Order of play

[Adwiti]

I created seven turn-based tables with the same four persones in different games.
After the games started, it turns out that we are 'sitting' in the same order in each of the games, which means that you have to wait quite a bit and then make 7 turns at the same time.

So I wonder: How is the sitting order determined?

[Mathew5000]

Please provide links to the seven tables. (I certainly would not have expected that the order of play would be the same in each of the games.)

[euklid314]

Indeed interesting that the order A-P-C-T appeared that often in your games. You are playing approx. 10 or 11 games with these players and 7 or 8 of those games are in said turn order.

Still possible that it is random and pure coincidence (as it should be to my knowledge), since there are only 6 turn orders.
But it is approx. 1:45.000 to get same turn order in 7 consecutive 4-player games, thus quite unlikely to happen. If your 7 games were not started consecutively (as I said, you have more than 7 games with these players) then it immediately gets much more likely. 7 same turn orders out of 10 games is perhaps a 1:1000 event (I am too lazy to calculate).

[mikkashar]

This is apparently deliberate.
See https://boardgamearena.com/bug?id=15582 -- particularly, the entry by lordalx.
" If you think player should be shuffled around the table each time for a specific game and this is not the case, don't hesitate to raise a suggestion on this specific game bug and suggestion"

An older thread on the topic: https://boardgamearena.com/forum/viewto ... 9&start=10
That points to an even earlier discussion: https://boardgamearena.com/forum/viewtopic.php?t=9942

There's a suggestion with a general request for randomization: https://boardgamearena.com/bug?id=124173
No action taken on that, and it seem unlikely to happen

There are suggestions for several specific games:
https://boardgamearena.com/bug?id=12591 (7 Wonders, no action)
https://boardgamearena.com/bug?id=55851 (7 Wonders Architect, no action)
https://boardgamearena.com/bug?id=13177 (7 Wonders, implemented) (does this address 12591 as well?)
https://boardgamearena.com/bug?id=22942 (Papayoo, rejected)

There may be specific bug reports/suggestion requests for other games.

[Mathew5000]

I guess I may have misinterpreted the OP's post. Does "the same four persons in different games" mean that, for example, it was Catan at one table, Wingspan at another, and so forth? Or was it "different games" just in the sense that you could be playing a turn-based game of Catan, for example, at one table and a different game of Catan at another table. The problem is that the English word "game" could mean the game in general, such as baseball, or it could mean an instance of the game being played (e.g. "the Blue Jays have only won 4 games against the Yankees this season").

[mikkashar]

I guess I may have misinterpreted the OP's post. Does "the same four persons in different games" mean that, for example, it was Catan at one table, Wingspan at another, and so forth? Or was it "different games" just in the sense that you could be playing a turn-based game of Catan, for example, at one table and a different game of Catan at another table. The problem is that the English word "game" could mean the game in general, such as baseball, or it could mean an instance of the game being played (e.g. "the Blue Jays have only won 4 games against the Yankees this season").

Oh! That interpretation didn't even cross my mind. Having seen the player order issue discussed repeatedly (and griped about it), I may've leapt to a similar looking but incorrect problem.

A clarification from Adwiti would be welcome.

[euklid314]

Looking at the turn based games of OP, he is playing different games (Splendor, Through the Ages, Great Western Trail, Azul, Mischwald,....) with his 3 friends.

[Mathew5000]

Looking at the turn based games of OP, he is playing different games (Splendor, Through the Ages, Great Western Trail, Azul, Mischwald,....) with his 3 friends.

Thanks; that's how I originally understood what OP said. I guess Mikkashar interpreted it the other way.

Still possible that it is random and pure coincidence (as it should be to my knowledge), since there are only 6 turn orders.
But it is approx. 1:45.000 to get same turn order in 7 consecutive 4-player games, thus quite unlikely to happen. If your 7 games were not started consecutively (as I said, you have more than 7 games with these players) then it immediately gets much more likely. 7 same turn orders out of 10 games is perhaps a 1:1000 event (I am too lazy to calculate).

If we're on the page, it's the same as the probability of getting exactly 7 of the same face when you throw 10 standard dice, which is:
(6*(10 C 7)*5^3)/6^10 = 15000/6^9 = 1/671.85

For the probability of getting at least 7 of the same face when you throw 10 dice:
((10 C 7) * 5^3 + (10 C 8) * 5^2 + (10 C 9) * 5 + (10 C 10)) / 6^9
= 337/209952 ≅ 1/623

I also asked ChatGPT, but it went wrong somewhere and told me the answer is 3.85%: https://chatgpt.com/share/68190835-ab68 ... 86f0c3da1f

Edited to add: I eventually got ChatGPT to agree that my answer is correct: https://chatgpt.com/share/68190835-ab68 ... 86f0c3da1f

[Jellby]

I eventually got ChatGPT to agree that my answer is correct

I'm pretty sure you can get ChatGPT to agree with anything.

[Meeplelowda]

If we're on the page, it's the same as the probability of getting exactly 7 of the same face when you throw 10 standard dice, which is:
(6*(10 C 7)*5^3)/6^10 = 15000/6^9 = 1/671.85

I'm getting something pretty different using the binomial probability formula: probability of exactly k successes is P(X=k) = (n C k)*(p^k)*(q^(n-k)), where n=10, k=7, p=1/6, and q=5/6

Works out to about 1/4032, which happens to be almost exactly 1/6 of your result, so either you're missing a factor of 1/6, or I have an extra factor of 1/6.

Ed.: Leaving my mistake for intellectual honesty. My calculation is for a specific number to appear exactly 7 times. You correctly calculated the chance of any number (or in this case, order of players) appearing exactly 7 times, which is 6 times my result.