[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.

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26 minutes ago

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.