two pairs of dice

a ppt is here

comparing probabilities, maybe helped by a sample space
[the variety of 1 to 4 dice shown here rolls better than a tetrahedron]

2 dice, 2 way tables

a ppt is here

considering which, if any, of four games are theoretically fair

two dice and generalising

start off looking at how many times a 4, 5 or 6 is obtained on any or both of two dice

identify theoretical probabilities from a sample space

compare this with experimental data: student results that have been collected together

explore further, seeking/developing a general rule

the powerpoint

fair games or not?

sample space diagrams provide a way to decide whether a game is fair or not

a ppt is here

quirky dice

a ppt is here

there are several examples of three or more non-transitive dice

















in the long run,
A beats B
B beats C
but A doesn't beat C...

links with Condorcet's paradox

and like 'rock - paper - scissors'

students can consider long term outcomes by entering 'A' or 'B' etc. in the sample space diagrams

 there are several other varieties...

Sicherman dice

a ppt is here

dibingo

a ppt is here

a slight variation of work on summing two dice
experimental work before theoratical
students selct one of the four cards (so it's helpful for them to play in groups of 4)

students may well select the bingo 'cards' with more numbers on them

as well as actually rolling two dice
the interactive from Shodor.org is good to use (as a class demonstration) because it keeps a tally of totals that have been generated (click on the dice icon and keep the number of throws at one)
but there are several other interactives on the net...

including typing 'roll a dice' into google and clicking one more 6 sided dice, to have two dice

or the teacherled one (click dice 3 because you do not want to use that)