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OHex

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Jul 23, 2005, 3:47:08 PM7/23/05
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Hi folks,

Welcome to the new home. It looks like it should serve us well.

Chief among the things I like about this place is various forms
of flexibility, both for members (you) and for managers.

Here's one thing that was not feasible when I was hosting this
group from home -- I can nominate others to take over if I cannot
continue to run this for any reason. So: I'm looking for a
volunteer or two. You don't have to do anything for now except
to say you'll keep watching this group. Later, if anything needs
to happen and it does not appear that I'm doing it, you can step
in and apply your own judgement.

Any of you old-timers willing to do that much?

++ kevin

Misha Orel

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Aug 14, 2005, 4:17:08 PM8/14/05
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Hi guys,

I am wondering, on what board sizes the area where the
2nd player should (or should not) swap has been
determined ? I know it has been done for 7X7, but not
sure about larger sizes.

Thanks
-Misha



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OHex

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Aug 14, 2005, 10:48:12 PM8/14/05
to playhex
The 7x7 board has been solved in a semi-strong manner: the
game-theoretic value of every opening move is known, along with an
effective strategy for the player who should win.

An effective strategy is known for only 1 8x8 opening, and that was
only recently published. There are no others above 7x7 that I'm aware
of. Earlier today, I put
scanned pages of the paper that revealed this analysis onto my Hex
Theory page.
It had to go in the secure area, so you'll need a password to view it
(email me if
you don't have one).

++ kevin

Glenn

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Aug 15, 2005, 5:38:46 AM8/15/05
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There is also a known effective strategy for the central hex in
the 9x9 game. It was found by the same person who resolved the
central hexes in the 8x8 game.

-- Glenn C. Rhoads


Kevin OGorman

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Aug 15, 2005, 9:23:15 AM8/15/05
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Is there a published version of this?

++ kevin
Kevin O'Gorman, Ph.D. (805) 756-2986 mailto:kogo...@pacbell.net
Home Page: http://www.csc.calpoly.edu/~kogorman

Glenn

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Aug 15, 2005, 4:37:19 PM8/15/05
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Jing Yang's web page has a downloadable windows program that demonstrates
the strategy (I'm not on windows so I haven't bothered downloading it).
The link is near the bottom of his homepage at

http://www.ee.umanitoba.ca/~jingyang/

William McWorter

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Oct 21, 2005, 3:37:35 PM10/21/05
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In this 10x10 game between brocha and de_pedro (#974399) I thought white had
the win after 5. .. H4; but black still won.

brocha de_pedro
1. H2 F5
2. G6 G8
3. H7 H8
4. I7 I8
5. F7 H4
6. C6 C8
7. E6 E5
8. B7 C9
9. D7

Could white have won if he had gone 5. .. G4 instead of 5. .. H4?

Can anyone verbalize the strategy of these players? At times I think they
are trying to close the gap between their walls, or are setting up multiple
lines of attack; but I'm unable to implement these vague ideas with any
significant effect. I still can't make sense of the miracles performed by
Kurnik!'s red devils.

William


William McWorter

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Oct 21, 2005, 11:45:55 PM10/21/05
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Sorry, guys. White's 5. .. H4 is a winner. After 7. E6, white wins with 7.
.. E4.

William


rhoads

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Oct 22, 2005, 5:06:56 AM10/22/05
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William McWorter wrote:

> In this 10x10 game between brocha and de_pedro (#974399) I thought white had
> the win after 5. .. H4; but black still won.
>
> brocha de_pedro
> 1. H2 F5
> 2. G6 G8
> 3. H7 H8
> 4. I7 I8
> 5. F7 H4
> 6. C6 C8
> 7. E6 E5
> 8. B7 C9
> 9. D7
>
> Could white have won if he had gone 5. .. G4 instead of 5. .. H4?

If he could have, the above try is not the way.
After 9.D7, the vertical player's group is attached to the bottom
(e.g. 9... D10 10.F9 F8 11.D9 and the D9 has two independent threats
to connect to the bottom and two independent threats to connect to
the big group). So the horizontal player needs to block C6-B7 from
connecting to the top. Hence,
9.... C5 (D5 loses to C4 and D3 loses to D4)
10. D5 E3
11. E4 F3
12. G4 wins since there are two independent winning threats.

Now if white had gone 5...G4 instead, then this wouldn't be available.
But this gives the vertical player a winning play on the right.

9.... C5
10.H4

Now 10...H5 (or any similar try) loses immediately to I4 -- the
pair H4-I4 cannot be stopped from connecting to the top (because
of the H2 piece) and the pair has two distinct ways of connecting
to the main group. Hence,

10.... H3
11.J2 I3
12.J3 I4
13.J4 I6
14.I5 H6
15.H5 and it's over.



> Can anyone verbalize the strategy of these players? At times I think they
> are trying to close the gap between their walls, or are setting up multiple
> lines of attack; but I'm unable to implement these vague ideas with any
> significant effect. I still can't make sense of the miracles performed by
> Kurnik!'s red devils.
>
> William

I'll give it a try.

1. H2 F5

H2 probably shouldn't be swapped. F5 is a standard block on a central hex
so it should be a good play. I might try E6 instead (there is no obvious
reason to prefer one over the other if there any reason at all).

2. G6

A good play. G6 is actually connected to the bottom via a huge template
that includes all of row 10, B9--J9, C8--J8, E7--I7, plus F6 and H6.
(It's not obvious how to reconnect G6 after F8, D8, or F10 but it can
be forced after each of these three tries.)

2.... G8

This is exactly what I would play. The most obvious try is 3.H4 but
intuitively, this doesn't look so good. I would be reluctant to
give the potentially good forcing move G4. I would only play this
move if I couldn't find anything better. The problem with 3.G4 is
that your push along the bottom after breaking off the ladder does
not seem strong enough. So that leaves moves that intrude on the
G6 template. G8 comes immediately to mind to because it is about
as far away from the right side that is still a valid ladder escape
for second and third row ladders. G8 also contains the strong
threat of F7 cutting off G6 from the bottom. The vertical player
must respond to this threat.


3. H7

I agree with this move too. It reconnects G6 to the bottom
and ruins G8's use as a ladder escape.

3.... H8

Again threatening to cut off vertical from the bottom and
restablishing a valid ladder escape for second and even third
row ladders (e.g. 4.G4 G5 5.I4 H5 6.I5 H6 and either 7.I6 G7
or 7.J6 I6 8.J5 I7 etc.)

4. I7

Again.


4... I8

And again. 4...H9 is equivalent. An alternative is
4...F7 5.I8 H9 6.I9 7.H4 C6 but this almost can't be an
improvement over the line played because the group
F7-G8-H8-H9 is not connected to the right.

5. F7

To stop the threat of being cutoff at the bottom. Note that this
does *not* give vertical a guaranteed connection from G6 to the
bottom since horizontal has E8 leading to a ladder situation.

The direct connection move is 5.F8 but this creates a weakness
that allows horizontal to get away with 5...G4. The line goes
5.F8 G4 6.H4 H3 7.J2 G7 (horizontal could ladder down before
playing this move) Now horizontal has a valid ladder escape
and if horizontal blocks this (say by I4 or H6), then horizontal
plays F7 threatening both to push F7 to the left and to connect
F7 up with F5-G4.
happy here.

A reasonable alternative to 5.F7 is 5.E7 F7 (not 5...G7? 6.D7!
and horizontal can resign) 6. F6 or D7 or perhaps even G7 or F8.

5.... H4

A fateful decision. The alternative is 5...E8. Then the play
splits into a couple of possibilities.
A. 6.F7 E10 and the ladder gets broken off at either B9 or C9.

B. 6.E7 and now horizontal should probably play 6...D9 instead
of 6....D8. If D8, then 7.F7 E10 followed by breaking off the
ladder at B9 should be better for the vertical player than the
similar line in A because the threat to connect the B9 upward
push to the big group is now stronger. So we have

6.E7 D9 7.C9 or
6.E7 D9 7.C8 B10 8.A10

I played around with some of these lines and I currently have
the horizontal player winning after 5... E8 but the lines are
long, subtle, and very close. I wouldn't take them as gospel.

6. C6 C8

C6 seems like the proper block on the left side and C8 seems
correct as well -- the idea is to try to make use of the two
potential connections, C8 to F5 or C8 to G3. Note that the
play 6...E8 shouldn't work now because the C6 piece helps
when breaking off the second row ladder at B9 and then pushing
up from B9.

7. E6

Good. This breaks the the C8-F5 connection while still not
allowing horizontal to cut off the bottom. (the best horizontal
can do is ... ) Oh my goodness. This appears to be a mistake!
It looks like horizontal can win with 7... E9

8.D8 C10 9.B9 B8! 10.C9 E5 11.D6 D4 or similarly
8.B9 B8! 9.E8 E5 10. D6 D4

Instead, the unlikely looking 7.E7 seems to win. After E7,
the E7-F7-G6 group is connected to the bottom via a template.
Horizontal has two main tries.

7.... E5 threatening both D4 and D7
8.B7!! covers both threats!
8..... C9 reconnecting to the left. (8...D7 loses to 9.A9)
9.D7 D10
10.D9 C10
11.F9

Now 11....D4 loses to 12.C4 -- horizontal can't escape the
ladder at the bottom and the H2 piece ruins any attempt at
the top. 11....D5 loses to 12.E3 E4 13.F3 G4.

The other main try is against 7.E7 is 7...D6

7... D6 8.C7 D7 9.A9 D4 laddering up and pushing across
the top doesn't work because of the forcing plays G4 and E5.
Now moves like 10.C4 or D3 lose to 10....E5 11.F3 G4 etc.
while 10.E3 loses to C4.

7...D6 8.C7 D4 9.B6!! B6 and E5 are the key moves in this
line and either move could come first (i.e.9.E5 also wins)
9.D5 and D7 lose to 9... E3! and 9.E4 loses to 9...D7!
Also, 9.B6 or 9.E5 could be preceded by 9.G4 G5 which is
also needed at some point. (The details on these lines
are in the attached Jhex file).

9.B6 C9 10.D7 D3 11.E5 F3 12.G4 G5 13.F4 E6 14.D5 wins
or
9.B6 D3 10.G4 G5 11.E5 E6 12.D5 F4 13.E4 C9 14.D7 wins

Finally, back to game!

7.... E5

As mentioned above, this is a mistake since E9 wins.
This is the next best play. It helps to block vertical
from pushing upwards and threatens to connect to C8.
There are no other reasonable options.

8. B7

Yep. The C8 piece is involved in two important threats.
There is the obvious connection threat through D6 but
if you make a straightforward block via 8.D6 (or D7),
then 8... D4 9.C4 (forced) C5 and now the C8 piece is a
winning ladder escape. You need to stop both threats
and B7 is the natural play and hence the first move I
would look at to do this. This obviously stops the ladder
escape in the above line and it prepares to meet 8...D6
with 9.D7 C7 10.A9 now you have to verify that A9 can't
be stopped from connecting to the bottom. So 10...A10
11.B9 B10 12.C9 C10 13.E9 D9 D8 and the connection is
completed. So that's what I would play.

For completeness, there are only two other moves which
might work B6 and C7. 8.C7 D4 ... break off ladder with
12...B9, 13.B8 D7 14.D6 E7 15.E6 E9 and horizontal defeats
you. The other try is 8.B6 D6 9.C7 D7 10.A9 A10
11.B9 B10 12.C9 C10. Now 13.E9 loses to D9 14.D8 E8 and
13.D9 loses to D10 14.F9 E9 15.F8 E8.

8... C9

If 8...D6 9.D7 C7 10.A9 and we just saw that A9 can't
be stopped from connecting to the top. Since we don't
have any good ladder threats when trying to connect to
the left side, the best we can do is block B7 and A6
upwards. H2 is a valid ladder escape for second and
third row ladders and if we give a fourth row ladder,
then G4 will be a killer. So D6 is no good. The only
other try is 8...C9. This reestablishes C8 with the
left side and thus makes D6 a winning threat while at
the same time strengthening the position along the
bottom. So the only thing to do is to play 8...C9
and hope.

9. D7

So much for our hope as vertical makes the only
winning play. Vertical must stop the winning threat
and ensure his pieces are connected to the bottom and
this is the only move that does both. If instead
9.D6(C7), then horizontal wins with 9....E9 10.D9 E7
11.E8 (if 9.D7 had been played, you could respond with
11.F6) F6 and horizontal wins.

It's all but over as the win is now straightforward.

I'm attaching a Jhex file that has details on the
alternative lines I looked at.



game.hgt

rhoads

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Oct 22, 2005, 5:39:31 AM10/22/05
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I didn't look at 7...E4 but did you consider the response 8.B6? (B6 could
come either immediately or possibly after the forcing moves H4 and/or E5).

7... E8 seems to win for white.

But this may be superseded by 7.E7. This may win -- I hadn't considered
your move 7... E4. (neither 7...E5 nor 7...D6 seem to work)
After 7.E7 E4, 8.E5 is necessary. I'll look at this later if I have
the time.


William McWorter

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Oct 22, 2005, 12:22:30 PM10/22/05
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> Now if white had gone 5...G4 instead, then this wouldn't be available.
> But this gives the vertical player a winning play on the right.
>
> 9.... C5
> 10.H4
>
> Now 10...H5 (or any similar try) loses immediately to I4 -- the
> pair H4-I4 cannot be stopped from connecting to the top (because
> of the H2 piece) and the pair has two distinct ways of connecting
> to the main group. Hence,
>
> 10.... H3
> 11.J2 I3
> 12.J3 I4
> 13.J4 I6
> 14.I5 H6
> 15.H5 and it's over.
>
*************
Did I miss something? Doesn't 13. .. J6 instead of I6 win it for white?
*************
>
>
>> Can anyone verbalize the strategy of these players? At times I think
>> they
>> are trying to close the gap between their walls, or are setting up
>> multiple
>> lines of attack; but I'm unable to implement these vague ideas with any
>> significant effect. I still can't make sense of the miracles performed
>> by
>> Kurnik!'s red devils.
>>
>> William
>
> I'll give it a try.
>
**************
Thanks. I'll study this analysis below.
**************

William McWorter

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Oct 22, 2005, 1:00:48 PM10/22/05
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> I didn't look at 7...E4 but did you consider the response 8.B6? (B6 could
> come either immediately or possibly after the forcing moves H4 and/or E5).
>
*************
No, I didn't, but this seems to yield a white win with the original 5. ..
H4.

7. .. E4
8. B6 D5
9. C4 D6
10. C7 D7
11. A9 A10
12. B9 B10
13. C9 C10
14. E9 D9
15. D8 D8
*************

> 7... E8 seems to win for white.
>

**************
How does white stop black from connecting C6 to the bottom?
**************

> But this may be superseded by 7.E7. This may win -- I hadn't considered
> your move 7... E4. (neither 7...E5 nor 7...D6 seem to work)
> After 7.E7 E4, 8.E5 is necessary. I'll look at this later if I have
> the time.
>
***************
After 7. E7, 7. .. D7 seems to preserve a white win.

William
***************


rhoads

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Oct 23, 2005, 4:05:28 AM10/23/05
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William McWorter wrote:

> > Now if white had gone 5...G4 instead, then this wouldn't be available.
> > But this gives the vertical player a winning play on the right.
> >
> > 9.... C5
> > 10.H4
> >
> > Now 10...H5 (or any similar try) loses immediately to I4 -- the
> > pair H4-I4 cannot be stopped from connecting to the top (because
> > of the H2 piece) and the pair has two distinct ways of connecting
> > to the main group. Hence,
> >
> > 10.... H3
> > 11.J2 I3
> > 12.J3 I4
> > 13.J4 I6
> > 14.I5 H6
> > 15.H5 and it's over.
> >
> *************
> Did I miss something? Doesn't 13. .. J6 instead of I6 win it for white?

Is this a typo?
13.... J6 14.I6


rhoads

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Oct 23, 2005, 4:49:49 AM10/23/05
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William McWorter wrote:

> > I didn't look at 7...E4 but did you consider the response 8.B6? (B6 could
> > come either immediately or possibly after the forcing moves H4 and/or E5).
> >
> *************
> No, I didn't, but this seems to yield a white win with the original 5. ..
> H4.
>
> 7. .. E4
> 8. B6 D5
> 9. C4 D6
> 10. C7 D7
> 11. A9 A10
> 12. B9 B10
> 13. C9 C10
> 14. E9 D9
> 15. D8 D8
> *************

That looks good to me.


For reference,
1.H2 F5 2.G6 G8 3.H7 H8 4.I7 I8 5.F7 H4 6.C6 C8 7.E6

> > 7... E8 seems to win for white.
> >
>
> **************
> How does white stop black from connecting C6 to the bottom?
> **************

Sorry that should be 7... E9.
The line is in the previous Jhex file.



> > But this may be superseded by 7.E7. This may win -- I hadn't considered
> > your move 7... E4. (neither 7...E5 nor 7...D6 seem to work)
> > After 7.E7 E4, 8.E5 is necessary. I'll look at this later if I have
> > the time.
> >
> ***************
> After 7. E7, 7. .. D7 seems to preserve a white win.
>
> William
> ***************

Yes, it does but white still needs the E4 move which I hadn't considered.
(7...E4 immediately also seems to work).

7.E7 D7 8.G4 G5 9.E6 E4! 10.E5 F4

A. 11.B6 D5
B. 11.C5 D3 12.C3 C4 and the C8 piece is a ladder escape
C. 11.B5 D5 12.D6(B7) C5 13.B6 C3
D. 11.A6 C5 12.B4 B6 and again the C8 piece is a ladder escape.

So in summation, 5.... H4 seems to win after all.
Also, 5... E8 wins if the analysis in the Jhex file holds up.


William McWorter

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Oct 23, 2005, 1:09:03 PM10/23/05
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*************
Je suis un cretin! Yes, I meant 13. .. H6, threatening I6 or G7.

William
**************

William McWorter

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Oct 23, 2005, 1:09:08 PM10/23/05
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> Sorry that should be 7... E9.
> The line is in the previous Jhex file.
>
**************
Got it; reviewed the jhex file.
***************
(snip)
> Yes, it does but white still needs the E4 move which I hadn't considered.
> (7...E4 immediately also seems to work).
>
> 7.E7 D7 8.G4 G5 9.E6 E4! 10.E5 F4
>
> A. 11.B6 D5
> B. 11.C5 D3 12.C3 C4 and the C8 piece is a ladder escape
> C. 11.B5 D5 12.D6(B7) C5 13.B6 C3
> D. 11.A6 C5 12.B4 B6 and again the C8 piece is a ladder escape.
>
> So in summation, 5.... H4 seems to win after all.
> Also, 5... E8 wins if the analysis in the Jhex file holds up.
>
*************
I agree with this. I also examined your alternative, 5. D7, to 5. F7. This
seems to win for black whatever white does. I really like the strategy of
multiple lines ({F5,H4} and {G8,H8,I8}), even though your 5. D7 thwarts them
both. So much flexibility!

William


rhoads

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Oct 24, 2005, 4:26:30 PM10/24/05
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How did I miss that? Dumb, Dumb, Dumb, ...

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