Let's assume that this whole discussion really is about resource redistribution. I don't actually think so, but we can take that as a hypothetical.
A winner comes over to the losers bar, and you want him to give every loser, white or black, the same number of chips.
The problem is that after you all get your re-up, you get to go play at the white table again, and they go back to play at the black table again, which means that you have a way greater chance to not come back to the losers' bar.
Ideally, you'd make both games have the same probability distributions, and that might happen eventually, but until then, the underprivileged losers should get more resources to have similar outcomes.
Expected value is everything.