... calculate the probability precisely?
How precise? Sure, it's an estimate. But we still make the best
estimate we can. For starters, it's more than 0 and less than
1. But, we can do better than that.
Start with your analytical probabilities with all teams and conditions
equal. Post 4's probability is 12.4%. I contend that number is
unchallengeable, as it's a by-product of the rotation. But wait,
there's more 
It's Goiko, so the real probability must be higher. How much higher?
Well, ... um, ... that's a tough one. Then you can add in all
the other etc., etc., etc. on top of that. No matter how you do
it, I contend that the number you come up with is still your best
estimate for the probability of #4 (and all your probabilities
will total to 1). Whether you're good at it or not is determined
at the betting window.
