#557469
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.
Professor Scott wrote: ↑Tue Jul 06, 2021 2:07 pm I think the only way to gather an evidence is to follow these steps:I think folks overthink it. All we need is, in addition to our existing "who won", is "who went first".
<snip>
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.
What deck should you play next?
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