Combat is decided by die-rolling, though it's acted out in the B-round if there are any mafia Family members involved.
When one person attacks another, their respective strength scores are added. A die with this number of faces is rolled and if the result is lower than the attacker's strength then the attack succeeds.
Strongarm-vs-Strongarm: The outcome is determined by a single die-roll. Whoever wins the die-roll wins the combat.
Strongarm-vs-Mafia/Mafia-vs-Mafia: There is a die roll for each action. When someone is successfully attacked they lose 2 strength. When they're reduced to 0 strength, death occurs.
Example: The Montague Family owns a successful speakeasy on 34th street and the Capulet Family wants to put a stop to it. So the Capulets send two of their Family (Antonio and Baranzo) and one hired Civilian (Carlos) along to raid the joint. The Montagues have hired Freddy Fourfingers to protect it, and they decide two of his men (Daryl and Edwin) will be there at the time of the raid (all they are told is "the Capulets are raiding your speakeasy", they have no idea how many men are attacking).
<Acting> Antonio walks into the bar and lets rip with his pistol. His strength is 4, and he fires at Daryl, whose strength is 2. They roll 2 on a d6 and since 2 < 4 Antonio gets his shot in. Daryl's strength is reduced to 0 and he dies. Edwin has time to whip out his gun and fire back before Baranzo leaps in. Edwin (strength 2) rolls a 3 on a d6 and since 3 > 2 he misses, his shot putting a hole in the wall behind Antonio. Baranzo now rushes over to Edwin (who's ducked behind the bar) shooting as he goes. His strength is 2, so rolling 3 on a d4 he misses, his shots thudding into the woodwork of the bartop. An innocent bystander has arisen from his table and rugby-tackled Antonio. His strength is 2 and rolling 2 on a d6 he manages to knock Antonio off his feet so he falls and hits his head (now Antonio's on 2 strength). Edwin shoots from behind the bar and rolls 1 on a d4, killing Baranzo with a shot to the head. Carlos, seeing the carnage and noticing that it's not going his way, runs back out into the street and escapes. Edwin finishes off Antonio and the raid has failed.</Acting>