When you say 3x for example, do you mean that you might get 1500 points instead of 500 points? If so it may be that the 500 point relay is not releasing at the end of the 1st Score Motor cycle as it should. Usually a 500 (or 5000) point relay fires when a target (or rollover) switch closes and holds itself on after the target switch opens while the Score Motor runs through a 120 degree turn. Near the end of that cycle a motor 2B switch opens which lets the 500 point relay relax.

Watch what your 500 (or 5000) point relay does when the game misbehaves. Does it let go after 500 points or does it stay active for more points? If it doesn't let go after one Score Motor cycle you'll need to sort out why.

An example of this circuit is animated and explained in more detail at:
https://www.funwithpinball.com/learn/animated-score-motor-circuits

/Mark

500 or 5000 points are usually scored by a switch on the Score Motor at position 1A which closes 5 times each time the Score Motor rotates through 1/3 of a turn, or a Score Motor cycle. The closing switch sends 5 pulses to the 100 or 1000 point relay which in turn sends 5 pulses to the appropriate Score Reel. The point relays send 5 pulses to the chimes too.

Dropping one or more of the 5 pulses often means that the Score Reel can't keep up because of a mechanical restriction or friction of some kind. A few experiments you might try:
- Listen to the chime. If the chime sounds 5 times while the Score Reel advances fewer than 5 positions the point relay is probably working properly.
- Jumper a reliable Score Reel coil to an unreliable one by connecting the non-black wires on the Score Reel coils together. Then score 500 or 5000 points so both score reels advance at the same time. (Avoid rolling over from 9 to 0 to avoid unnecessary complications.) If either one reliably advances 5 positions the driving circuit is likely fine and the problem is likely a mechanical issue in the unreliable Score Reel.

If the chime and score reel fire the same number of times that implies that they're getting the same number of pulses. That in turn would imply that the 100 and 1000 point relays that drive them aren't pulsing 5 times. You could watch the relays and see if they reliably pulse 5 times when scoring 500 or 5000 points.

If the point relays don't always pulse 5 times then the score reels and the point relays are the victims, not the culprits. When scoring 500 or 5000 points the point relays are probably driven by a Score Motor switch at position 1A. You might have a close look at that switch to see if it's closing reliably, if it's damaged or loose or dirty or maybe has a loose contact at the end of the switch blade.

Excellent observation. The D and E relays should both hold themselves on, once activated, through their own lock in switches and the Motor 2B switch in the red box until 5 scoring pulses reach the score reels. The Motor 2B switch then opens after the 5 scoring pulses to let the D and/or E relay relax. If the Motor 2B switch opens early you'd only get the points scored before the D or E relay relaxed.
Ship Ahoy D relay (resized).jpg
Check the Motor 2B switch. Its switch stack could be loose, a contact could be loose, it could be dirty, it might need more tension, etc.

You could do some more experimentation to support or disprove the theory that the 2B switch sometimes opens early before taking things apart. The switch serves the same purpose for the D, E and U relays. You could try manually closing two or more of them together to see if they relax simultaneously. If they don't all release at the same time the 2B switch may not be the issue.

You could also try jumpering across the 2B switch (yellow-black wire probably to red-white wire) with an alligator clip test lead which would effectively prevent it from opening. If the relays never release prematurely the 2B would be the likely culprit. Note that they may never release until you remove the test lead.

The suspected fault isn't that the switch activates spontaneously before the score motor post activates the 2B switch stack. It may however chatter or vibrate as the motor turns just enough for the contacts to disengage momentarily which would be enough to drop out the relays. The same might be happening to the lock in switches on each relay, but since it happens to multiple relays 2B is more likely.