Getting first player bias?

[Ceaseless]

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?

I see no reason to believe the dice aren't random.

If you're trying to demonstrate some sort of bias there needs to be evidence displaying it. A lot of games showing that certain characteristics will lead to certain biases. You talk about weird odds of 7s being rolled but post no evidence of such consistent anomalies occurring. Can you actually demonstrate an ability to predict biases that contradict what would be expected of random games on a larger scale?

A lot of players overestimate how good they are. Say I played a game of Splendor and got paired against a very low rated player, idk, a 300. If I chose to play mindlessly against them, I might only win the majority of my games, and as a result of an occasional loss, my rating would get crushed. If you don't enough attention, you can let upsets happen. Yeah, some games are going to go worse for you than others, just as some will go better, and they'll randomly clump together at times too. That's just variance.
Edit: Also, the reasons they're at the 300s could differ. They could be a beginner still learning the basics, or a new account getting to their actual rating, etc.

As for winning/losing streaks, that is also to be expected. As you win your rating goes up and you tend to be paired vs stronger players, leading to more losses. On top of that, you'll get less for winning and more for losing vs the same players, so to keep up your gains you either have to win more often or win vs stronger players at the same rate you used to win against weaker ones.

[ahrnge]

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.

Ah, I agree. I mistakenly thought you were endorsing the fourth approach, which seemed an odd choice to me. The first approach makes sense.

[euklid314]

I have to correct my post. In every 2-player game that just finished there is one player (lets call him player A) that was starting player in this specific game and one player, player B, that was 2nd in turn order.

Only player A can finish a 9-game streak of always being starting player. Since he just was starting player there is a 1/256 chance that he was also starting player his previous 8 games.

Player B was just *not* the starting player, thus he has a 1/256 chance of also *not* having been starting player in his previous 8 games.

Thus, as ahrnge wrote, there are (number of games)*1/256 9-long streaks of some player being starting player AND (number of games)*1/256 9-long streaks of some player *not* being starting player.

In case of 16.000 2-player games per day approx. 60 9-long streaks of somebody always being 2nd player will end per day.

[Solly321]

I am not a premium player, and over 5 days of Azul game play, I went from my high of 435 EOL to 275 !! I have not changed any strategy or game play methods. Sure, part of the game has "luck", but it was like a "switch" was flipped, that limits the success of non-premium players. I have no proof, just posting for wider community of my recent experience.

[Archisian]

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?

I see no reason to believe the dice aren't random.

If you're trying to demonstrate some sort of bias there needs to be evidence displaying it. A lot of games showing that certain characteristics will lead to certain biases. You talk about weird odds of 7s being rolled but post no evidence of such consistent anomalies occurring. Can you actually demonstrate an ability to predict biases that contradict what would be expected of random games on a larger scale?

A lot of players overestimate how good they are. Say I played a game of Splendor and got paired against a very low rated player, idk, a 300. If I chose to play mindlessly against them, I might only win the majority of my games, and as a result of an occasional loss, my rating would get crushed. If you don't enough attention, you can let upsets happen. Yeah, some games are going to go worse for you than others, just as some will go better, and they'll randomly clump together at times too. That's just variance.
Edit: Also, the reasons they're at the 300s could differ. They could be a beginner still learning the basics, or a new account getting to their actual rating, etc.

As for winning/losing streaks, that is also to be expected. As you win your rating goes up and you tend to be paired vs stronger players, leading to more losses. On top of that, you'll get less for winning and more for losing vs the same players, so to keep up your gains you either have to win more often or win vs stronger players at the same rate you used to win against weaker ones.

Damn, a 300 ELO is considered very low? God I hate myself lol.

[BarnardsStar]

I am not a premium player, and over 5 days of Azul game play, I went from my high of 435 EOL to 275 !! I have not changed any strategy or game play methods. Sure, part of the game has "luck", but it was like a "switch" was flipped, that limits the success of non-premium players. I have no proof, just posting for wider community of my recent experience.

Tough break. Now, how does one rig Azul? Given how the only random bit is the initial arrangement of tiles in the factories, and everything after that is player-driven, you’d have to be incredibly brilliant and subtle to somehow arrange those tiles to favor one player. And to what end? The idea that this site would rig Backgammon or Can’t Stop is ridiculous; the idea that they would somehow rig Azul is both ridiculous and nigh impossible.

Isn’t it simply more likely—by far—that you went up against players who were better able than most to challenge your “strategy and game play methods”?

[Ceaseless]

I am not a premium player, and over 5 days of Azul game play, I went from my high of 435 EOL to 275 !! I have not changed any strategy or game play methods. Sure, part of the game has "luck", but it was like a "switch" was flipped, that limits the success of non-premium players. I have no proof, just posting for wider community of my recent experience.

Tough break. Now, how does one rig Azul? Given how the only random bit is the initial arrangement of tiles in the factories, and everything after that is player-driven, you’d have to be incredibly brilliant and subtle to somehow arrange those tiles to favor one player. And to what end? The idea that this site would rig Backgammon or Can’t Stop is ridiculous; the idea that they would somehow rig Azul is both ridiculous and nigh impossible.

Isn’t it simply more likely—by far—that you went up against players who were better able than most to challenge your “strategy and game play methods”?

Or they just played bad and don't want to admit it. A nice mix of not playing well and a bit of bad luck can do things. A lot of players just refuse to accept the possibility that they have an influence on why things aren't going well for them. There's luck, and there will be moments where there was nothing you could do to avoid a loss, but that's not what happens every time, and a player's ability to sort out what they do have an influence over and what they don't matters.

[dschingis27]

but it was like a "switch" was flipped,

That's your brain working there, not your maths. (I don't mean that negatively, it's very normal that brain and maths are enemies.) Sequences of roughly +/-100 Elo happen inevitably in games like Azul, 7Wonders, etc., because of the intrinsic randomness, even if you had a constant skill level (which is inhuman, your skill fluctuates, too, not only your luck). I made a simulation recently to showcase the intrinsic Elo fluctuation if we assumed a constant skill level. https://boardgamearena.com/forum/viewto ... 28#p248828
That was based on a 300 Elo playing against 200 Elo constantly, if you play more players closer to your skill, the variance in game results is even higher, and outrageous sequences are even more likely.

It's mostly just randomness doing it's ugly job but us humans can't help but seeing patterns.

[tbhp]

I haven't done extensive testing on this game, but I do notice that over 17.5 million games of Azul have been played on BGA since roughly the end of 2021.

With over 16,000 games per day on average, I would barely blink at a 1/128 chance cropping up.

That's not how probabilities work. When you see someone say they had something unlikely happen to them, that's to be expected. But if that same thing happens to you, you are in a different position. In this case it's legitimate to wonder which possibility is the more likely explanation.

It's why miracles are a thing. For other people, it's easy to dismiss miracles as some people just being crazy. But for the person witnessing the miracle, they are not wrong to think that maybe it does mean something. The odds assessment is totally different from their perspective.

[Andrei3009]

Damn, a 300 ELO is considered very low? God I hate myself lol.

It all depends on the game and the player. Splendor is a very high elo ceiling and compared to this 300 is really not much. No one will say that 300 elo is weak in challengers\can't stop

Also, Ceaseless is a extremely good Splendor player and for his level 300 elo players pose almost no threat (he should win ~95% of games against them)