"The lotto, on the other hand, has the exact same odds of winning for every person who buys a ticket."
You're expanding the lotto analogy way beyond the scope that I used it to explain. I didn't intend it to mean the entire economy is like lotto.
Limit the analogy to how not everyone can win lotto, and the bigger the prize won, the more losers there need to be to fund that prize.
In the economy, total spent is total received. Savings is the result of an imbalance. For some to spend less than they earn, accumulating money, other have to be spending more than they earn, going into debt. The more money in some peoples' hands, the more debt in other peoples' hands.
The scope of the lotto example is just that. Even though some can win, not everyone can. For some to win big (accumulate a lot of money), the masses have to lose (be in debt, creating the money).
"We were talking about the likelihood of someone to succeed in America."
No. No percentages were offered. Anecdote was offered that some do go from rags to riches. This was used to imply that all could. Sorry, but no. Just because some win, does not mean everyone can. Even if everyone took risks, worked their asses off, did the "right thing", most are still going to be struggling paycheck-to-paycheck and some are still going to be cleaning toilets for minimum wage.
Just like lotto, for some to win big, the majority have to lose.