Indulging Patrician's last ability looks at how much life you've gained in the turn, even if it wasn't on the battlefield when you gained life. It doesn't care if you also lost life, even if you lost more life than you gained.

Each opponent loses just 3 life, no matter how much life you've gained past 3 life.

If you haven't gained 3 life by the time your end step begins, Indulging Patrician's last ability won't trigger at all.

In a Two-Headed Giant game, Indulging Patrician's last ability causes the opposing team to lose 6 life.