[Literature] Game Balance ch4 - Cards, Dice, and Other Randomness

My notes from course 4 of the Game Balance class of Summer 2010, by Ian Schreiber.

Monte Carlo simulation = good way to approximate stats when the maths are too hard.

Dices are used for independent game events: each dice roll is independent of the previous roll. XdY = throw X items that have Y sides at the same time (ex: 1d6 = one 6-sided dice). For custom dices, eg a 6-sided dice with 1-1-1-2-2-3 on the sides: p(1)>p(2)>p(3).
More dice = less random (= smaller std deviation)> Example: p(7) for 1d10 is 1/10, but it is 10/32 for 5d2.

Cards are used for dependent game events: some events may not happen again if they have happened a certain number of times Revealing information as the game goes does not change the odds in previous player choices, but it changes the odds of non-player variables. Famous related problems: Monty Hall's 3 doors or families with at least one boy.