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Author Topic: A Bowler's Riddle, courtesy of FiveThirtyEight  (Read 834 times)

bradl

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A Bowler's Riddle, courtesy of FiveThirtyEight
« on: June 18, 2021, 04:16:35 PM »

An interesting post I just came across that is asking for answers. At first glance, this question screams FIGJAM to every league bowler, but when I read the article, it's actually a good one.

https://fivethirtyeight.com/features/can-you-bowl-three-strikes/

Quote
Can You Bowl Three Strikes?

By Zach Wissner-Gross
Filed under The Riddler

Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. Two puzzles are presented each week: the Riddler Express for those of you who want something bite-size and the Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either, and you may get a shoutout in the next column.

Riddler Express

Scoring in bowling can be a tricky matter. There are 10 frames, and in each frame you get two chances to knock down as many of the 10 pins as you can. Each pin knocked down is worth 1 point, and the pins are reset after each frame. Your score is then the sum of the scores across all 10 frames.

If only it were that simple. There are special rules for spares (when you’ve knocked down all 10 pins with the second ball of a frame) and strikes (when you knock down all 10 pins with your first ball). Whenever you bowl a strike, that frame is scored as 10 plus the scores of your next two rolls. This can lead to some dependency issues at the end of the game, which means the final frame has its own set of rules that I won’t go into here.

For example, if you bowled three strikes and missed every subsequent shot (i.e., they were gutter balls), your third frame would be worth 10 points, your second frame would be worth 20 and your first frame 30. Your final score would be 30 + 20 + 10, or 60 points.

This week, Magritte is going bowling, and the bowling gods have decided that he will bowl exactly three strikes in three randomly selected frames. All the other frames will consist of nothing but gutter balls. Magritte also lacks patience for bowling’s particular rules. If one of his three strikes comes on the 10th and final frame and he is prompted to bowl further to complete the game, he will bowl gutter balls out of frustration.

What score can Magritte expect to achieve? (That is, with three randomly placed strikes, what is his average score?)

What makes this "fun" (read: pain in the ass) is that when the strikes are bowled, they don't say that they are consecutive strikes, so you wouldn't know which frame they are in.. So what would you think the answer would be?

BL.


 

Bowler19525

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Re: A Bowler's Riddle, courtesy of FiveThirtyEight
« Reply #1 on: June 18, 2021, 06:29:02 PM »
I hate stuff like this.

If none of the strikes are consecutive, he gets 30

If two strikes are consecutive, he gets 40

If his strikes come in the 8th, 9th, and 10th he gets 60.

I think by stipulating that the strikes are random, they mean none are consecutive.  But random strikes could result in a double or triple.

MI 2 AZ

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Re: A Bowler's Riddle, courtesy of FiveThirtyEight
« Reply #2 on: June 18, 2021, 11:23:43 PM »
I hate stuff like this.

If none of the strikes are consecutive, he gets 30

If two strikes are consecutive, he gets 40

If his strikes come in the 8th, 9th, and 10th he gets 60.

I think by stipulating that the strikes are random, they mean none are consecutive.  But random strikes could result in a double or triple.

+1
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LiverDance

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Re: A Bowler's Riddle, courtesy of FiveThirtyEight
« Reply #3 on: June 19, 2021, 12:09:13 AM »
As mentioned previously, "30", "40", and "60" are the only possible answers for a single game.   

A game of no two strikes being consecutively thrown is the most likely outcome (the math says 'barely').  Therefore, "30" is the "expected" outcome.

Since only one game is thrown ("...10th and FINAL frame..."), no averaging of possible scenarios is needed.