yes if you take a fraction of the richer agent's wealth instead of the poorer the system stabilizes, so it's specifically that the poor are betting a significant portion, always, makes them the losers in the yard sale model.
that is, they stand to win 20% of their wealth but also can lose 20%, whereas to the rich agent that may be 1% or 0.01% of their wealth at that stage.
If the poor could take 20% of the rich agent's wealth, then it would bounce around more.