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# Mathematically Correct Bowling

Score every frame like the 10th
 (+9) [vote for, against]

Those who understand what I'm talking about, just from the Title and Subtitle, need read no further. For everyone else, you should consider the fact that in ordinary bowling, to obtain the maximum possible score, "300 pins", you actually only have to knock over 120 pins (12 consecutive strikes).

The reason that's true relates to the scoring system. If you knock over 0-9 pins in a frame, then your score for that frame will be that number of pins.

If you knock over all 10 pins, but need two attempts to accomplish it ("make a spare"), then your score for that frame is 10, plus all the pins you knock over with the next ball, in the next frame.

And, if you knock over all 10 pins on your first attempt ("make a strike"), then your score for that frame is 10, plus all the pins you knock over with the next two balls (which, if they are also strikes, will occur in the next two frames).

So, in any frame but the 10th, you only have to knock over 10 pins to possibly score as many as 30 pins for that frame, thanks to being able to "borrow" the pin-fall from the following frame(s).

The 10th and last frame is special, because in order to be able to accommodate the scoring system, if you score a spare in that frame, you need to be able to roll the ball once more --or if you score a strike in that frame, you need to be able to roll the ball twice more.

So, to score 30 pins for the 10th frame, you actually have to knock over 30 pins in that frame. The net result is, as previously stated, 12 consecutive strikes are scored as "300 pins".

In this variation of bowling, you actually have to knock over 300 pins to get a score of 300 pins. And it is simple, because every frame is scored like the 10th.

So, in any frame of this game, if you roll a spare, the "next ball" that adds to your score for that frame is also counted in that frame. There is no "borrowing" of the score from the next frame.

And, of course, if you roll a strike in any frame, the next two balls are also counted in that frame. Every frame can be directly associated with knocking over 0-30 pins. So you have to get 30 consecutive strikes, knocking over 300 pins total, to achieve an absolutely mathematically perfect score of "300 pins".

Obviously, for anyone who normally bowls some number of spares and/or strikes, the game will last longer than normal. But that's okay! Those folks typically do lots of bowling, anyway; they are used to it. The really-average person-off-the-street, lucky to bowl even one strike in a game, will hardly notice the difference, from the normal method of scoring, and the normal length of the game.

 — Vernon, Jan 15 2012

 This is interesting. I know a bit about physics and engineering, yet [vernon]'s physics and engineering posts make no sense to me. I know nothing about bowling, and yet this idea makes sense.

I have no idea what this proves.
 — MaxwellBuchanan, Jan 15 2012

Another solution to the discrepancy would be to have the 10th frame carry forward into your next game -- for life. You'd get a lot more repeat business if people had to come back another day just to finish their previous game!
 — phundug, Jan 17 2012

That's great too - it's self-contained within one game.
 — phundug, Jan 17 2012

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