ForumForum Games ► New and Improved Gender Race
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Been thinking about this game a bit and I'm pretty sure it's skewed in the NBs' favor. NBs have an "ally" for both numbers, but boys and girls each have a column where they're 1 against 2. A fairer game might be one with 3 numbers, with the goal being getting your column to a certain number and the other two to 0, that way everyone's got two columns with an ally and one column where they're 1 against 2.
  
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Yeah, I somewhat agree. That's probably the only reason I could hold out on my own back when I was the only person pushing for an NB victory. I think part of that issue is no one goes for a 500/500 (or Bigender, as per the first post) victory. Due to no one defending that win condition, it naturally skews towards the NB win condition.

From a logician's point of view, the win conditions are equal, as a logician assumes equal participation amongst all parties. However, there's definitely a party missing here, which seems to be causing the issue with game balance.
  
157/158

Also, it's never explicitly stated in the rules of this game whether the stacks can go into the negatives or over 500. In the original GR it was impossible to reach that scenario because someone would always win before getting there, but in this version it might be possible to reach, say, 500/100, in which case Airbud logic would dictate that the boys could push it to 501/100.
  
157/157

That's an interesting proposition
  
156/157

I'm not sure I'm completely happy with it, but here's my version of 3-way gender race:
  • Start at (125,125,125)
  • Girls win at (375,0,0), NBs win at (0,375,0), boys win at (0,0,375)
  • It must always be the case that 0 ≤ x,y,z ≤ 375

I've got some other ideas floating around but this version is simple while also accomplishing many of the things we'd presumably want to accomplish with a design like this. Some notes on this version:
  • Each team's win state is taxicab distance 500 from the starting point. This is also true of the O.G. Gender Race and of Kylljoy's version we are currently playing.
  • Assuming that each team's propensity towards incrementing/decrementing each of the stacks is proportional to the difference between that stack's current value and the value required of that stack in order to satisfy that team's win condition, and assuming that all teams have equal player activity, the starting point is an equilibrium point. This is true of the OGGR, but not of Kylljoy's version (assuming that boys, girls, and NBs are the only ones playing).*
  • Each win state is the same taxicab distance from each of the other win states. In this version that distance is 750, in the OGGR it is 1000, and in Kylljoy's version it varies (win_boys and win_girls are 1000 apart, but win_NBs is only 500 away from each of them).
  • The space of valid play-states is finite. True in OGGR but not in Kylljoy's version (via Airbud technicality).
  • The maximum taxicab distance possible from each of the win states is 1125. In the OGGR this distance is 1000, while in Kylljoy's version there is no upper bound. However, employing a Modified Kylljoy Ruleset which includes the stipulation that no stack can go below 0 or above 500 leads to a maximum distance of 1000, the same as in the OGGR.
  • The minimum taxicab distance to any win state has a maximum value of 750. In both the OGGR and MKR this value is 500.

*I could definitely elaborate on this point, as there is a modicum of calculation required to achieve these results, but I don't feel like doing that elaboration right now.
  
156/156

An interesting proposition. Under your given assumption, I'd say that the rules seem definite and fair. However, that's assuming the assumption holds. It would be interesting to elaborate on different problem/game structures depending on the associated parties, because OGGR and this race is not balanced for the population; it merely describes the current active population willing to spend time on the race. Although the new race you provide scales to the current population, it's but an iteration to normalize against current data, not all possible data.
  
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