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# Gaming Guru

### Bowling

3 December 2010

Sometimes proposition bets rely on misleading language.  For example, a person at a bar might tear a small hole in a bar napkin and declare: "I'll bet you I can push this glass of beer through that hole."  If the sucker bites then the proposer simply sticks his finger through the hole and pushes the glass of beer.  You might be a winner with this type of bet, but it can also get you punched in the nose.

A better type of proposition bet is one where the proposition is not misleading but sounds impossible.  If someone takes you up on such a bet and you deliver, they will probably shake your hand and pay up.  In this article I am going to show you just such a bet.  It involves the game of bowling.

Here is the proposition.  In a bowling game it is possible to roll a triple strike, a double strike, and three single strikes, not bowl any gutter balls, and score less than 100.  Sound impossible?  No, it is possible and here is how.

First off, let me point out that it is possible to get a score of 1 in a single frame.  One would have to knock out the seven or ten pin with the first ball and then roll the second ball in that same space.  Notice that no gutter ball has been rolled.  That settled, let me describe the game for you.  Here is the game frame by frame (Xs stand for strikes):

 1 2 3 4 5 6 7 8 9 10 X X 1 X 1 X 1 X 1 XXX

Let's add up the score. The first frame is ten plus the score on the next two balls, which is ten plus one or eleven.  Hence the first frame is 21.  The second frame is ten plus one plus zero or eleven, so we're now at 32.  The third frame is just 1, so we have a score of 33.  The fourth frame is ten plus one, so we're up to 44. The fifth frame is 1, so our score is 45.  In the sixth frame we add 11, so we now have a score of 56 and the seventh frame is 57.  The eighth frame adds 11 for a score of 68 and thus the ninth frame is 69.  The triple in the tenth adds 30 so our final score is 99.  Told you so!

See you next month.

Don Catlin can be reached at 711cat @ comcast.net

Recent Articles
Best of Donald Catlin
Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

#### Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers
Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

#### Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers