After paying the juice you will have $347.90 after third win. Deduct you initial $50 stake and you will end up with $297.90 profit which is exactly how much 3 team -110/-110/-110 parlay will pay you.

So the hole in your logic is that you forgot to deduct your initial stake from payout.

Plus, where did this
Regardless, the payout is higher than a 3-1 payout would be.
come from?