puzzle
Tom
swap 0 and net to reply via e-mail
Anyone know what position and roll give the maximum equity change from
pre-roll to post-roll? How about a twe roll sequence (a rolls then b)?
Does allowing a double with a legimate take (then bad roll for
doubler, then good roll for taker) produce the greatest change? Does
the greatest single roll change include a game ending roll? I haven't
thought much about this, but I know that the fertile minds of the
regular posters will produce some fascinating situations (bonus points
awarded for events that actually happened at the table). I can't wait
to see the results.
Tom
Don Banks
Tom <net@usa.0> writes:
>swap 0 and net to reply via e-mail
>Anyone know what position and roll give the maximum equity change from
>pre-roll to post-roll?
How about this:
___________________________________________________
| | | |
|12 11 10 9 8 7 | | 6 5 4 3 2 1 |
| X | | X X X X X O |
| | | X X X X X |
| | | X X |
| | | |
| | | |
| |BAR| |
| | | 14 |
| | | O |
| | | O |
| | | O |
| X | | X O |
|13 14 15 16 17 18 | |19 20 21 22 23 24 |
|_______________________|___|_______________________|
After O rolls 6-6, his equity (according to jf level 6)
goes from -0.747 to 1.605, for a swing of 2.352.
Kit Woolsey
Tom (net@usa.0) wrote:
: swap 0 and net to reply via e-mail
: Anyone know what position and roll give the maximum equity change from
: pre-roll to post-roll? How about a twe roll sequence (a rolls then b)?
: Does allowing a double with a legimate take (then bad roll for
: doubler, then good roll for taker) produce the greatest change? Does
: the greatest single roll change include a game ending roll? I haven't
: thought much about this, but I know that the fertile minds of the
: regular posters will produce some fascinating situations (bonus points
: awarded for events that actually happened at the table). I can't wait
: to see the results.
: Tom
Best I could come up with off the top of my head was the following:
13 14 15 16 17 18 19 20 21 22 23 24
+------------------------------------------+
| | | O O O O O O |
| | | O O O O O O |
| | | |
| | | |
| | | |
| | O | |
| | O | |
| | O | |
| | | X X X X X |
| X X X X X | | X X X X X |
+------------------------------------------+
12 11 10 9 8 7 6 5 4 3 2 1
O is on roll. According to Jellyfish level 7, O's equity on a 1-cube is
-1.557. However, if O rolls 6-6, his equity becomes +1.841.
Kit
Bill Taylor
kwoo...@netcom.com (Kit Woolsey) writes:
|> Best I could come up with off the top of my head was the following:
|>
|> 13 14 15 16 17 18 19 20 21 22 23 24
|> +------------------------------------------+
|> | | | O O O O O O |
|> | | | O O O O O O |
|> | | | |
|> | | | |
|> | | | |
|> | | O | |
|> | | O | |
|> | | O | |
|> | | | X X X X X |
|> | X X X X X | | X X X X X |
|> +------------------------------------------+
|> 12 11 10 9 8 7 6 5 4 3 2 1
|>
|>
|> O is on roll. According to Jellyfish level 7, O's equity on a 1-cube is
|> -1.557. However, if O rolls 6-6, his equity becomes +1.841.
What an excellent top-of-the-head effort!
Just a thought though. Could it be made the tiniest tad sharper, by
putting X's spares on 12 10 9 8 7 ? This affects almost nothing EXCEPT,
it gives X one more doubles, viz 1-1, to use to fill up his board.
Could someone jellyfish that and report back please?
Thanks.
-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-------------------------------------------------------------------------------
God does not play dice with the universe - god *is* the dice.
-------------------------------------------------------------------------------
Morten Wang
* Bill Taylor
| Just a thought though. Could it be made the tiniest tad sharper, by
| putting X's spares on 12 10 9 8 7 ? This affects almost nothing EXCEPT,
| it gives X one more doubles, viz 1-1, to use to fill up his board.
| Could someone jellyfish that and report back please?
With O on roll his equity is -1.564 (evaluated level 7), while after
the 6-6 O's equity is 1.778 (same), according to my JF v3.0
Morten!
--
"God does not deduct from our alloted life span
the time spent playing backgammon."
--> Morty on FIBS
--> Backgammon homepage: http://home.sn.no/~warnckew/gammon/
Kit Woolsey
Bill Taylor (mat...@math.canterbury.ac.nz) wrote:
: kwoo...@netcom.com (Kit Woolsey) writes:
: |> Best I could come up with off the top of my head was the following:
: |>
: |> 13 14 15 16 17 18 19 20 21 22 23 24
: |> +------------------------------------------+
: |> | | | O O O O O O |
: |> | | | O O O O O O |
: |> | | | |
: |> | | | |
: |> | | | |
: |> | | O | |
: |> | | O | |
: |> | | O | |
: |> | | | X X X X X |
: |> | X X X X X | | X X X X X |
: |> +------------------------------------------+
: |> 12 11 10 9 8 7 6 5 4 3 2 1
: |>
: |>
: |> O is on roll. According to Jellyfish level 7, O's equity on a 1-cube is
: |> -1.557. However, if O rolls 6-6, his equity becomes +1.841.
: What an excellent top-of-the-head effort!
: Just a thought though. Could it be made the tiniest tad sharper, by
: putting X's spares on 12 10 9 8 7 ? This affects almost nothing EXCEPT,
: it gives X one more doubles, viz 1-1, to use to fill up his board.
My guess is that this will cut down on O's gammons and backgammons, since
it will be more difficult for O to scoop up all the blots. In your
position O needs specifically an ace to get the checker on the 7 point,
which makes both his 6's and his 5's bad. In my position O can
profitably use an ace to split the back men, so his only bad number is a
6. I expect this difference will be big enough to show up in rollouts.
Kit
Morten Wang
* Donald Kahn
| But what about after O's 6-6? I wasn't satisfied to
| accept Level 7 for this, so I rolled it out 7776 times at Level 5, not
| truncated, same dice.
to set the record straighter I did my usual set of rollouts, 1296
games on level 6 with identical dice of all four positions (that is
both before and after the 6-6). I got these results:
Play | Kit's before | Kit's after | Bill's before | Bills after
| | | |
-------+---------------+----------------+---------------+----------------|
O: | 11.0 2.6 0.6 | 96.4 88.3 20.0 | 10.9 2.6 0.5 | 96.4 85.2 17.4 |
X: | 89.0 69.5 4.9 | 3.6 0.0 0.0 | 89.1 69.6 5.1 | 3.6 0.0 0.0 |
Eq O: | -1.491 | 2.012 | -1.497 | 1.953 |
Sd: | 0.007 | 0.006 | 0.007 | 0.006 |
Eq to: | 24733 | 16802 | 24530 | 16885 |
-------+---------------+----------------+---------------+----------------+
so Kit's swings from -1.491 to 2.012 for a total of 3.503.
while Bill's swings from -1.497 to 1.953 for a total of 3.450.
I'm hereby announcing Kit Woolsey as the winner in 'The "See How Much
Equity You Can Gain On One Roll" Contest of 1997' scoring a total of
3.503. (insert sound effect of applauds here) we'll now return to
our regular broadcast, film at 11.
I'll sit and wait eagerly for someone to post the 32000 games level 6
rollout.
NOT!
Donald Kahn
On 22 Dec 1997 04:51:18 GMT, mat...@math.canterbury.ac.nz (Bill
Taylor) wrote:
>kwoo...@netcom.com (Kit Woolsey) writes:
>
>|> Best I could come up with off the top of my head was the following:
>|>
>|> 13 14 15 16 17 18 19 20 21 22 23 24
>|> +------------------------------------------+
>|> | | | O O O O O O |
>|> | | | O O O O O O |
>|> | | | |
>|> | | | |
>|> | | | |
>|> | | O | |
>|> | | O | |
>|> | | O | |
>|> | | | X X X X X |
>|> | X X X X X | | X X X X X |
>|> +------------------------------------------+
>|> 12 11 10 9 8 7 6 5 4 3 2 1
>|>
>|>
>|> O is on roll. According to Jellyfish level 7, O's equity on a 1-cube is
>|> -1.557. However, if O rolls 6-6, his equity becomes +1.841.
>
>What an excellent top-of-the-head effort!
>
>Just a thought though. Could it be made the tiniest tad sharper, by
>putting X's spares on 12 10 9 8 7 ? This affects almost nothing EXCEPT,
>it gives X one more doubles, viz 1-1, to use to fill up his board.
>
>Could someone jellyfish that and report back please?
>
This is interesting. Bill Taylor's suggested improvement should
increase X's equity, and JF Level 7 confirms this, raising it from
1.557 to 1.564. But what about after O's 6-6? I wasn't satisfied to
accept Level 7 for this, so I rolled it out 7776 times at Level 5, not
truncated, same dice.
Results:
Kit's position: Win .961, g/bg .877, bg .193, equity 1.993
Bill's position: Win .967, g/bg .856, bg .169, equity 1.960
This is sort of mysterious: I can see that having more space could
slightly increase the number of times you pick up all 5 blots, and
thus win more triple games, but how can you possibly win 2.7% less
single games, which amounts to 210 games in 7776? Of course there is
a certain amount of random error here, but I would not have thought it
could make so much difference.
deekay