The table above follows five players, Ana, Ben, Cleo, Dev and Eli, through a whole game. The hot sauce set is the gift everyone wants: Ben takes it on turn 2 and Eli takes it from Ben on turn 5. Under rules with a freeze after two steals, it would have stayed with Eli for good at that point; here it simply stays because the game is over.
The other thing to notice is Ana. She's robbed twice and opens three gifts in all, yet the game still lasts exactly five turns. That's the effect of the one-steal-per-turn rule: whoever loses a gift opens a new one, a new gift ends the turn, and the pile goes down by one gift every turn. With 10 players you'll see at most 9 steals, and with 20 players at most 19.