I have a dull-as-ditchwater construction problem.
Construct a money position where the optimal checker play is unique but
where the loss in equity from choosing the second-best play is as small
as possible.

Paul

On 4/14/2023 6:18 PM, peps...@gmail.com wrote:
> I have a dull-as-ditchwater construction problem.
> Construct a money position where the optimal checker play is unique but
> where the loss in equity from choosing the second-best play is as small
> as possible.

My intuition is that this is almost equivalent to the
task of constructing a position where the player on roll has
the smallest possible nonzero winning probability. The best
candidates for that problem are nearly hopeless pure races,
where the underdog has to roll boxcars over and over and the
favorite has to roll 21 over and over. I would imagine that
a small variant of that position would yield an excellent
solution to your problem. For example, if the favorite
misplays a 21 then that's not going to cost much equity.

---
Tim Chow

On Saturday, April 15, 2023 at 4:55:15 AM UTC+1, Timothy Chow wrote:
> On 4/14/2023 6:18 PM, peps...@gmail.com wrote:
> > I have a dull-as-ditchwater construction problem.
> > Construct a money position where the optimal checker play is unique but
> > where the loss in equity from choosing the second-best play is as small
> > as possible.
> My intuition is that this is almost equivalent to the
> task of constructing a position where the player on roll has
> the smallest possible nonzero winning probability. The best
> candidates for that problem are nearly hopeless pure races,
> where the underdog has to roll boxcars over and over and the
> favorite has to roll 21 over and over. I would imagine that
> a small variant of that position would yield an excellent
> solution to your problem. For example, if the favorite
> misplays a 21 then that's not going to cost much equity.
>
> ---
> Tim Chow
Yes, that's a great way to get a candidate solution.
The problem is almost certainly unsolvable.
I think the standard most-unlikely-loss position is:
Favourite has 14 checkers on their 3 point and one
on their ace point. The underdog has 15 checkers on their 22 point.
The underdog is on roll.
Misplaying the underdog's initial roll is probably a bad idea as the extra
backgammons suffered by the underdog are likely to be significant.
So the underdog should be given a 33 and play that optimally.
Now it's not clear to me that, if the favourite rolls a 21, there is any loss
of equity by misplaying. But anyway, it's not an interesting problem, and this
is certainly a good approach for anyone who is desperate to waste time
on this issue.

Paul