Yes, but you seem to be forgetting most stakers
get half the profits PLUS their ENTIRE buy-in amount. Since your staker is only putting half in this time, the buy-in amounts cancel each other out, imo and you're still left with the 50/50 split.
Remember your backer is making it possible for you to play in said game. If it's not for him, you wouldn't have the
chance to make any money.
Usually, stakers receive either a higher percentage or their buy-in amount back plus the 50/50, unless you can guarantee him that you ARE a winning player, like most pros do...and in that case you can surely go about changing the terms of the deal.
Most stakers won't like it, and in your case...you might not only lose him as a staker if you change the deal on him, but he might decide to stop mentioning the new/good games around the area, to you.
What I would suggest is you playing the first game under his deal, 50/50 sounds good. If you win, then you have the upper hand in making a better deal for yourself for the next game he stakes you in (since you showed him proof, you can be a winning player). Good luck in whatever you decide to do.
