Acutally, in the bowling world, if you throw 3 strikes in the 10th, they are commonly referred to as the 10th, 11th and 12th frames. They aren't actually seperate frames though. On a score sheet, those three balls all fall into the slot designated as the 10th. The actual scoring rules are different than they are being applied here, but it doesn't change the result. There are several ways to look at the tenth frame.

1 - The score for the 10th is the total pinfall.
2 - the score for the 10th is the first "frame" type score (strike, spare or open) and then the bonus ball(s) are used to calculate the score, using the rules for strikes and spares, but the actual pinfall is discarded.

The scoring for the 10th is in fact the same as any other frame. For any other frame, the score for that frame (given a mark), is the total pinfall (which would be 10) plus the next 1 or 2 balls. In the tenth, there are no frames after the 10th, there's no frames to count and therefore the score for the 10th is just the total pinfall. So for understanding purposes, it isn't the same as comparing strikes in the 1st and 2nd frames.

In your example, you said that the strike in the second frame effects the 1st, but is not part of it. In the tenth, it's the other way around, the second strike is part of the frame and therefore can't effect it in the way that the strike in the 2nd effected the 1st.

Not that your methodology (and what I used in my golf) changes the outcome of the scoring.. but I just thought I'd clarify.

Rich