If we give 20/1 odds for each split decision (prob not too far off from vig free odds), we'd be looking at something like 160k/1 to happen in a row.
I was giving a shorthand example. If you want to get technical, it would depend on each of the fight's probability to go to a decision and then extrapolate the odds of it being a split decision either way; so some fights might have a much higher likelihood than others. The judges are not the same for each fight either, so it would be pure speculation to guess who it is and what kind of bias they have.
It would be interesting to see the odds of a split decision occurring after one just occurred. If 1 in 20 decisions goes to a split decision, perhaps the probability of a SD immediately after a SD is higher than 1/20. That's pretty much my point. But yeah, I'm not sure how much the judges change fight to fight.
Could be but that would be looking at psychology and finding trends etc. Ultimately it still depends how likely the fight is to go to dec that's the main influencer, i.e. what weight class etc. You'll have something like a HW fight between be like +500 or something to got to a dec and then assuming like a 15% chance of a split you'd be looking at at something like 40/1+ for a split but a girl's fight that's something like -200 to go to dec. you'd be looking at something like 10/1 only. So putting in 4 women's fights in a row vs. 4 HW in a row is gonna result in something like a 250x likelier chance. As to the judges, they rotate them a bit, not entirely. You can look a http://www.mmadecisions.com/, there were 7 judges for these 4 fights.