Formula for calculating luck?

Question

Mathematics

Let's say there are 2 people who play in a casino. The first played 250 games and won 180 of them. The second played 40 and won 24.
How can you calculate which of them is more lucky?
With the same number of games, you can simply calculate the percentage of winnings. But what if the first player has hundreds of games and the second has 3 games and 3 wins? In this case, the second will have 100%. That is, you need to somehow take into account the number of games played and the percentage of wins at the same time.
Tell me please.

Answer 1

Read a textbook on probability theory and statistics.

Answer 2

Are casinos the same?
Then to compare "luckiness" it is enough to look at the net winnings of each at the moment.
And yes, if there are only three games and three wins, you need to take the jackpot and leave)

Answer 3

If nothing depends on the player, say it is necessary to guess a random number in a range, then luck (rather the ratio of wins) should be equal, regardless of the past result (the principle of player error comes to mind https://ru.wikipedia.org/wiki/ player_error ). Another thing is if something depends on the decisions made by the player. In this case, it is probably necessary to compare the policies of the players, and to compare the mathematical expectation when using the policies.
A small example of the second option. Imagine a game with the following rules. If you leave the game, you get 10p and that's it. if you keep playing you get 4p and roll the die. If it rolls 1 or 2 then the game ends otherwise the game continues you start over again (decide whether to continue or not).
Here is how the game can be represented graphically (Markov decision model):
It can be seen that the "go out and get 10p" policy yields 10p, while the "continue game" policy tends to 12p. And luck, as it were, is an unscientific value.

Answer 4

The ratio of winnings to the total number of games.
+
it is necessary to set some confidence interval for this value, which shows how the calculated value of luckiness can differ +\- from the real one.
That. the confidence interval for 3 games will be 100%
and for 250 - 2.5%,
so you should take the worst luck values ​​​​and compare them.
The confidence interval can be somehow calculated from the statistics. There are even tables for this case, google it.

Answer 5

https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D...
https://ru.wikipedia.org/wiki/%D0%92%D0%B5% D1%80%D...

Answer 6

Probably you need to know, in addition to probability theory, the Hurwitz criterion

Answer 7

СуммаВыигранныхДенег / СуммаПотраченныхДенег

Answer 8

How can you calculate which of them is more lucky?

Obviously, divide the number of wins by the total number of games and multiply by 100. You get the winning percentage.
But that doesn't mean anything. Because it all depends on the distance. Those. about a large number of games played. On a long stretch, all the suckers still remain in the suckers, because all the games in the casino are sharpened to bring profit to the sucker. If you take the same roulette, then the probability of winning in it is not 50%, but about 45%, because. there are two more zero fields 0 and 00.
+ here it should be added that all guessers have no memory (and in the case of automatic machines, they can generally be imprisoned by wise programmers for the total undressing of a sucker), i.e. each subsequent result does not depend on the previous one.
Loch always stays in suckers.
In this light, checkers, chess games with complete information compare favorably, you can safely play them for money, if skill allows.

Answer 9

You need to calculate the statistical confidence. This can be done on Wikipedia or any boring theory textbook. And you can read a simple and understandable text here italylov.ru/blog/all/ctatisticheskaya-dostovernost...

Answer 10

It makes sense to talk about the calculation of luck if the results of the games depend only on luck, as far as I understand. If the result depends not only on luck, this is a completely different story.
Since there is no such thing as “luck” in TV and MS, you have to invent it yourself. For example, you can compare the probability of winning at least 180 games out of 250 and at least 24 out of 40. If the probability of winning in each game is the same, this is a binomial distribution.