For a single roll of a fair s-sided die, the probability of rolling each value is exactly 1/s; this is an example of a discrete uniform distribution. For n multiple rolls, with a s-sided die the possibility space is equal to sn. So, for n rolls of an s-sided die the probability of any result is 1/sn.
However, if we are rolling two dice and adding the result together, as in the game craps, the total is distributed in a triangular curve; the case for common dice follows:
where Fs,1(k) = 1/s for 1 ≤ k ≤ s and 0 otherwise.
A faster algorithm would adapt the exponentiation by squaring algorithm:
In the triangular curve described above,
Equivalently, the probability can be calculated using combinations:
where is the floor function. The probability of rolling an exact sequence of numbers is 1/sn.
Read more about this topic: Dice Cup
Other articles related to "probability":
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Famous quotes containing the word probability:
“Legends of prediction are common throughout the whole Household of Man. Gods speak, spirits speak, computers speak. Oracular ambiguity or statistical probability provides loopholes, and discrepancies are expunged by Faith.”
—Ursula K. Le Guin (b. 1929)
“Only in Britain could it be thought a defect to be too clever by half. The probability is that too many people are too stupid by three-quarters.”
—John Major (b. 1943)
“Liberty is a blessing so inestimable, that, wherever there appears any probability of recovering it, a nation may willingly run many hazards, and ought not even to repine at the greatest effusion of blood or dissipation of treasure.”
—David Hume (17111776)