Probability and Statistics

 Counting shots

 From: Koyunbaba Address: m.a.nolan@Mntlworld.com Date: 14 June 2007 Subject: Training aids Forum: rec.games.backgammon Google: rc0ci.1157\$Yc4.610@newsfe7-gui.ntli.net

```Hi I'm just going through backgammon bootcamp and Trice recommends
learning to visualise the number of shots when learning to count shots.

Now I'm a beginner, it's hard to do at the moment.  I wondered if there
are any training aids which follow a question/answer format which you
can learn to start counting shots more efficiently and be confident that
you've actually got the right answer.  Because at the moment I can't
find the correct answer accurately.  Whenever I think i've got the
answer I find I've missed some combination, or counted something twice.
Is there any software that can do this simple test and generate more
random tests for you so you can develop this essential skill?

Koy
```

 Stick  writes: ```If I remember correctly Walter spells this out pretty plain in simple. You should start by knowing that a plain single shot is 11 shots. That's to say a blot 1 pip away is 11 shots. You will need an ace to hit it, and you can roll 11 combinations containing an ace, 61, 51, 41, 31, 21, and 11. Remember there are two different ways to roll all the rolls except doubles, you can roll 61 or 16, so it's actually 61, 16, 51, 15, 41, 14, 31, 13, 21, 12, and then there is only one way to roll doubles because each die must contain the same number, so add 11 to the mix and that's 11 hitting number for a direct single shot. Once you can visualize this and accept this as fact it gets easier. Now say there's a blot two pips away. You start off knowing it's 11 shots because your dice must contain a two, so again, 62, 26, 52, 25, 42, 24, 32, 23, 21, 12, and 22 make 11. On top of that any combination of the dice that add up to two, in this case 11, gets added [as long as ones aren't blocked] giving you a total of 12 numbers to hit a blot two pips away. It is important enough to be able to count shots, and as Walter goes on to explain, it helps in other situations also (like endgames being able to figure out how many rolls take off checkers). In general, if you want/need to leave less shots, bring the checker closer to where the hitter is. 1 pip away - 11 shots (61, 51, 41, 31, 21, 11) 2 pips away - 12 shots (62, 52, 42, 32, 21, 22, 11) 3 pips away - 14 shots (63, 53, 43, 32, 31, 33, 21, 11) 4 pips away - 15 shots (64, 54, 43, 42, 41, 44, 31, 22, 11) 5 pips away - 15 shots (65, 54, 53, 52, 51, 55, 41, 32) 6 pips away - 17 shots (65, 64, 63, 62, 61, 66, 51, 42, 33, 22) [hope I got that right lol] So if you're forced to leave a shot and the only thing you're concerned with is minimizing that amount of shots (safety) it's best to leave the blot as close as possible. I doubt this helped much as all that information was contained in Bootcamp but I thought I'd give it a try, I've never tried to explain it to anyone so if you have any more questions just ask. Stick ```

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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)
Calculating winning chances  (Douglas Zare, June 2000)
Chance of rolling x doubles in y rolls  (Raccoon+, July 2007)
Chance of rolling x or more pips in y rolls  (Tom Keith, Feb 2004)
Clumping of random numbers  (Gary Wong, Sept 1998)
Counting shots  (Koyunbaba+, June 2007)
Counting shots  (John Little+, Mar 2007)
Distribution of points per game  (Roland Sutter, June 1999)
Distribution of points per game  (Stig Eide+, Sept 1995)
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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