Why don't you think it's the 2nd player 1000s score reel 9th position switch?

If it occurs only on player 2, the pulse to the 10,000s score reel is most likely coming from the 1000 point relay switch, through the 2nd player relay switch and through the 2nd player 1000s score reel 9th position switch as @currieddog suggested.

If you block the 2nd player 1000s score reel 9th position switch (green-white wire to orange-red wire) with a piece of paper, does it still happen? It could be that the switch is stuck closed, or there could be a short elsewhere like a bent solder tab or solder blob somewhere, etc.

/Mark

When you blocked the switch on the 2nd player 1000pt score reel it was the switch that connects the green-white wire to the orange-red wire, right?

I'd like to eliminate the 100s score reel from the equation since it shouldn't directly affect the 1000s or 10,000s score reels. Normally the 100pt relay only fires the 1000pt relay when the 100s score reel shows a 9. So can you reproduce the error (10,000s score reel advances when it shouldn't) by just hitting 1000pt targets, or manually closing the 1000pt relay? If so, that simplifies the problem and makes it easier to recreate.

Can you repeat this experiment and watch the 1000 point relay? It's probably in the backbox near the score reels. From your description it sounds like when the problem occurs with the 10,000 point score reel, the 100 point relay does fire but the 1000 point relay does not. I'd like to confirm that.

Please clarify. The schematic shows that the 1000s and 10,000s score reels can only advance if the 1000 point relay fires or if the Score Reset relay fires. So when you add 100 points to 900 points for example both the 100 point and the 1000 point relays should fire. Similarly, when you go from 14,900 to 25,000 (in error) both the 100 point and 1000 point relays should fire. So when you see the error when adding 100 to xx900, does the 1000 point relay fire?

Also, if you manually close the 1000 point relay repeatedly, do the points reliably add correctly on the 1000s and 10,000s score reels?

Your last reply has two key bits of information:
- advancing the 100s score reel from 800 to 900 can advance the 10k score reel.
- the 10k score reel can advance when the 1000pt relay doesn't fire.
If these are true I think you're looking at a short between unrelated parts of the schematic rather than a maladjusted switch.

The way a score reel works is that its solenoid receives a very short pulse from the circuit which causes the plunger to be pulled into the solenoid. This effectively 'cocks' the score reel. When the pulse ends the solenoid relaxes and a spring returns the plunger to its rest position and simultaneously advances the score reel by one position. Any lingering with the solenoid active is an indication that something isn't right. You should be able to manually push the plunger all the way into the solenoid and then release it and have the score reel advance. Does that work with the 10k score reel?

Figuring out how your 10k score reel solenoid gets power from the 100 score reel solenoid is a little trickier. Here are a few things to try to see if you can zero in on the problem:
- Have a close look at the 100 point score reel. Since the error seems to happen only when the 100 point score reel shows 800, that may indicate that your 9th position switch and maybe others are mangled somehow. Ordinarily nothing should happen on the 8th position of the 100s score reel. Compare it to the 1st player 100 score reel.
- Pull the 10k score reel out from the bracket partially or even all the way to see if the problem persists.
- Do the same for the 100 score reel to see if its position affects the error.
- Have a close look at all the wires on the 100 score reel. Look for worn insulation, bent solder tabs, solder blobs, etc.
- Have a close look at the 100pt relay and the Score Reset relay just above it. Do the switches all open and close if you manually activate the relay? Any signs of shorts?
- Dim the lights to see if you can catch any arcing when the error happens. Any arcing not on switch contacts would be bad.

One more experiment:
Since you can get the 10k score reel to advance going from 800-900 I'm curious if you can get the 10k score reel to make the 100 score reel advance. Manually set the score to 9800 and then manually close the 1000pt relay. The 1000s score reel should force the 10k score reel to fire. If there's a short you may see the 100 score reel advance too.