In all the electro-mechanical games, the match unit is a ten position "stepper unit". This is a ratcheting unit powered by a solenoid that has 10 circular positions (a circular saw tooth pattern with 10 teeth is stepped by a solenoid with each actuation).
In different games, it was stepped "randomly" by different features, but when I was in College, we discovered some interesting behavior on certain games:
On Williams Gulfstream, there was a tick-tack-toe board in the center that always had 1 square spotted (by a lit arrow). We discovered that the stepper unit that did the spotting was also the match unit (but in a different order). The playfield numbers cycled in the following sequence: 1-2-3-4-5-6-7-8-9-5. Each lit number corresponded to a match number (note that the 5 that followed 4 was different than the 5 that followed 9). We mapped the sequence by wathing game ends, and then started rigging double, triple and quadruple matches.
On many of the mid 70's Bally games (Ro-go, Flicker, Old-Chicago, Air-Aces) the match unit was stepped every time 10 points was scored, however, the unit was wired in reverse. This means with each 10 point activation, the match number decreased by 10. For a one player game, this meant you could never match after the match was odd, and if the match was even there were two numbers that would match as follows:
Last game match: This games match numbers (1 player)
00 00 50
20 10 60
40 20 70
60 30 80
80 40 90
So, while playing 1 player games, you would try and keep the match on zero, or follow the sequence 20, 60, 80, 40.
Using the simple formula that the sum of all players 10's digits, plus the new match number will (mod 100) add up to the previous match number shows you how we set up double, triple and quadruple matches at will (with timely tilts).
There is one hitch... The 10 point score drums, and the match stepper unit are separate mechanical units that are being pulsed simultaneously with each 10 point score event. It is not unusual for either unit to mis-step, or double step during frantic scoring.
If you run across any Bally games of this era, simply watch a
couple of games and see if the math works out. If it does . . .
have fun.