ForumForum Games ► New and Improved Gender Race
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Hol up I think I've cracked it! I'm pretty happy with this version:
  • Start at (250,250,250)
  • Girls win at (750,0,0), NBs win at (0,750,0), boys win at (0,0,750)
  • Each post must increment one stack and decrement one stack, so that the total of all three stacks is always 750.

Notes on this new version (jaded-750) as opposed to the one I posted above (jaded-375):
  • Assuming similar things* to the second point of my last notes section, every valid play-state (excluding win states) is a (metastable**) equilibrium. This is true of OGGR and j750, but not of (M)KR or j375.
  • Each win condition is a distance of 500 moves from the starting configuration. True of all of OGGR, (M)KR, j375, j750.
  • The space of valid play-states is two-dimensional in j750. Also 2D in (M)KR, but 1D in OGGR and 3D in j375.
  • Each win state is 750 moves from each other win state. Also 750 in j375, but 1000 in OGGR and variable in (M)KR.
  • The maximum distance from any given win state is 750 moves. 1125 in j375, 1000 in OGGR, and variable in (M)KR.
  • The distance from each win state to each of the other win states is the maximum distance from any win state to any other point. Also true in OGGR, but not in j375 or (M)KR.
  • Girls win when the first stack reaches its maximum value. True of OGGR, j375, j750, but not (M)KR, which put boys first (which isn't, like, a real problem, but my stubborn, picky brain didn't see a reason to break from precedent).

*this could use some fleshing out given the slight change in what each move consists of, but I'm fairly confident you'll know what I mean
**don't think I'm using this term 100% correctly, but I'm close enough that I don't really care. can elaborate if needed.

edit: Just noticed that this post, which contains a description of the j750 ruleset, was the 750th reply to this thread. That's pretty rad.

edit 2: j750 also needs the stipulation that no stack can go below 0.
  
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That is indeed awesome.

I do like the idea of constraining a 3-way problem into 2 dimensions. Makes it easier to analyze without sacrificing the spirit of the game. I think this version also allows for more counterplay to be utilized, as a singular move must cause benefit to one team and harm to another, with the third team left neutral through a singular exchange. Unlike j375 or (M)KR, this version would have active fights rather than passive ones.
  
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The one problem I can see is that we might get situations where two teams gang up on the third and just absolutely demolish them. Especially if those two team are just a bit more active than the third. Which might all lead to the third team being even less active than they were before, which might not be very fun. Guess we won't know without trying it out tho.
  
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Game theory and actual implementation has some cool effects. It is possible to attempt and simulate those targeted attacks, mainly because they've been done before on other races. In the country race, a few guys teamed up to perfectly time their decrements against opposing countries in order to take advantage of getting ninja'd. When both of them posted at the exact same time, then no matter how much a single person defends, their combined power always decremented the stack by double what the defender could put in.

I believe the thread was WWIV. Instead of taking gender identity, people could freely choose a nationality to defend, and there was less reason to stay on a sinking ship, as the race wasn't as personal.
  
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Man, I had completely forgotten about WWIV. It's really a very similar game to my n-team gender race*, with two big differences. In WWIV, once you're out, you're out, whereas you're not truly out of the gender race until someone else wins. And WWIV starts with each stack at a fixed number (50), regardless of how many stacks there are, which means the minimum amount of moves to victory from the starting point increases with the number of teams, while my n-team gender race always takes (approximately) 500 moves for any team to win.

*Never posted about it, but it's a simple extension of OGGR** and j750:
  • Start at the n-tuple (x,x,x,…,x), where x=round(500/n-1)
  • Each move increments one stack and decrements another.
  • No stack can go below 0.
  • Each team wins when all stacks but theirs reach 0.

**if you notice that OGGR is equivalent to a game with a second "phantom stack" that also starts at 500 but always moves the opposite direction of the single stack in OGGR

Also:
It is possible to attempt and simulate those targeted attacks, mainly because they've been done before on other races.

This was a very concerning sentence the first time I read it. Took me a few tries to figure out what you actually meant.
  
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This was a very concerning sentence the first time I read it. Took me a few tries to figure out what you actually meant.

Upon reading this sentence out of context, I understand where you're coming from. This is indeed a very concerning phrasing that I mistakenly made.

I forgot about the country elimination part. It does add an interesting dimension to the game, but you're right that it's different from OGGR and like derivatives.
  
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Two squares!
  
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