Suppose that you start with $10, and you wager $1 on an unending, fair, coin toss indefinitely, or until you lose all of your money. If
X
n
{\displaystyle X_{n}}
represents the number of dollars you have after * n* tosses, with
X
0
=
10
{\displaystyle X_{0}=10}
, then the sequence
{
X
n
:
n
∈
N
}
{\displaystyle \{X_{n}:n\in \mathbb {N} \}}
is a Markov process. If I know that you have $12 now, then it would be expected that with even odds, you will either have $11 or $13 after the next toss. This guess is not improved by the added knowledge that you started with $10, then went up to $11, down to $10, up to $11, and then to $12.