  We introduce new black hole solutions to the Einstein-Yang-Mills-Born-Infeld
(EYMBI), Einstein-Yang-Mills-Born-Infeld-Gauss-Bonnet (EYMBIGB) and
Einstein-Yang-Mills-Born-Infeld-Gauss-Bonnet-Lovelock (EYMBIGBL) gravities in
higher dimensions $N\geq 5$ to investigate the roles of Born-Infeld parameter
$\beta $. It is shown that, these solutions in the limits of $\beta \to 0,$ and
$\beta \to \infty ,$ represent pure gravity and gravity coupled with Yang-Mills
fields, respectively. For $0<\beta <\infty $ it yields a variety of black
holes, supporting even regular ones at $r=0$.
