<human>: Can you condense the text into three sentences or less?

Today a friend and I were playing our remixed version of Rummy. The main rule is "The first player to reach 200 points wins." Since you can gain or lose points during each hand, it is not uncommon for the opponents to reach this threshold at the end of the same hand, however my friend has an odd idea about the scoring. 

In today's scenario, he was up 182-180. I ended up scoring several points more than him and the final score was 254-242. That means I won and should have been the end of it, right? Wrong. He asserted that he won because he was ahead in the previous round and if you were to add up the points 1 by 1, and simultaneously for the both of us, he would reach 200 sooner. I argued how ludicrous that sounded and tried to sway him otherwise. He made an analogy to 2 men stacking bricks until one can reach a ceiling. Whether or not you break the ceiling doesn't matter, but who gets there first does. I retaliated saying that if you graphed the point increases as points on a plot versus time, I would reach 200 before him because I had gained more points in the same time period. We still have yet to decide who rightfully won that match. So, what do you guys think?
<bot>: If 2 people play a game to 200 points and both pass it in the same round, is the winner the one who was closer before or the one with the higher score at the end of the round?