There are always people in the world who say, ‘I live on a pittance’, while at the same time some of the super-rich own assets the size of national budgets. The following website will let you understand the mechanism of and for these super rich people.
Why the super rich are inevitable
https://pudding.cool/2022/12/yard-sale/
In order to intuitively understand how money flows in the world, we first prepared a scenario, which is "playing a coin tossing game in a room of 100 people."
Set everyone's money to $1000 and the bet to 20%. Everyone then bets $200 on the first game.
In the first game, the person on the right won. The person on the left now has $800, and the person on the right has $1,200.
In the second game, if the loser of the first game and the winner of the first game play against each other, the loser of the first game can only bet $160 (20% of $800), but the winner of the first game. Those who do so can wager $240 (20% of $1,200).
Under the above conditions, if the person who lost in the first game wins the second game, his or her money will be $960. On the other hand, the person who wins the first game, despite losing the second game, still has a fortune of $1040, which is more than his original fortune. In other words, even in a game where both sides have the same chance of winning, the side with more money still has an advantage.
As the number of games overlaps, the situation of "people with more money have an advantage" becomes more obvious. The chart below shows the distribution of your bankroll by the time you finish playing the two games above. At this point, the person with the least money has $640, and the person with the most money has $1,440. The currency distribution when the
game is repeated 10,000 times is as follows. Although the winning rate is always 50%, the minimum amount is $0 and the maximum amount is $77428. If the win rate was 50%, it might seem like the participants' money would change the same, but in reality there would be an overwhelming difference. In this way, the mathematical model in which the difference increases even if the winning rates are the same is called the "yard sale model (yard sale model)".
In the above game, the amount held at the beginning is constant, but if there is a difference in the amount held at the beginning, the amount held changes as follows. First, assume that the person on the left has $100 and the person on the right has $1,000, and the bet is set to "20% of the money held by the person on the left."
In the first game, the person on the left won, winning $20. The bet for the second game is set at $24 (20% of $120).
In Game 2, the guy on the left lost, losing $24.
Since the game continues, the person on the left wins the third game and loses the fourth game. At this point, they both have two wins, but the left has less money than the initial state and the right has more money than the initial state.
The results of repeating the game 64 times are as follows. Both have 32 wins and 32 losses, but you can see the guy on the left has less money.
can alleviate the above-mentioned "people with more money have an advantage" situation by introducing a redistribution mechanism, that is, "collecting a certain proportion of money from everyone and distributing it equally to everyone". The image below shows the distribution of funds when executing 1000 coin tosses, each with $1000 of money and 20% staked. The yellow lines are not reassigned, the purple lines are reassigned. Looking at the chart, you can see that after reallocation, the difference in currency holdings is smaller.
The results of repeating the game 2000 times are as follows. Without redistribution, the difference in owning money would be larger, but with redistribution, the increase in difference would be suppressed.This kind of redistribution is equivalent to social taxation. Even if taxation is carried out at a certain tax rate, it can inhibit the expansion of inequality.
