  We review the existence of the infinite length self-avoiding walk in the half
plane and its relationship to bridges. We prove that this probability measure
is also given by the limit as $\beta \rightarrow \beta_c-$ of the probability
measure on all finite length walks $\omega$ with the probability of $\omega$
proportional to $\beta_c^{|\omega|}$ where $|\omega|$ is the number of steps in
$\omega$. The self-avoiding walk in a strip $\{z : 0<\Im(z)<y\}$ is defined by
considering all self-avoiding walks $\omega$ in the strip which start at the
origin and end somewhere on the top boundary with probability proportional to
$\beta_c^{|\omega|}$ We prove that this probability measure may be obtained by
conditioning the SAW in the half plane to have a bridge at height $y$. This
observation is the basis for simulations to test conjectures on the
distribution of the endpoint of the SAW in a strip and the relationship between
the distribution of this strip SAW and SLE$_{8/3}$.
