Hi Toyguy and Davey
the schematics "Hearts and Spades" shows a Switch on "D-1st-Ball-in-Play-Relay". The switch is shown / drawn closed.
The schematics usually are drawn as "a game has started - reset is done and the ball is kicked over to the shooter alley ready to be launched --- NOW the main power cord is unplugged".
This makes reading schematics complicated --- I do not want to dg-in into logic on Hearts and Spades - maybe the relay should be better named "D-1st-Ball-has-not-yet-been-in-Play-Relay" (?).
I make it easy to me and say "at the time the "Hearts and Spades" pin kicks out the very first ball - the ball rolls over the Trough-Switch: Switch on "D-1st-Ball-in-Play-Relay" must be open to SUPRESS the firing of "Subtract Ball Count" Coil".
I would look for an "D- (and DB- ) Relay" and check "pulling / not pulling" and the Switches on the relay(s). Greetings Rolf