  We divide the circular boundary of a hyperbolic lattice into four equal
intervals, and study the probability of a percolation crossing between an
opposite pair, as a function of the bond occupation probability p. We consider
the {7,3} (heptagonal), enhanced or extended binary tree (EBT), the EBT-dual,
and {5,5} (pentagonal) lattices. We find that the crossing probability
increases gradually from zero to one as p increases from the lower p_l to the
upper p_u critical values. We find bounds and estimates for the values of p_ l
and p_u for these lattices, and identify the self-duality point p*
corresponding to where the crossing probability equals 1/2. Comparison is made
with recent numerical and theoretical results.
