Luck of the Draw?

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gnuvag
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Luck of the Draw?

#1 Post by gnuvag » Thu Jun 04, 2020 8:34 pm

Hello all.

Is country selection in any given game completely random?

I've recently played seven Classic games and been each of the countries once, which seems pretty unlikely, so I was wondering if there was some kind of assisted randomness or weighting to it?

Same seems to apply with 1v1 games with friends, it seems to have been neatly alternating which side we are in games.

Or am I just currently in some kind of weird probability paradox?

Cheers...
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mhsmith0
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Re: Luck of the Draw?

#2 Post by mhsmith0 » Thu Jun 04, 2020 9:11 pm

My understanding is that the ppl in charge of site adjusted the assignment process so it over weights powers you haven’t been lately and underweights those you have been more of.
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cdngooner
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Re: Luck of the Draw?

#3 Post by cdngooner » Thu Jun 04, 2020 9:38 pm

That's great.

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Re: Luck of the Draw?

#4 Post by Squigs44 » Thu Jun 04, 2020 10:36 pm

mhsmith0 wrote:
Thu Jun 04, 2020 9:11 pm
My understanding is that the ppl in charge of site adjusted the assignment process so it over weights powers you haven’t been lately and underweights those you have been more of.
This is true, but only to a certain degree. Getting all 7 countries in 7 games is still unlikely.
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Re: Luck of the Draw?

#5 Post by Minister of Silly Walks » Thu Jun 04, 2020 10:49 pm

Squigs44 wrote:
Thu Jun 04, 2020 10:36 pm
mhsmith0 wrote:
Thu Jun 04, 2020 9:11 pm
My understanding is that the ppl in charge of site adjusted the assignment process so it over weights powers you haven’t been lately and underweights those you have been more of.
This is true, but only to a certain degree. Getting all 7 countries in 7 games is still unlikely.
Happened to me in my first seven games, too. Would be interesting to hear more about the algorithm, unless, of course, this is a secret of some sort.

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Re: Luck of the Draw?

#6 Post by RoganJosh » Thu Jun 04, 2020 10:53 pm

Squigs44 wrote:
Thu Jun 04, 2020 10:36 pm
This is true, but only to a certain degree. Getting all 7 countries in 7 games is still unlikely.
Remind me to revisit this once all of the 21 Valis gunboat games are over.
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gnuvag
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Re: Luck of the Draw?

#7 Post by gnuvag » Fri Jun 05, 2020 6:20 pm

Interesting!

I'd like to hear more about the algorithm too...

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Re: Luck of the Draw?

#8 Post by RoganJosh » Fri Jun 05, 2020 8:08 pm

Squigs, maybe you know, the Hungarian algorithm as implemented in the code at the moment, does it have any randomness? Or is it actually a deterministic algorithm?

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Re: Luck of the Draw?

#9 Post by mhsmith0 » Fri Jun 05, 2020 8:16 pm

RoganJosh wrote:
Thu Jun 04, 2020 10:53 pm
Squigs44 wrote:
Thu Jun 04, 2020 10:36 pm
This is true, but only to a certain degree. Getting all 7 countries in 7 games is still unlikely.
Remind me to revisit this once all of the 21 Valis gunboat games are over.
I can say with no spoiling that with 17 games done, the power assignments revealed so far are EXTREMELEY consistent with a materially skewed algorithm that adjusts weights substantially based on power assignment history (no one at 0 of any individual power, no one at more than 4 of any individual power, and only a small handful of 1s and 4s)

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Re: Luck of the Draw?

#10 Post by RoganJosh » Fri Jun 05, 2020 11:17 pm

mhsmith0 wrote:
Fri Jun 05, 2020 8:16 pm
I can say with no spoiling that with 17 games done, the power assignments revealed so far are EXTREMELEY consistent with a materially skewed algorithm that adjusts weights substantially based on power assignment history [...]
To be fair, the algorithm is supposed to adjust for power assignment history, and that's actually a good thing. Choosing uniformly at random would not be a good fit for a slow seven player game like Diplomacy. I think it was more the format with 21 games between the same 7 players. This is setup which the algorithm can't handle. (For people who don't know what I'm talking about, see viewtopic.php?f=7&p=155961#p155961).

It is worse that just distributing the powers basically evenly. The games actually appear in groups where, within each group, the power assignment is the same up to one or two transpositions. This is what it looks like so far. Player order is: brain, meme, chaqa, smith, rj, valis, wusti. In paranthesis the number of transpositions needed to obtain one distribution from the previous.

F I G E R A T G1
F I G R E A T G8 (one)

E A I T R G F G7
R A I T E G F G10 (one)

R F T G A I E G6
R F A G T I E G15 (one)
E F A G T I R G21 (one)
E G A T F I R G14 (two)

I G E R F T A G2
I G R E F T A G9 (one)
G I R E A T F G17 (two)

G T A F I R E G3
A T E F I R G G11 (two)

G E T I A F R G13
T E G I R F A G20 (two)

F R T A E G I G16
T R F A G E I G12 (two)

These are all the games that have finishes so far. The probability to get a distribution like this, if randomizing uniformly, is around .000001.

Now, there are four games remaining. Where in this table do you think they will end up? I know we're not allowed to discuss ongoing gunboat games on the forum... but... since I know what power I'm playing in each of those games...

1M$ question: when the algorithm counts weights, it counts the number of games you've played with each power in the variant. Does bot games count?

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Re: Luck of the Draw?

#11 Post by Claesar » Sat Jun 06, 2020 7:12 am

RoganJosh wrote:
Fri Jun 05, 2020 11:17 pm
...
These are all the games that have finishes so far. The probability to get a distribution like this, if randomizing uniformly, is around .000001.
...
In math problems with many options, each individual option will always have a low probability. If you flip a coin randomly ten times, the probability of the final outcome will be .001. That seems very low, but doesn't mean the coin is off.

If you create the games truly random and then apply your grouping methodology, what is the probably of a final outcome?
Now, there are four games remaining. Where in this table do you think they will end up? I know we're not allowed to discuss ongoing gunboat games on the forum... but... since I know what power I'm playing in each of those games...
Feel free to PM me your predictions. I'm not in the games.
1M$ question: when the algorithm counts weights, it counts the number of games you've played with each power in the variant. Does bot games count?
At some point we did discuss the bot games counting for this. You're correct that we added country selection later, which could have created a loophole that allows you to weigh your own results and thereby control what countries you end up getting in games that matter. I'll look into it.

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Re: Luck of the Draw?

#12 Post by Claesar » Sat Jun 06, 2020 8:01 am

Squigs44:
If you select a country in a bot game it does not affect which country you draw in future games
I personally coded the country selection portion for bot games and jmo in reviewing the code double checked this
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Re: Luck of the Draw?

#13 Post by RoganJosh » Sat Jun 06, 2020 12:48 pm

Claesar wrote:
Sat Jun 06, 2020 7:12 am
If you create the games truly random and then apply your grouping methodology, what is the probably of a final outcome?
If by a specific outcome you mean a distribution of powers for the sequence of games (i.e., that you don't just look at patterns up to permutations of powers and games), then the probability for a specific outcome is 10^(-63).

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Re: Luck of the Draw?

#14 Post by mhsmith0 » Sat Jun 06, 2020 11:45 pm

I’m going to hold off on getting TOO far into the weeds, especially given four games are remaining, but I’m somewhat inclined to dispute the assertion that what we’re seeing is problematic.

First of all, I’d like to redefine the problem a little bit.

RJ discusses in terms of transpositions, but I think that’s a limited framework. Instead, I’d rather just look at number of power assignments specific games have in common.

To start with: One transposition games necessarily have five powers in common (6 is impossible for obvious reasons). Games 1 and 8 reverse England and Russia (me and RJ), while the ave the exact same values for France (bomb), Germany (chaqa), Italy (meme), austria (valis), and Turkey (Wusti). So “five in common” or “one transposition” are synonymous

There are, by my count, 5 such pairings among the 17 completed games (1/8, 2/9, 6/15, 7/10, and 15/21). This is above average for a rand event (I did a pure rand setup twice, and I got one or two depending)

TWO transition games, however, aren’t quite as useful a framework imo. Two transitions can either have four powers in common (such as games 3/11, where Wusti, Chaqa, and bomb shuffled up, while the other four of us were held constant), or three in common (such as games 9/17, where meme and bomb flipped IG, RJ and Wusti flipped AT, and the other three of us were constant)

The latter example SEEMS potentially problematic, but really isn’t. If, for instance, g9 was over and g17 wasn’t, if RJ wanted to solve for expected opponents, he’d be using the entirely wrong framework! Since he was Austria in g17, he’d use g6 and g13 as guides. Game 17 featured ZERO of the other player power assignments as g6/13, despite Chaqa randing Turkey in BOTH of RJ’s other Austria games (in g17 he randed Russia)

So for 4 of the 7 powers, the entire comparison framework would be busted because THEY were transposed (and obv you don’t know when it happens to you). Even if you happen to be one of the three nit moved, it’s not super useful. Say Valis wanted to solve for g17 powers. He MIGHT use g9 as a closer analogue, since it happened closer together to g17, but that’s not guaranteed

G2 comparison: ZERO powers are identical! Sure, it’s three simple flips, but if valis wanted to analogue it, he’d have no reasonable way to do it
G9 comparison: only TWO other powers are identical! Again, it’s two simple flips, but there’s no way for Valis to know for sure.

So I tend to think the only ones to care about are cases where 4+ powers are identical, because everything else is just way too noisy to draw meaningful predictions. Looking at the 17 games so far:

5 pairings of 5 matches among the 17 completed games (1/8, 2/9, 6/15, 7/10, and 15/21)
2 pairings of 4 matches among the 17 completed games (3/11, 14/21)
Combined that’s just 5% of competed pairings, which is pretty meh

However, we can dig deeper:
Highly comparable games have TENDED to be among those randed 7 or 6/8 apart (sort of the “sweet spot” for a model that de-emphasizes what you’d recently randed in a seven power structure)

Among the 7 apart pairings: 1/8, 2/9, etc

Two had five matches (1/8, 2/9), one had four matches (14/21), one had three matches (13/20) and the rest (so far) had zero, one, or two. This is, I think, not super useful for trying to tease out matches, though it is SOME info.

Among the 6/8 apart pairings: 1/7, 1/9, 2/8, 2/10, etc
One had five matches (15/21), one had four matches (3/11), one had three matches (9/17) and the rest were two or lower.

Again, SOME info but not that much, and of course you have no way to know in a given game if you should use 7 apart of 6/8 apart (you can use the shorthand “what was MY power rand, but even that can get you very very wrong answers)

TLDR 3/10 of the seven apart games had heavy overlap (4+ matches) and just 2/18 of the 6/8 apart games did. It’s enough to give SOME info but is far from breaking. I’d also note that even this much only comes about with a full 17 of 21 games done, and at, say, 12 of 21 done, it’d be FAR harder to crack anything at all.

Ps I could be wrong, but iirc the games were finalized and randed in exact numerical order. On an even mildly adjusted series (for instance, let’s say Valis does a 28 game series where he does all 28, but others can sign up for some smaller number if they like, and a TD assigns games to ppl), it’d be nearly impossible to track, EVEN IF all games randed in order (which they wouldn't). Even small doubt about which players were in which games (and an unknown/difficult to track order of games randed would break it further) would mainly break any attempted power assignment solving, or at least I’d think so...

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Re: Luck of the Draw?

#15 Post by RoganJosh » Sun Jun 07, 2020 12:27 am

mhsmith0 wrote:
Sat Jun 06, 2020 11:45 pm
Ps I could be wrong, but iirc the games were finalized and randed in exact numerical order.
Your memory fails you. If I remember correctly, we started with something like games 21 to 15 in reverse order, and then the remaining 14 started the day after, somewhat in order but not perfect. Something like that, even though I don't remember exactly. I also don't know if that information can be recovered.

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