"I don't see how the warrant buyer ever gets ahead of someone buying at todays price of say $1. If the price goes to $20 the warrant holder makes 20-4.5=$15.50. If you bought at $1 on the open market you make 20-1=$19."

By your calculations investing $50,000 gives you:

100,000 Warrants x $15.50 = $1,550,000

50,000 Shares x 19$ = $950,000

Someone may know something that most of us are earger to find out.