Is first pick truly random?

[itakeitback]

Hi,
I was trying to figure out how the first player to go is determined. I recall reading it was random, but in a duel, I should roughly be awarded first turn half the time. Seeing how I wasn't receiving nearly as frequent first turns, I decided to do a little experiment across 30 games and discovered I had received first turn on only 8 games. That is a 25% chance of going first and I think this is abysmally low. Are there other factors that determine first turn? Is it truly random and should I continue to observe how this averages out over a longer period?

[Silene]

[...] should I continue to observe how this averages out over a longer period?

This!

[itakeitback]

Currently at 51 games and still only 12 games I've went first. That is clearly below 25%. I'm starting to doubt this is purely random and suspect some other factor is at play here.

[Earthboundia]

I've always wondered what the method was, it seemed a bit weird. Never did any definitive testing but I always thought that it had something to do with the order that players joined a lobby.

[Cos-]

Currently at 51 games and still only 12 games I've went first. That is clearly below 25%. I'm starting to doubt this is purely random and suspect some other factor is at play here.

12 out of 51 is very very close to 25%. Randomness is NOT the same as even distribution; the odds that you'd get picked exactly 1/4 of the time are quite low even for that many games, yet you ended up really close to it.

People complain about randomness all the time when it doesn't give the results they want, but in a small number of games you're likely to see proportions that vary very far from the "ideal" distribution. That's how randomness works, and it's normal.

Also, this has nothing to do with Wingspan as far as I can tell. BGA picks who goes first for all games, it doesn't have special logic for Wingspan. So this is a topic that belongs on the main discussion forum, unless you have a reason to believe there's something Wingspan-specific about it (in which case, please say what that is).

[itakeitback]

Thanks for filling me in - didn't know BGA determined first pick, not a special logic in Wingspan. Apologies if this violated rules for posting, and appreciate not deleting the post if so.

Prior to my tallying first picks, there was a streak of games where I was rarely awarded first pick. This prompted me to start the count. So in all fairness, my odds were below 25% if you account for those uncounted matches. It was 25% once I started the tally.

To be clear, I wasn't complaining about randomness not suiting my agenda, I merely pondered if there was more to it under the hood. Anyone new to the site going through those improbable odds will also have the same curiosity whether there are other hidden mechanisms. It appears I was simply unlucky.

35/97 if you're curious.

[Soetriet]

According to ChatGPT you will need a few hundred to a thousand games for an even distribution

"The concept of probability is based on the idea that over an infinite number of trials, the observed outcomes will approach the theoretical probability. However, in practice, the number of games needed for the observed probability to converge to the expected probability can vary.

In your case, if the true probability of going first is 50%, you could expect the observed probability to be closer to 50% as the number of games increases. However, it's challenging to pinpoint an exact number of games needed for this convergence in a real-world scenario. It could happen sooner or later due to the inherent variability of random processes.

If you're looking for a rough guideline, a few hundred games might start to give you a clearer picture, but keep in mind that even with thousands of games, there can still be fluctuations around the expected probability."

[Mathew5000]

Currently at 51 games and still only 12 games I've went first. That is clearly below 25%. I'm starting to doubt this is purely random and suspect some other factor is at play here.

12 out of 51 is very very close to 25%. Randomness is NOT the same as even distribution; the odds that you'd get picked exactly 1/4 of the time are quite low even for that many games, yet you ended up really close to it.

People complain about randomness all the time when it doesn't give the results they want, but in a small number of games you're likely to see proportions that vary very far from the "ideal" distribution. That's how randomness works, and it's normal.

If you flip 51 coins and only 12 of them are heads, that is quite suspicious. If these are fair coins, the probability that the number of heads would be 12 or lower, in 51 flips, is on the order of 1 in 10000. At that point you'd have to start thinking that the coins are weighted to favour tails.

Regardless of what chatgpt says, you certainly do not need a few hundred games before the number of heads is likely to be close to 50% (for any reasonable definition of "close"). For example, if you flip a fair coin 51 times, there's about a 95% chance that the number of heads will be from 19 to 32 inclusive.

Of course it's possible that the OP is just very unlucky; there's presumably more than 10000 players on BGA, playing predominantly two-player games, so a few of them would be expected to go first less than a quarter of the time, in a given run of 51 games. And obviously those few are more likely to post on the forum saying "why am I hardly ever chosen to go first" than someone who gets chosen to go first roughly half the time.

But for me, the OP's post raises a valid question about whether the player who goes first is a random 50-50 draw, or is it something else like who signs up first in the game lobby. I would be interested in hearing that question answered by BGA staff.

And as for Wingspan on BGA specifically, going first is a huge advantage in a two-player game, because it means that not only do you get first pick from the tray, but you know you'll get first pick from the tray so you can make your initial discards accordingly, and then in round 4 at the end of the game you'll go last, which could be advantageous in a close game. See https://boardgamearena.com/forum/viewtopic.php?t=31374 and https://boardgamearena.com/forum/viewtopic.php?t=30245

[Jellby]

For example, if you flip a fair coin 51 times, there's about a 95% chance that the number of heads will be from 19 to 32 inclusive.

Don't overestimate that 95%. It looks like a lot, but it means that 1 in 20 will be out of that range. So by assuming 95% is the "norm", 1 in 20 people would complain about unfairness. And and 1 in 20 is not a few, given the number of players...

[itakeitback]

Hi all,

Thanks for the lively discussion and taking interest in my post. Like Mathew5000 pointed out, my odds were (and still are) pretty unfavorable so it piques my interest whether this is simply luck. As an update, I am currently at:

58/176

Which is just about 33%. It's improving but very gradually.
As an addition, I started the tally with the hypothesis that league tiers factored in determining first pick. But after tracking 176 games it seems it didn't have much of an influence. I wish I tracked elo distribution as well, but that didn't cross my mind at the time.