Deadlands Reloaded, p. 130:
Manitous don’t generally interfere in a hero’s day to day life. It’s just not interested in whether he orders whiskey or beer, for example. That said, if a demon sees an opportunity to spread a little fear around, it’ll jump on it faster than you can say “Amen.”
Just remember that a manitou won’t knowingly endanger its host, because if a Harrowed dies, the manitou dies along with him.
So, once the marshal decides the Manitou can raise some fear or havoc and not get got, the Marshal antes the fate chip. The Manitou has a spirit a die type higher than the character, but the player gets to add the dominion modifier... Spend them if you got them, because you want at least a +1 dominion. (Why? Because the difference of a die-type is an average of +1... See below.) So, if you can, you want to push your roll up. Note also - your extra d6 for being a PC is a bit of a help, but it's not as important as the dominion modifier.
If, after an hour, the Marshal isn't done, he can automatically extend that hour with a fate chip. But first, he's GOT to win control. And you do not have to let him...
Now, if the PC wins, A bad GM could simply try again the next round. A good one will instead give the PC time to leave the situation, first. The rules don't require it, but since Dominion lasts an hour, simple fairness implies winning lasts an hour for either side. The rules don't state any such thing, but it's not a bad measure.
Some rough stats
Die Type: d4 d6 d8 d10 d12
Average Roll: 2.5 3.5 4.5 5.5 6.5
Comparison: PC D4+1 vs Manitou d6 Open ended Subtable
P Manitou P Manitou
C 1 2 3 4 5 6 C 7 8 9 10 11 12
2 P T M M M M 6 M M M M M M
3 P P T M M M 7 T M M M M M
4 P P P T M M 8 P T M M M M
5 P P P P P† ‡ 9 P P P† T# § §§
==================== ====================
11 P, 9 M, 3 T... 5.25 P, 2.5 T, 15.25M, 1 undecided...
† Because of open ending, the player's 5 is 5+1d4, thus never being a tie.
‡ Because of open ending, it's actually 5+1d4 vs 6+1d6 - see the right side
# Because of open ending, Tie minimum, 75% chance of P win
§ 25% chance of M, 25% T, 50% P
§§ Looks grim for the Player, but it's doable
Final odds of 1d4+1 vs 1d6 to a single open ending level of calculation:
P 269.25/576 = 46.7%
T 74.50/576 = 12.9%
M 231.25/576 = 40.1%
Ok, on to the next level...
Comparison: PC D4+2 vs Manitou d6 Open ended Subtable
P Manitou P Manitou
C 1 2 3 4 5 6 C 7 8 9 10 11 12
3 P P T M M M 7 T M M M M M
4 P P P T M M 8 P T M M M M
5 P P P P T M 9 P P T M M M
6 P P P P P ‡ 10 P P P P† T# §§
==================== ====================
P 14 T 3 M 6 P 7.75 T 3.25 M 12
P 343.75/576 = 59.7
T 75.25/576 = 13.1
M 156.00/576 = 27.1
Similar tables can be worked out for 1d6+1 vs 1d8, and 1d8+1 vs 1d10. I'm not doing so right now, but know that it's really quite potent to add 2, and adding 3 is insanely good. The extra d6 for being a PC is not figured, but also adds a lot of chances. (I could do the math, but not at 03:30hrs...)