St. Petersburg paradox

1. Expected value diverges

 St. Petersburg paradox is interesting, but it's very difficult.

I watched the video about the paradox by a Japanese YouTuber.
He was explaining it so that we could understand easily.
・期待値が無限大な賭け(サンクトペテルブルクのパラドックス) (YouTube)

2. Diminishing marginal utility of money

 The classical resolution uses the presumption of diminishing marginal utility of money.

It's classical but I think it uses advanced mathematics enough.
It's an economical explanation rather than a mathematical resolution.

Mathematics is absolutely logical, and classical economics is also logical.
It presumes that human being can act rationally.
But in fact human being has emotion.

Pasion often drives humans.
Bias sometimes misleads us.
Behavioral economics is newer studies about decision models.

3. Finite lotteries

 The paradox assumes that the casino has infinite resources.

But any real casino has finite resources.
In this case, expected value don't diverge, and it's intuitive value.

It's real.
We can calculate expected value of almost all lotteries which is similar to the paradox, and it will be intuitive enough.
・Visualizing the St. Petersburg paradox: https://tanakah17191928.blogspot.com/2023/05/visualizing-st-petersburg-paradox.html

4. Currency issue and monopoly of resources

 No one has infinite resources.

No country can issue currency infinitely.
There is the limit of money supply whether the economy has gold standard or managed currency system.
If the country supplies money infinitely, hyperinflation will occur.

No one wants worthless stones or papers.
But the stones or papers are finite resources.
So if someone can monopolize the stones or papers, he can make a lot of money.

To speak of extremes, if you can continue to win the infinite lottery, you will be the emperor of the world.
The infinite expected value maybe intuitive.
Many crazy gamblers will come to bet their lives.

5. Infinity

 Infinity often misleads us.

When we can't understand the paradoxes, there may be the problem of infinity.
For example, 0.999... is equal to 1.

How many people can be satisfied by the logic?
It's very interesting but a little difficult.

- To read this article in Japanese