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The reason why most people think the rich win more than the poor is they judge it based on the winning amounts. Let's say the rich has $10B net worth and he only use $1M to gamble, then he earn like $200K and people think he earn more. While the poor that only has $10K net worth and he use $100 to gamble, when he already earn tenth amounts of his bankroll which is $1K, they don't see the poor earn more than the rich.
$100 x 100 bets = $10,000.
$1M x 10,000 bets = $10B.
The given example only shows that the rich have a hundred times more chance to bet than the poor. Meaning, that the rich can stay longer in gambling, and they can make more money the more they stay on betting. Given that poor people can earn the tenth amount of their bankroll, the rich can also do the same using the same strategy.
Aside from that, you stated that the rich used $1M to gamble then he earned $200k, that's 20% already. While the poor used the $100 and made it to $1k which is only 10% of his money. How come that the poor earn more than the rich?
Sorry I don't get you. Won 1000 dollar with 100 dollar, isn't it 100%? I didn't quite get your math!
Anyway, it doesn't matter. As long as you have greater resources, you'll have greater opportunity. How can I gambler test out his luck if he doesn't have anything to gamble at the first place. Four-five games and you are all out. That's the whole point. When rich are getting multiple chances, poor's have limited changes. It's like a cat's life, they have nine lives many says.
Apologies if the computation is unclear. The computation only states how many times a rich gambler can make a bet. To make it clear, the given example by @Solosanz says that a poor gambler uses $100 as his bankroll, given he has a $10k net worth. Using $100 as an
example, he can make a total of 100 bets until he reaches his net worth limit. While the rich gambler uses $1M as his bankroll, given he has a $10b net worth. It will take a hundred times more chance than the poor before they reach the limit of their net worth. It only means that he has more capability to bet because of the size of his money.
However, what is stated below is right. Whatever the size of the bankroll, the point is whether you are rich or poor, it's all the same. All people experience losing and winning.
The point is don't think that rich people will always win even if they use large amounts of capital and only win a little but it's bigger in the eyes of poor people. In fact, if we go back to discussing logically, winning and losing are all the same, everyone has experienced winning, whether it's him or her. rich or poor and will definitely experience defeat too..