Agree Tsunade is underrated as a Hokage
But it was still stupid to bet on Naruto against Pain and making him come back to fight him
Risky, I accept. Stupid? I dunno, she lost a pretty stupid bet when she met Naruto and had a ton of faith in him ever since.
The decision to send him away to become a Sage also came not long after Naruto created a S-Rank jutsu she had to forbid him from using after he killed Kakuzu with it - a man who fought her grandfather and lived to tell the tale.
She must've also known about the power of Sage Mode considering she appeared familiar with it when it was brought up, and her grandfather was one also (and probably used the same summon).
I think it's fairer to say Tsunade took a big but educated bet.