The amount that you subtract from the selling price to determine the gain is called your basis. You have to calculate your basis separately for the share of the house that you paid for in the original purchase, and the share that you buy from your partner. How much of the original $500,000 purchase price did each of you pay? That will determine your respective percentages of ownership.
From the figures that you gave, it sounds like you are buying your partner's share of the house for considerably less than its current market value. If so, there is a gift element involved. That complicates the calculation of your basis, and your partner (not you) will almost certainly have to file a gift tax return, though he probably will not actually have to pay any gift tax. To calculate your basis you would need to know the fair market value at the time of the gift, and the amount of any gift tax that he pays, as well as how much he paid towards the original purchase. Fair market value at the time of the gift should be determined by a professional appraisal, not a guess by you or a real estate agent.
If you made any improvements to the house, either before or after the buyout, the cost of the improvements will also affect your basis. The effect of the improvements will be different depending on whether they were made before or after the buyout. Since you don't know what future improvements you might make, you can't really determine right now what your basis will be when you sell the house, but you could come up with a tentative number on the assumption that you will not make any improvements.
Obviously calculating your basis is fairly complicated. If you have a need to know, it would probably be best to consult a local tax professional. But if you want to pursue it here, please give actual amounts, not "let's assume."
