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To see the difference, consider the probability for a certain event in the game. In the above-mentioned dice games, the only thing that matters is the current state of the board. The next state of the board depends on the current state, and the next roll of the dice. It does not depend on how things got to their current state.
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.
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 ...
This leads to different choices of sample space. The σ-algebra is a collection of all the events we would like to consider. This collection may or may not include each of the elementary events. Here, an "event" is a set of zero or more outcomes; that is, a subset of the sample space. An event is considered to have "happened" during an ...
A sample space is usually denoted using set notation, and the possible ordered outcomes, or sample points, [5] are listed as elements in the set. It is common to refer to a sample space by the labels S, Ω, or U (for "universal set"). The elements of a sample space may be numbers, words, letters, or symbols.
Another way to describe collectively exhaustive events is that their union must cover all the events within the entire sample space. For example, events A and B are said to be collectively exhaustive if = where S is the sample space. Compare this to the concept of a set of mutually exclusive events. In such a set no more than one event can ...
Such information corresponds to a 3D point in the graph's space. If this point is inside the gray solid, the player should roll. Otherwise, the player should hold. Many 2-dice variants have been analysed, [7] and human-playable Pig strategies have been compared to optimal play. [8] For example: Hold at 20 is a popular strategy.
The winner is the player with the most chips at the end of the game. If two or more players have the same number of chips, the winner is the player with the most dice. If two or more players are tied in both chips and dice, there is a "roll-off." Each player gets one die and rolls; the first player to roll lose a die to the center loses.