[We haven't forgotten about games here at OE. Quite the opposite. I've been working on a post about games of perfect and imperfect information for a while now and it should be going up soon. While I was thinking about the backgammon section of the post, I remembered a variant for math teachers I've been meaning to write up for a few years now.]
FIVE-PENNY BACKGAMMON
Played exactly like traditional backgammon except:
The dice are replaced with five coins;
instead of rolling the dice, each player tosses the five coins using the cup, adds one to the number of heads then repeats the procedure a second time;
the two (h + 1) totals are treated like the results from rolling a pair of dice.
For example, tossing two heads then tossing three would be the same as rolling a three and a four.
PLAYER'S CHOICE
In this variant, the player can choose dice or coins on a turn-by-turn basis.
FIVE-PENNY BACKGAMMON IN THE CLASSROOM
Though this is largely matter of preference, I would introduce five-penny games well before any kind of formal or semi-formal introduction to the underlying probability theory. This gives the students a chance to become comfortable with these examples before they see them in lectures and it also gives them the opportunity to discover on their own that there's a difference between having the same possible outcomes and having the same probabilities associated with those outcomes.
Cool!
ReplyDeleteI dunno if any interesting games have only one die, but if someone needed a simpler place to start, I could imagine that working well.