Optional doubles at odd-away post crawford
Scott Steiner
what are the advantages and disadvantges when the trailer doesn't double
on his first opportunity when he is odd-away and it is post crawford
e.g. let's say we have a 7 point match and score is 6-4 post crawford.
If the trailer doesn't decide to double on his first opportunity, when
is the right time to double? And when should the leader take?
Thanks.
Michael Sullivan
The leader should take up to the point where wins plus gammons equal or
top 100%. If there are no gammons, the leader should take anything that
is not absolutely gin. This is on the assumption that trailer will know
enough to double immediately next round after a drop. That's why this
is known as a forced take.
With equity greater than 1, it may be a drop
The advantage of the trailer not doubling immediately is that it's very
difficult to lose one's market, so if the opponent doesn't understand
the match score, you can often pick up drops when you double at 80%
wins, 10% gammons, or some such, gaining some equity from opponent's
mistakes. Obviously, threading the needle looking for mistakes from an
opponent who understands the score is not worth it. But you can usually
get to a money drop or close take without ever facing a serious threat
to lose your actual market at this score. If you wait until such a
time, it's easy to sucker your opponent into a mistake and you haven't
risked much.
Michael
jthyssen
> The leader should take up to the point where wins plus gammons equal or
> top 100%. If there are no gammons, the leader should take anything that
> is not absolutely gin. This is on the assumption that trailer will know
> enough to double immediately next round after a drop. That's why this
> is known as a forced take.
>
> With equity greater than 1, it may be a drop
>
> The advantage of the trailer not doubling immediately is that it's very
> difficult to lose one's market, so if the opponent doesn't understand
> the match score, you can often pick up drops when you double at 80%
> wins, 10% gammons, or some such, gaining some equity from opponent's
> mistakes.
Ah, this reminds me of a recent online match of mine:
GNU Backgammon Position ID: vn4CABC2zYQALA
Match ID : cAmgAEAAEAAA
+24-23-22-21-20-19------18-17-16-15-14-13-+ O: opponent
O | X O O O O | | X | 4 points
| X O O | | |
| O O | | |
| O O | | |
| O 6 | | |
| |BAR| |v 5 pt match (Cube:1)
| | | |
| | | |
| | | |
| X X X X | | X | On roll
| O X X X X | X | X X | 2 points
+-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: Jørn Thyssen
This is a huuuuuuuuuge take since O has one chequer off, so he can
never lose a gammon, hence he can take any non-gin position. Although
X is a big favourite it's certainly not a gin.
My opponent passed giving up more than 6% MWC.
Even though this my move #16 in the game I didn't lose my market at
any time. In fact, the position above is still "optional double, take"
as there is no way I can lose my market within the next 10 rolls or
so.
Jørn
Michael Sullivan
If there are no gammons, you can't lose your market ever until you win.
Oh, I suppose there's the difference between having and not having the
free drop, but that can't be worth giving up more than .5% gwc or so.
While this double is still "optional", it's an ideal time to send it
over, since this is a fairly easy money pass, but still pretty far from
gin. if you're going to get a mistake here, it will be by players who
treat it the same as money, either because they don't know enough to do
differently, or react without thinking. So to maximize mistake equity,
you want positions that are good enough that few would want to take them
for money, but not so good that a pass hardly loses any equity. This
position is ideal. If your opponent gets signficantly better, it starts
to look like a money take, or close enough that someone working on that
philosophy might get the right answer in spite of themselves. OTOH, if
your opponent gets significantly worse, all that happens is that any
mistake to come is worth less. this has got to be pretty close to the
maximum of how much equity can be lost by a bad pass * the chance of
getting one from a typical non-match-score-aware opponent.
Michael
Douglas Zare
Scott Steiner wrote:
I wrote an article on this for Bibafax last year. I think it was in
the March issue.
The leader should take any immediate double, but it gets tricky at
post-Crawford 3-away, and very tricky at post-Crawford 5-away
or more. The trailer gains if the leader makes a bad pass. The
trailer does not gain if the leader makes a bad take. So, to save
energy, the leader can simply take everything, which is like forcing
the trailer to double immediately.
The take point is very low, perhaps 3% at pC 3-away and 5% at
pC 5-away. Gammons are very valuable at pC 3-away, and not
nearly so valuable at pC 5-away. Backgammons are extremely
valuable at pC 5-away. The leader can take with about
3% + gammon losses, at pC 3-away.
5% + 3/5 gammon losses + 8/5 backgammon losses, at pC 5-away.
Many players will pass huge takes at both scores. You might
want to double when your opponent just rolled an awkward
number that increased the gammons a lot or the first possibility
of a market loser.
Douglas Zare
Michael Sullivan
> I wrote an article on this for Bibafax last year. I think it was in
> the March issue.
> The leader should take any immediate double, but it gets tricky at
> post-Crawford 3-away, and very tricky at post-Crawford 5-away
> or more. The trailer gains if the leader makes a bad pass. The
> trailer does not gain if the leader makes a bad take. So, to save
> energy, the leader can simply take everything, which is like forcing
> the trailer to double immediately.
> The take point is very low, perhaps 3% at pC 3-away and 5% at
> pC 5-away. Gammons are very valuable at pC 3-away, and not
> nearly so valuable at pC 5-away. Backgammons are extremely
> valuable at pC 5-away. The leader can take with about
> 3% + gammon losses, at pC 3-away.
> 5% + 3/5 gammon losses + 8/5 backgammon losses, at pC 5-away.
How do you derive those numbers for the win percentage?
I would have figured that the gammonless take point is equivalent to the
value of the free drop, and I have a hard time believing that's as much
as 3%.
I'm also having a hard time figuring out how the take point at -5 would
be higher, because you can only use one free drop. I guess the idea is
that you don't drop a marginal disadvantage at your first opportunity,
so you have two tries to get a significant boost from the free drop
because of a good roll by the opponent. It still seems like 2% is a lot
for that.
Michael
Douglas Zare
Michael Sullivan wrote:
> Douglas Zare <za...@math.columbia.edu> wrote:
>
> > I wrote an article on this for Bibafax last year. I think it was in
> > the March issue.
>
> > The leader should take any immediate double, but it gets tricky at
> > post-Crawford 3-away, and very tricky at post-Crawford 5-away
> > or more. The trailer gains if the leader makes a bad pass. The
> > trailer does not gain if the leader makes a bad take. So, to save
> > energy, the leader can simply take everything, which is like forcing
> > the trailer to double immediately.
>
> > The take point is very low, perhaps 3% at pC 3-away and 5% at
> > pC 5-away. Gammons are very valuable at pC 3-away, and not
> > nearly so valuable at pC 5-away. Backgammons are extremely
> > valuable at pC 5-away. The leader can take with about
>
> > 3% + gammon losses, at pC 3-away.
> > 5% + 3/5 gammon losses + 8/5 backgammon losses, at pC 5-away.
>
> How do you derive those numbers for the win percentage?
Educated guesses and rollouts. The important part is that
the racing take point is extremely low, and that the gammon
price is 1 at pC 3-away but much lower than 1 at pC 5-away.
If you are much more comfortable using a value of 2.5% for
the racing take point at pC 3-away, go ahead, but it won't
make much of a difference.
> I would have figured that the gammonless take point is equivalent to the
> value of the free drop, and I have a hard time believing that's as much
> as 3%.
A 3.0% racing take point is consistent with pC 2-away
being worth 51.5% for the leader. The risk:reward ratio of
taking is 1.5:48.5 = 3.0:97.0.
> I'm also having a hard time figuring out how the take point at -5 would
> be higher, because you can only use one free drop.
First, you can either use the free drop, or possibly retain the
option of using the free drop later.
Second, pC 4-away is more volatile than pC 2-away, since
in addition to variations of winning chances, gammon
chances also vary. I believe that would make the free drop
worth significantly more in relative terms even without the
ability to use the free drop later if you take now.
At both pC 2-away and pC 4-away, the trailer can play on
for the gammon after some good sequences. It is not clear
how much this is worth, but it decreases the value of the
free drop slightly.
Douglas Zare
puppe...@hotmail.com
> Ah, this reminds me of a recent online match of mine:
>
> GNU Backgammon Position ID: vn4CABC2zYQALA
> Match ID : cAmgAEAAEAAA
> +24-23-22-21-20-19------18-17-16-15-14-13-+ O: opponent
> O | X O O O O | | X | 4 points
> | X O O | | |
> | O O | | |
> | O O | | |
> | O 6 | | |
> | |BAR| |v 5 pt match (Cube:1)
> | | | |
> | | | |
> | | | |
> | X X X X | | X | On roll
> | O X X X X | X | X X | 2 points
> +-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: Jørn Thyssen
>
> This is a huuuuuuuuuge take since O has one chequer off, so he can
> never lose a gammon, hence he can take any non-gin position. Although
> X is a big favourite it's certainly not a gin.
>
> My opponent passed giving up more than 6% MWC.
>
> Even though this my move #16 in the game I didn't lose my market at
> any time. In fact, the position above is still "optional double, take"
> as there is no way I can lose my market within the next 10 rolls or
> so.
Mmmm... Position analysis, love it.
Ok, I'm clearly missing something here. I don't see this as an
automatic take. Chances are excellent that X could send a second
checker back if he wanted. Though he *might* decide one O back was
superior for X than two O's back. Or not, depends. There's even
some excellent chances to send a third back, though I have not
stopped to work out the rolls that will do that.
If I were O here, I'd have to think really carefully about this.
What is it I'm missing here? (He asked expecting to be taught
some basic thing about BG that most 8 year olds should know.)
Socks
Jørn Thyssen
>
> Mmmm... Position analysis, love it.
>
> Ok, I'm clearly missing something here. I don't see this as an
> automatic take. Chances are excellent that X could send a second
> checker back if he wanted. Though he *might* decide one O back was
> superior for X than two O's back. Or not, depends. There's even
> some excellent chances to send a third back, though I have not
> stopped to work out the rolls that will do that.
>
> If I were O here, I'd have to think really carefully about this.
> What is it I'm missing here?
O has one chequer off, and so he can't lose a gammon. With a take point
of approx. 3% this is a huge take.
Another way of explaining this: if you drop this double, the score is
4-3 and it is effectively double match point (neglecting the leader's
free drop). So if you drop you have approximately 50% chance of winning
the match. On the other hand, what happens if you take: if you lose this
game the score is 4-4 and it's DMP yielding 50% MWC, but if you turn the
game around and win it, then you've won the match. Do you see it? You
don't lose anything by taking the double because you can't lose a gammon.
Jørn
Marttila
Ok. I modified the position and checked it with GnuBg. This new position
may be simple for some of you but it wasn't for me. I moved the
borne-off checker back, making the 6 point. So O can be gammoned. Now...
Cube action?
GNU Backgammon Position ID: vn4GACBsmwkBWA
Match ID : cAmgAEAAEAAA
+24-23-22-21-20-19------18-17-16-15-14-13-+ O: Gnu
| X O O O O | | X | 4 points
| X O O O | | |
| O O | | |
| O O | | |
| O 6 | | |
| |BAR| |v 5 point match (Cube: 1)
| | | |
| | | |
| | | |
| X X X X | | X | On roll
| O X X X X | X | X X | 2 points
+-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: Me
Michael Sullivan
> Ok, I'm clearly missing something here. I don't see this as an
> automatic take. Chances are excellent that X could send a second
> checker back if he wanted. Though he *might* decide one O back was
> superior for X than two O's back. Or not, depends. There's even
> some excellent chances to send a third back, though I have not
> stopped to work out the rolls that will do that.
>
> If I were O here, I'd have to think really carefully about this.
> What is it I'm missing here?
The match score. It's odd away post-crawford, which means the only
thing O risks by taking this double (given that O cannot lose a gammon)
is the free drop next game. OTOH, the gain when O wins is dramatic --
the match is over vs. sitting at DMP. It's essentially a forced take,
though situations very close to gin may be better to drop. Also,
gammonish positions may be drops (your wins - gammon losses < 3%).
Michael
puppe...@hotmail.com
[snip]
> O has one chequer off, and so he can't lose a gammon. With a take point
> of approx. 3% this is a huge take.
>
> Another way of explaining this: if you drop this double, the score is
> 4-3 and it is effectively double match point (neglecting the leader's
> free drop). So if you drop you have approximately 50% chance of winning
> the match. On the other hand, what happens if you take: if you lose this
> game the score is 4-4 and it's DMP yielding 50% MWC, but if you turn the
> game around and win it, then you've won the match. Do you see it? You
> don't lose anything by taking the double because you can't lose a gammon.
Ok, I see what it is that I don't understand.
You are saying that the difference between being ahead 4-3 vs
being tied at 4-4 in a 5pt match game is overwhelmed by the
chance of winning the match this round, even if the chance of
winning this round is only 3%. (A number I'm not really able
to calculate in my head.)
I guess that's what I don't see. Supposing the players are
fairly evenly matched, which seems to go with your 50% MWC
esitimate, then isn't there a very large difference between
4-3 and 4-4? At 4-4, the match ends after one round, no
other choice. At 4-3, the leader has the opportunity to
try again if things go south, providing he only gives up
a single point. Surely the difference is larger than 3%?
Or does the trailer simply pick up the cube as soon as
the next round starts?
Socks
Michael Sullivan
> Ok, I see what it is that I don't understand.
> You are saying that the difference between being ahead 4-3 vs
> being tied at 4-4 in a 5pt match game is overwhelmed by the
> chance of winning the match this round, even if the chance of
> winning this round is only 3%. (A number I'm not really able
> to calculate in my head.)
> I guess that's what I don't see. Supposing the players are
> fairly evenly matched, which seems to go with your 50% MWC
> esitimate, then isn't there a very large difference between
> 4-3 and 4-4? At 4-4, the match ends after one round, no
> other choice. At 4-3, the leader has the opportunity to
> try again if things go south, providing he only gives up
> a single point. Surely the difference is larger than 3%?
> Or does the trailer simply pick up the cube as soon as
> the next round starts?
> Socks
the trailer should pick up the cube as soon as the next round starts.
Why not? at 3-4 post crawford to 5, a single game loss loses the match
anyway, so the risk from doubling is zero. The leader will only take if
her chances are 50-50 or better (since next round after a drop is just
DMP), so it's very easy to lose your market. Since there's no cost to
doubling early, losing your market is extremely painful, while waiting
and getting a bad take only rescues you from the mistake of failing to
double before you lost your market. It doesn't gain you anything over
doubling immediately.
Given that the trailer should double immediately at 4-3, the difference
between 4-4 and 4-3 is only the "free drop" since the leader can drop
any game where he is the underdog, eliminating any games where the
trailer wins first roll, except awful rolls like 4-1, 5-1, 5-2 etc.
Even most of those, i think the leader can drop. this amounts to around
51.5% match winning chances for the leader at 4-3 according to Doug Zare
(I had estimated 50.5% or so), which results in a 3% take point for the
leader at the 4-2 post crawford score.
Michael