Damn... You're good. Anyway, 1 and 0 aren't probabilities because Bayes Theorem break down there (in the log-odds/information base where Bayes Theorem is simple addition, they are positive and negative infinity). You can however meaningfully construct limits of probabilities. I prefer the notation (1 -) epsilon.
Log-odds aren't what probability is, they're a way to think about probability. They happen not to work so well when the probabilities are 0 and 1; they also fail rather dramatically for probability density functions. That doesn't mean they don't have their uses.
Similarly, Bayes's Theorem breaks down because the proof of it assumes a nonzero probability. This isn't fixed by defining away 0 and 1, because it can still return those as output, and then you end up looking silly. In many cases, not being able to condition on an event with probability 0 is the o...
I was very interested in the discussions and opinions that grew out of the last time this was played, but find digging through 800+ comments for a new game to start on the same thread annoying. I also don't want this game ruined by a potential sock puppet (whom ever it may be). So here's a non-sockpuppetiered Irrationality Game, if there's still interest. If there isn't, downvote to oblivion!
The original rules:
Enjoy!