Getting first player bias?

[Jellby]

If every day's somebody made a post about it these forums would be nothing but people asking about bias in random systems.

Ermm... What do you mean "if"?

[h_illes]

Don’t use 16000 games but 1778 groups of 9 games.

Using 16000 games is correct. Let's assume 2-player games and both parties played at least 9 games for simpicity. Then for any single game, there is a 1/512 chance that for one of the players it is the 9th consecutive game as second player. Sure, this event might not be independent between the games, but expectation is additive regardless of independence. So on average, you get 16000/512 such games per 16000 games, that is, about 30 per day.

At least get your math correct before you start lecturing folks.

After a statement like this, the bottom line is that you make sure you get the math correct yourself.

[nik592]

In addition to the fact that the number of tables makes this a more likely probability that 1 in 512 might seem, even if the odds were longer (or the number of tables was fewer), rare probabilities DO happen. As several people have said, this time you won the (statistical) lottery.

I've looked through my own history of (2p) Azul games and can find instances where I was against a non-premium player and played 2nd. So it does happen that way, it's not always the premium player goes first.

[euklid314]

Since OP never wrote about those 9 games being played on the same day, it is irrelevant on which days the games where played.

If 16.000 games are played on one day, one can look at the last 8 games preceding each of these 16.000 games because each of the 16.000 could have just completed a 9 game streak. Thus approx. 30 9-long 2nd player streaks and approx. 30 9-long 1st player streaks are completed each day.

P.S.: I assume not all of these 16.000 games are 2-player games, thus the actual number will be lower.

On the other hand some players will not only consider 1st player/2nd player streaks in one specific game (like Azul) but over all their 2-player games, e.g., "I played 3 games of Backgammon, 4 games of Cant Stop and 2 games of Azul and was 2nd player in all of them". This will also occur approx. 30 times a day.

[ahrnge]

Don’t use 16000 games but 1778 groups of 9 games.

Using 16000 games is correct. Let's assume 2-player games and both parties played at least 9 games for simpicity. Then for any single game, there is a 1/512 chance that for one of the players it is the 9th consecutive game as second player. Sure, this event might not be independent between the games, but expectation is additive regardless of independence. So on average, you get 16000/512 such games per 16000 games, that is, about 30 per day.

At least get your math correct before you start lecturing folks.

After a statement like this, the bottom line is that you make sure you get the math correct yourself.

Isn't there a 1/512 chance for EACH of the two players in each of these 16000 games? i.e. shouldn't there be ~60 occurrences of a "9 game second player streak" per day, assuming 2-player games only?

Like if we we assumed further that these 16000 games were all played between the same two players, player A would hit on average about 30 of these "9 game second player streaks," and player B would hit an additional ~30. (It also might be worth noting unrelatedly that these streaks would sometimes overlap, for example a 12-streak would be counted as four 9-streaks, so you would likely get fewer than 60 such forum posts per day).

Maybe I'm misunderstanding how bga tracks "games played." Would a 3-player game of Azul contribute 3 games toward the 16000? Is that why everyone is saying 30?

[h_illes]

Isn't there a 1/512 chance for EACH of the two players in each of these 16000 games? i.e. shouldn't there be ~60 occurrences of a "9 game second player streak" per day, assuming 2-player games only?

Like if we we assumed further that these 16000 games were all played between the same two players, player A would hit on average about 30 of these "9 game second player streaks," and player B would hit an additional ~30. (It also might be worth noting unrelatedly that these streaks would sometimes overlap, for example a 12-streak would be counted as four 9-streaks, so you would likely get fewer than 60 such forum posts per day).

You have a point, but it ultimately depends on how the original problem is defined precisely. Let me elaborate. What you consider is essentially whether we look for the streak for a prescribed player or either one, and it indeed corresponds to a factor of 2. There is another ambiguous issue that hasn't been brought up yet: whether we want to count 10th, 11th etc. games in the streak, or only strictly the 9th. This essentially corresponds to a factor of 1/2.

Altogether, if you...
- consider either player and only the 9th game, then the probability is 1/512;
- only consider a prescribed player each game and only the 9th game, then the probability is 1/1024;
- consider either player and any game from the 9th game on, then the probability is 1/256 (this scenario gives your ~60 games per day);
- only consider a prescribed player each game and any game from the 9th game on, then the probability is 1/512.

I took the liberty to assume that out of the 4 options, we consider the first, in which case the probability is 1/512, but all the others are legit answers in the corresponding scenarios.

Maybe I'm misunderstanding how bga tracks "games played." Would a 3-player game of Azul contribute 3 games toward the 16000? Is that why everyone is saying 30?

No, see above.

[lazyjane25]

New reader here ....sorry if this is likely redundant:

Are dice truly random? I've played way too many games of Catan, and I've noticed:

-The number of sevens is disproportionate to statistical likelihood of 7s being rolled (16% per game versus reality of around 30%)

-When I play against 'new' (very low scoring) players, they almost always win - seems like there's an algorithm that grants them the win

-When I win a lot of games and my ELO goes over 200, I suddenly lose almost every game -- and my resource on a six, say, never hits. I can play the game pretty well, but I have recently lost 10 in a row - very frustrating!

Anyone have insight into this or is it truly random?

[Jellby]

Are dice truly random?

Yes. until proven otherwise.

-The number of sevens is disproportionate to statistical likelihood of 7s being rolled (16% per game versus reality of around 30%)

Can you prove that? Not one game where it is ~30%, that proves nothing. But a number of consecutive games with a cumulative total of say 1000 rolls with 30% 7?

-When I win a lot of games and my ELO goes over 200, I suddenly lose almost every game

Yes, when you had a lucky streak, it ends with an unlucky streak. If it didn't, you'd continue with your lucky streak and it would simply end later (with an unlucky streak). Also, as you increase your elo you're more likely to be matched with higher-ranked players, so you'll be more likely to lose.

[h_illes]

Anyone have insight into this or is it truly random?

It is truly random. Once again, it's not fun when it happens to you, but similar scenarios occur to many other players regularly. It's nothing extraordinary.

[Cile]

New reader here ....sorry if this is likely redundant:

Are dice truly random? I've played way too many games of Catan, and I've noticed:

-The number of sevens is disproportionate to statistical likelihood of 7s being rolled (16% per game versus reality of around 30%)

This comes up occasionally. In a previous thread a user created a simple page that plots 99 graphs of randomized dice rolls and 1 outlier that wasn't randomized. See how quickly you can spot the fake: https://onecompiler.com/python/3zvmdjamm

You can see the code used on the page so you know it's not rigged, and it uses 56 rolls which is about average for a game of Catan.

You can also use this page to quickly graph a series of dice rolls yourself: https://academo.org/demos/dice-roll-statistics/
Just set the number of dice to 2 and click the button as fast as you can. See how many rolls it takes for the graph to resemble a normal distribution.
I just tried it and it took 246 rolls before 7's caught up to be rolled as frequently as 8s, and I still have more 4s rolled than 5s. (You do not get nearly that many rolls in a game of Catan)

-When I play against 'new' (very low scoring) players, they almost always win - seems like there's an algorithm that grants them the win

In all likelihood the new players are not actually new to the game, just new to the site. BGA does not know if you have any experience with a game that you have not played here so starts everyone at 0, which is going to be lower than the player's actual skill level.
If someone has played Catan 100s of times in person, then starts playing on BGA, they will have a low score and be matched with other people with low scores until the win enough games to get their score up. In that process they will likely easily win games despite their "low score".

-When I win a lot of games and my ELO goes over 200, I suddenly lose almost every game -- and my resource on a six, say, never hits. I can play the game pretty well, but I have recently lost 10 in a row - very frustrating!

As stated above: You had a lucky streak and your ELO went up. You then had an unlucky streak.