## A Non-Random Walk

Main article:

A Non-Random Walk

Pick a card, any card. Half are red, half are black. Each time a
card is picked, the wheel moves. The distance moved is always
half the distance from the wheel to the origin (the black dot), *but*
the direction depends on the colour of the card: red moves left,
black moves right.

Because the cards are shuffled, the picks are random, and you might think
that it's not possible to tell where the wheel will stop, once all cards
have been turned over. However, that's not the case. The wheel always
stops at a distance *a* - *a* × 0.75^*n* from the origin, where *a* is
the starting position of the wheel, and *n* is the number of red (or black)
cards.