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First Edition Rules Master
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#557469
Professor Scott wrote: Tue Jul 06, 2021 2:07 pm I think the only way to gather an evidence is to follow these steps:
<snip>
I think folks overthink it. All we need is, in addition to our existing "who won", is "who went first".

Consider:

In the wide-view, there are three possible outcomes we're looking at for a given player, playing an opponent who can win on turn N:

1. They can win the game in N-1 (or fewer) turns, which means they would have won the game regardless of whether they went first or not,
2. They can win the game in N+1 (or more) turns, which means they would have *lost* the game regardless of whether they went first or not, and
3. They can also win the game in N turns, which means the winner was dependent on who went first.

#1 and #2 aren't relevant to what we're looking at (if you're a full turn faster/slower, it doesn't matter whether you went first or second). And if we assume (at least for now) that first player is being properly random, that means those decks should be scoring equally on each side of the balance sheet. So we can (again, for a first approximation) assume that those sides are equal and thus cancel out.

It's scenario #3 we're interested in, because this is where going first theoretically should make a difference, and we should see that in our numbers of "how many games did player 1 win".

Marking who went first is a small detail, but it's easy to track, doesn't involve adding a bunch of extra work/turns (that - let's face it, won't get done reliably anyway), and still gives us a lot of useful information. (Off the cuff - is there a correlation between "winner of tournament" and "times went first"? Are we really assigning first-player randomly, or is there bias there we haven't noticed?).

Once we have that basic stat, then we have something to start working with.
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By Professor Scott (Mathew McCalpin)
 - Delta Quadrant
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1E Cardassia Regional Champion 2023
#557499
I have to disagree with @AllenGould,

Simply tracking whether or not the winner went first or not is meaningless if we don't play out that 2nd player's turn. For instance, @sexecutioner and I played yesterday and we went first 100-30. Well unless I was going to get 70 points on might next turn, that fact that he went first is irrelevant. Did I need N+1, N+2, N+3 who knows? I can tell you N wasn't going to be enough.

If we don't play out those close endings, how else are we going to determine whether the second player could have won in N turns as well? For that matter all he is suggesting is that in addition the final result, we add whether the winner went or not, not the number of turns? At least if we add the number of turns, over the course of a tournament we might get some indication of how many turns a given deck takes to win. Unfortunately, we all changes decks so frequently that we as players don't even know the baseline average number of turns our deck needs to win. We might be able to guesstimate a minimum number for turns and heck maybe even script most of them, but we can't have absolute knowledge over every dilemma combo or interference strategy we might face.
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#557500
Professor Scott wrote: Wed Jul 07, 2021 8:13 am I have to disagree with @AllenGould,

Simply tracking whether or not the winner went first or not is meaningless if we don't play out that 2nd player's turn. For instance, @sexecutioner and I played yesterday and we went first 100-30. Well unless I was going to get 70 points on might next turn, that fact that he went first is irrelevant. Did I need N+1, N+2, N+3 who knows? I can tell you N wasn't going to be enough.
Which is kind of my point - if player 2 is more than one turn behind, it doesn't matter how much further behind they were, *or* if they went first. Player 1 was going to win.

Since starting player is random, all those "not close" games should be equally distributed in the 1st and 2nd player columns, which means that (again, assuming that we don't have shenanigans in determining first player and over large sample sizes a given player/deck should be roughly 50/50 1st vs 2nd).

What that means is that if we take PlayerX's 100 wins, all the not-close games *should* be equally distributed between "first" and "second" player, which leaves the variance as "games first player won because they went first".

Now, fair cop - I'm approaching this from a "if my boss asked me to figure this out" angle, rather than a proper science experiment. So I might be missing some subtlety - but I don't know if we need fine-grained details yet until we've vetted the basic premise. (And again - the less stuff we ask, the more of it we'll get. What we *don't* want is to only hear about the games where player 2 woulda won with an extra turn but not about the games where it wouldn't have mattered.)
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By Professor Scott (Mathew McCalpin)
 - Delta Quadrant
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1E Cardassia Regional Champion 2023
#557502
Sure, I agree all the not close games are irrelevant. I was hoping my omission of them in my original post was clear that they didn't even need to be discussed. My concern is how do you determine whether a 70 point deficit is doable in one turn. As player 2, I have have gone and on my last turn gone from 65-35 to 65-100 in a single turn so it is completely plausible. I submit the only to tell a whether 1st player wins by going first is play out that 2nd player turn. That's the only true way to tell if that 1 turn alone was the advantage or not. I don't believe a 100-90 is necessarily any closer than the 100-30 win. There are 2 many variables to say whether 10 or 70 points is out of reach in these 2 examples. Again its all going to boil down to whether or not the players choose to take the time to find out AND submit those results.
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By pfti (Jon Carter)
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2E Cardassia Regional Champion 2023
#557522
Yall are both right.
Allen is right that over time advantage will become appartent. But the sample set might be prohibitivly large to get good date

Playing out the turn gives us more data with fewer examples and can speed up the proof of concept (as would controling variables like ranking)
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#557527
pfti wrote: Wed Jul 07, 2021 12:50 pm Playing out the turn gives us more data with fewer examples and can speed up the proof of concept (as would controling variables like ranking)
If someone was inclined, I'd suggest doing this in a controlled environment - take two identical decks, find a friend, and play a *bunch* of games against each other, alternating first player. In theory you should be able to see the difference in win%, but if we're talking chess-level 5% margins you're expecting to find 11-9 splits over 20 games, and my stats is too old to remember how to calculate how many games you'd have to play to prove it's not just random chance. :)
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