Is this boringly easy? (bg or bust)
Steve Peterson
1 2 3 4 5 6 7 8 9 10 11 12
+------------------------------------------+ O: opponent - score: 0
| O O O | | O O O |
| O O | | O O O |
| O O | | |
| | | |
| | | |
| |BAR| |v 5-point match
| | | |
| | | |
| | | |
| | | |
| O | | O X |
+------------------------------------------+ X: pip - score: 0
24 23 22 21 20 19 18 17 16 15 14 13
BAR: O-0 X-0 OFF: O-0 X-14 Cube: 2 (owned by opponent) turn: pip
You roll 1 and 5.
Please move 2 pieces.
What's the right play here?
What's the correct play for money?
Chris W.
On Thu, 6 Mar 1997 09:48:39 GMT, spa...@netcom.com (Steve Peterson)
wrote:
I would definitely pass up the hit on 16 and make my opponent roll an
ace.
chrisw on FIBS
---
Chris Wilson
Emerald Island Consulting
Guam, USA
Kit Woolsey
Steve Peterson (spa...@netcom.com) wrote:
: 1 2 3 4 5 6 7 8 9 10 11 12
: +------------------------------------------+ O: opponent - score: 0
: | O O O | | O O O |
: | O O | | O O O |
: | O O | | |
: | | | |
: | | | |
: | |BAR| |v 5-point match
: | | | |
: | | | |
: | | | |
: | | | |
: | O | | O X |
: +------------------------------------------+ X: pip - score: 0
: 24 23 22 21 20 19 18 17 16 15 14 13
: BAR: O-0 X-0 OFF: O-0 X-14 Cube: 2 (owned by opponent) turn: pip
: You roll 1 and 5.
: Please move 2 pieces.
: What's the right play here?
: What's the correct play for money?
While getting an exact answer for a problem like this is virtually
impossible at the table unless you have brought your computer along (and
it's pretty difficult even with pencil, paper, and much time), one can
get pretty close. The key is to use simplifying assumptions and take
comparative differences between plays. This cuts down on the mental
arithmetic necessary.
In the above position, if X hits O has 21 return shots. If X doesn't
hit, O has 11 shots. That part is easy. So, what do we do with the
information.
It is clear that if X doesn't hit he doesn't get a backgammon. When X
hits, O has 15 missing rolls. On two of these (5-5 and 6-6), he gets off
the backgammon anyway. If he rolls one of the remaining 13, X still
might come back with 2-1 (a 17 to 1 possibility). So, we make the
simplifying assumption that on 12 of O's rolls he will be backgammoned.
Note that this isn't exact, but it is close. The idea is to avoid
fractions and a lot of multiplication.
We know that if X plays safe O hits 11 times, while if X goes for the
gusto O hits 21 times. Thus, O hits 10 more times when X goes for the
gusto. What happens when O hits? Not clear. Most of the time X will
win a single game. However O may fail to complete the prime, and X may
slither around and win a gammon anyway. Also, O might get lucky and
actually win the game. Note that O gains twice as much from winning the
game (from -2 to +2) as he loses when he fails to contain the checker
(from -2 to -4). I'm going to make the simplifying assumption that the
scenario where X gets away after being hit occurs about twice as often as
the scenario where O wins the game. Under this assumption, we can say
that if O hits he always loses a single game.
Now we have the numbers we need. X wins a backgammon instead of a gammon
12 times, and wins a single game instead of a gammon 10 times, so he is
getting 12 to 10 odds. For money going for the gusto is clear.
Now, look at the match situation. If X wins a gammon, he has 85%
equity. If he wins a backgammon he has 100% equity. If he wins a single
game, he has 66% equity. So, he is risking 19% to gain 15%. This is
more than the 12 to 10 odds he is getting, so he is slightly better off
playing safe.
My assumptions may not be valid. If you think X will get away more than
twice as often as he will lose the game (which I do), then you may revise
the match decision. Also, the assumption that X wins 12 backgammons was
slightly low. Thus, at the match situation I would make it too close to
call.
Note that I never had to do any great mental arithmetic or remember a
bunch of numbers. The above calculations can be done at the table quite
easily. We may not get the right answer exactly, but that is not too
important. What is important is to make sure we are in the ball park and
don't make a big blunder. Estimating backgammon positions is usually
guesswork anyway, so exact calculations are impossible. In this
position, we conclude that it is very clear to go for the gusto for
money, while at the match score it is a pretty close decision. That's
the best we can expect to do.
Kit
Alexander Nitschke
Steve Peterson wrote:
>
> 1 2 3 4 5 6 7 8 9 10 11 12
> +------------------------------------------+ O: opponent - score: 0
> | O O O | | O O O |
> | O O | | O O O |
> | O O | | |
> | | | |
> | | | |
> | |BAR| |v 5-point match
> | | | |
> | | | |
> | | | |
> | | | |
> | O | | O X |
> +------------------------------------------+ X: pip - score: 0
> 24 23 22 21 20 19 18 17 16 15 14 13
>
> BAR: O-0 X-0 OFF: O-0 X-14 Cube: 2 (owned by opponent) turn: pip
> You roll 1 and 5.
> Please move 2 pieces.
>
> What's the right play here?
> What's the correct play for money?
This is surely not boring easy :-)
1. Safe play 15/20 20/21:
If you are not hit, a gammon is sure (25 times out of 36)
If you are hit, it isn't all clear. You may lose some games, you may win
some games gammon. I assume, you win a single game. (11 times out of 36)
2. Hitting play 15/16* 16/21:
If you are hit, I assume a single win (21 times out of 36)
If your opponent rolls 55 or 66, you win gammon (2 times) otherwise you
win backgammon, if you don't roll 21 (about 12 times out of 36). If you
roll 21 you win only gammon. That accounts for about 1 more gammon.
Money game:
One won backgammon copensates one single win. Since the hitting play
wins about 12 backgammons in 36 games, but only 10 more single games
than the safe play, hitting seems right in money game.
Note: If your opponent had a six prime, the safe play would probably be
better.
Match score:
This is more difficult: Gammons are very valuable (gammon price 0.68,
considerably higher than money game), but backgammons aren't bad too (bg
price 0.55, a bit higher than money game). This favours the safe play a
bit because gammons are more important, but the result is too close to
call for me. I would play save.
Alexander