Probability and Statistics

Forum Archive : Probability and Statistics

Visualizing odds

From:   Daithi
Address:   (none)
Date:   22 March 2011
Subject:   Tavli question
Forum:   2+2 Backgammon Forum

Here's a simple tip I thought I'd share. This tip is REALLY basic, but it
helped me visualize odds.

When I progressed beyond the bare basics of backgammon I learned that it
was useful to know the odds of getting hit, or hitting someone, or coming
in off the bar, or similar situations. I learned how to count up these
odds, and knew that there was an 11/36 chance of rolling one specific
number, and a 20/36 chance of rolling one of two specific numbers, etc. The
problem was that although I had a general idea of what something like 11/36
or 20/36 meant, it was still a little fuzzy in my mind's eye. However, I
found a way to visualize these fractions so that they became crystal clear.

I divide the fraction by 3 and then visualize the result as time on a
clock. So 27/36 would become 9/12 and thus 9 o'clock (in practice I just
divide the top number by 3). When you can't divide the numerator evenly you
will be left with either 1 or 2 left over and these would correspond to 20
minutes or 40 minutes respectively. For example, 19/36 would be 6:20 (i.e.
20 past 6), and 11/36 would be 3:40 (but visualize on a clock with hands).
Now my mind's eye has a very clear reference for the odds of a roll.

I don't know if that helps anybody else, but it helped me. I also haven't
seen this tip in print anywhere, so I thought I'd throw it out there.
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Probability and Statistics

Average game and match length  (JP White, Dec 2000) 
Average luck of each roll  (Timothy Chow+, Mar 2013) 
Average luck of each roll  (Jørn Thyssen+, Feb 2004)  [GammOnLine forum]
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Chance of rolling x doubles in y rolls  (Raccoon+, July 2007)  [GammOnLine forum]
Chance of rolling x or more pips in y rolls  (Tom Keith, Feb 2004)  [GammOnLine forum] [Long message]
Clumping of random numbers  (Gary Wong, Sept 1998) 
Counting shots  (Koyunbaba+, June 2007) 
Counting shots  (John Little+, Mar 2007)  [GammOnLine forum]
Distribution of points per game  (Roland Sutter, June 1999) 
Distribution of points per game  (Stig Eide+, Sept 1995)  [Recommended reading]
Expected variation in points after a series of games  (Achim Müller+, Feb 1999) 
How many games to decide who's better?  (Stephen Turner, Mar 1997) 
How often is too often?  (Gary Wong, Oct 1998) 
Losing after bearing off 14 checkers  (Daniel Murphy, July 1999) 
Number of games per match  (Jason Lee+, Jan 2005) 
Number of rolls to enter x checkers from bar  (Michael Depreli+, Mar 2011) 
Visualizing odds  (Daithi, Mar 2011) 

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