non-atomic examples are closely related: a sequence (x 1, x 2, ...) ∈ {0,1} ∞ leads to the number 2 −1 x 1 + 2 −2 x 2 + ⋯ ∈ [0,1]. This is not a one-to-one correspondence between {0,1} ∞ and [0,1] however: it is an isomorphism modulo zero , which allows for treating the two probability spaces as two forms of the same ...
The problem of estimating the maximum of a discrete uniform distribution on the integer interval [,] from a sample of k observations is commonly known as the German tank problem, following the practical application of this maximum estimation problem, during World War II, by Allied forces seeking to estimate German tank production.
7th Sea and Legend of the Five Rings use only 10-sided dice, so it omits the number of sides, using notation of the form , meaning "roll eight ten-sided dice, keep the highest six, and sum them."Although using a roll and keep system, Cortex Plus games all use roll all the dice of different sizes and keep two (normally the two best), although a ...
Rolling a 4, 6, 8, 10 with a pair of the same number. Sometimes also known as "hard six", "hard eight", et cetera hi-lo a single roll bet for 2 or 12 hi-lo-yo a single roll bet for 2, 11, or 12 high A bet on or roll of 12, also see boxcars hop A single roll bet for a specific combination of dice to come out. Pays 15:1 for easy ways and 30:1 for ...