Well his first mistake was to think that it's going to be so cut and dry that he can still make poker Good chance he might be able to but also a good chance he wont. tell him how you feel about it and that they are moments you will never get back again. But to be fair after a few hours there isn't really a need to stay with you if everything is fine. If you are in a shared room and he's been up all the previous night with you then he wont be able to stay and have a snooze with you afterwards at all so it makes sense to go home and get rest, as should you.

Our first was born at 1.20pm and DH had left by 5, with #2 she was born at 7.50am and he stayed for about 4hrs, #3 he stayed overnight with me as I'd had a lot of dramas after her birth and he didn't want to leave me, plus it was late by then anyway and with #4 again he stayed the night as it was too late for him to drive home.