1. To bet or risk everything one has on something. Tech companies seem to be putting their shirts on virtual reality being the future of the industry. Anyone with a gambling addiction knows the feeling of putting your shirt on a hand of cards, feeling sure it will pay off big time, only to lose everything.

2. By extension, to be absolutely certain that something will happen. I would hope that the industry is moving towards a more customer-friendly position, but I wouldn't put my shirt on it.