Probability: Everyone having same chess position

I just got a weird thought, as to what would be the probability of everyone on Earth having same chess configuration at same time?
Considering 10^120 positions and 8 billion population, I would guess something about 1 in 10^millions or so.
If anyone knows then tell.

weird thought

Sounds also like a weed thought. I'm not against useless calculations. Sometimes it's fun to figure out the number. The difficulty in calculating this lies in the fact that the probability of that particular position decreases every turn, so you can't just multiply, you'd have to calculate it for all possible turns the games could be in and then add them up. Another problem is that the games don't start at the same time, under the same conditions and so on, so you'd have to include the chance of people arriving at this position. Finally, if you wish to know for 8 billion people you'd have to include the chance that all of them are playing chess in the first place.

All in all, I'd say pretty low.

some one gottta #dothemath

@Msharaj said in #1:

I just got a weird thought, as to what would be the probability of everyone on Earth having same chess configuration at same time?
Considering 10^120 positions and 8 billion population, I would guess something about 1 in 10^millions or so.
If anyone knows then tell.
Actually, let's assume there are 10^150 chess positions possible. 8 billion humans means 4 billion chess matches.
(10^150)^4,000,000,000 = 10^600B (B = billion, im gonna use that to save time)
But also, we have to consider the chance that a person is playing a chess match.
Im gonna use an average of people putting 0.5% of their time into chess (7 min 12 secs of chess per day), since a lot of people dont play chess.
thats 1 in 200, or about 10^2.3
(log(200) = 2.3)
(10^2.3)^8 billion = 10^18.4B
Multiplying these together we get 1/10^618.4B.
BUT, humans can cooperate. Unfortunately, the chances of all 8,000,000,000 humans agreeing on something is 0, so we will never see this.

@ThatRandomPerson111 said in #4:

Actually, let's assume there are 10^150 chess positions possible. 8 billion humans means 4 billion chess matches.
(10^150)^4,000,000,000 = 10^600B (B = billion, im gonna use that to save time)
But also, we have to consider the chance that a person is playing a chess match.
Im gonna use an average of people putting 0.5% of their time into chess (7 min 12 secs of chess per day), since a lot of people dont play chess.
thats 1 in 200, or about 10^2.3
(log(200) = 2.3)
(10^2.3)^8 billion = 10^18.4B
Multiplying these together we get 1/10^618.4B.
BUT, humans can cooperate. Unfortunately, the chances of all 8,000,000,000 humans agreeing on something is 0, so we will never see this.
i forgot, many people are born a second, meaning it is impossible for every human to be playing a chess match at one time.
So the odds? 0%

@ThatRandomPerson111 said in #4:

Actually, let's assume there are 10^150 chess positions possible. 8 billion humans means 4 billion chess matches.
(10^150)^4,000,000,000 = 10^600B (B = billion, im gonna use that to save time)
But also, we have to consider the chance that a person is playing a chess match.
Im gonna use an average of people putting 0.5% of their time into chess (7 min 12 secs of chess per day), since a lot of people dont play chess.
thats 1 in 200, or about 10^2.3
(log(200) = 2.3)
(10^2.3)^8 billion = 10^18.4B
Multiplying these together we get 1/10^618.4B.
BUT, humans can cooperate. Unfortunately, the chances of all 8,000,000,000 humans agreeing on something is 0, so we will never see this.

That's pretty well thought answer! And very close to modelled figure (with 7.8 billion population): (@Msharaj here's your answer)
1 in 1.0 * 10^456Billion
'Everyone on Earth playing the
exact same Chess configuration' -
There are 10*120 possible chess moves. If all 7.7 billon people on Earth played every chess move randomly with each other, this is the odds that all 3.8 8 games
played will have the exact same config.
Source:
https://youtu.be/RV-WV2g2muE
Skip to 9:11 time there to see.

@ThatRandomPerson111 said in #5:

i forgot, many people are born a second, meaning it is impossible for every human to be playing a chess match at one time.
So the odds? 0%
We can't take all factors, factors like those needs to be trimmed or ignored else it's virtually impossible to arrive at a computable number.

@ThatRandomPerson111 thanks for doing the calculation, and @Akbar2thegreat thanks for the reference for the same.

Considering every chess game starts with the same position, it doesn't really matter how many possible chess positions there are. The answer will be the probability that everyone starts a chess gale at the same time, plus a tiny tiny amount accounting for the probability that the same non-starting position occurs for everyone at the same time.

@mango-in-my-teeth said in #9:

Considering every chess game starts with the same position, it doesn't really matter how many possible chess positions there are. The answer will be the probability that everyone starts a chess gale at the same time, plus a tiny tiny amount accounting for the probability that the same non-starting position occurs for everyone at the same time.
Technically, the starting position isn’t considered a position as such cause the game isn't in progress yet if no move is made so the original question isn’t answered. It doesn't need to be complex middle game position either. At least one move on either side is needed to carry out the math.