2A. You do have the firepower to trade shots with the wimpy West Siders, so send your Thug and/or Racketeer to blow away one of their level-one Joints. That will trigger a Gang War situation (rule 12.6), sending all Public pieces scurrying back to the cup. The Syndicate won't be happy about it, but hey!
The Racketeer has a 69% chance of succeeding in triggering a gang war on your turn (83.33% chance to get into a brown joint and 0.8333 likely hits). The Thug has a 33.5% chance of success (50% chance to get into a brown joint with 0.67 likely hits). Fortunately, if you don't succeed on the first round, the joint will open fire on the next player-turn and you'll get another try.
Also, since your mob is also dependent on One-Jump joints, you'll want to get the public back into the cup to give yourself a chance to draw them on a roll of 2, 4 or 6!
Note that an already criminal public will pay Organized Crime fees before a shootout occurs (such that this may not be the best solution when a large payoff is due as opposed to threatening).
2B. 100%. There is no roll of the white die that will not yield a handsome payoff for the Southern Syndicate! The red devils get their best payoff on a white die roll of ONE (which is the only roll that allows every single public piece to shell out their dough)! Red will win the game on a roll of one or two (and be very close on a roll of six). Here's the payoff red can expect (without extortion):
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