6 outs out of 46 unseen cards in the deck is 6/46 = ~13% chance to hit your hand.

Now, 12.5% is 1/8 so when I said 8:1, that was remarkably wrong and that's twice this morning I kind of donked a post, so I do apologize. Of course, 1/8 is 7:1 against, and it is just a quick estimate, so yeah, 6.6:1 against is absolutely correct.

OK, so lets look at the implied odds again, considering 6 outs:
4.6*0.38 + $0.07 = $1.82

Hero will have ( $2.24 - $0.14 - $0.38 = ) $1.72 behind, which caps the amount of Villain's money he can win.

Again, this is more than Hero can afford, so I sucked out on my advice.