Duo to the Death

Blokus has taken over my life

(rejected) FW: complete solution, part 1

Posted by nand on October 16, 2009

Considering all the depressing news I usually post about hard-to-beat openings, I thought it time to post something on an eminently defeatable opening. Sometimes I have a little trouble with it, so I thought it worth trying to work out a solution in more detail to avoid mistakes. As always in duo, even bad openings can win if you make a single error in your defence…

So: FW, the favourite of beginning & some mid-level players. It’s an interesting opening in that it looks pretty good but is actually one of the flimsiest of the F openings. I think this can actually be defeated by orange in ALL cases, though I must confess that I haven’t (inevitably) worked it all out. I would be very interested to hear from people who have suggestions for lines I should examine in more detail.

*****

UPDATE: I’m no longer happy with the line given below, as I think violet has a strong reply to the orange Z5. I will try to post more shortly. I will keep this page here nonetheless as an interesting false start.

*****

Here’s the basic orange response:

FW basic opening

Violet must reply on the left. (If violet plays on the right, orange plays I5(D7u) and the game is easy: I won’t spell out that line here as it should only require basic understanding of duo strategy.) There are basically two possible replies: a hang or a kiss. My solution is simple: if it’s a hang, play Z5(K8ullu); if it’s a kiss, play F(K8uul). I’ll consider the various cases in turn.

Case 1a) Hang and circle

The usual pieces for the violet hang are Z5(E7lddl), T5(E7ldd) or N5(D9ddld or dldd). If violet circles, orange should keep going aggressively rather than block until violet pokes up around the side. Here’s the line:

FW with a Z hang, the circling game

Note that orange F grabs the V in the nook of the violet F (& note that orange Z4 is dependent on keeping the W for a block). This game should produce an orange win of about 3 points. If violet plays T5 not Z5 then orange needs a different path, playing W(A8urur) to grab the L4 spot in the nook and using a different blocking method on the right (you figure it out).

If it’s an N hang, then it’s a little trickier, but the I5 is still the best bet, I think. At worst it’s a tie but here’s my packing for a 3-point win:

FW with N hang, orange I5

Moves: 1. F – X / 2. W – N / 3. N – Z5 / 4. Z5 – I5 / 5. I5 – T5 / 6. T5 – F (very important to tee up the I3!) / 7. L5 and the rest is hole-filling and packing.

Or if you like to make things exciting this is a good line too, & possibly a larger win (I haven’t worked it out in full but in practice it can lead to bigger wins versus players who aren’t good with open games):

FW with N hang, circling

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XF Lerpy du jour #2

Posted by nand on October 1, 2009

Another line I’m thinking about. The orange V5 is an experiment… actually it’s not bad, 4pts loss is respectable though I usually try in “solved” lines to get it down to 3 or under. In general I want to find the key points where orange can play a defensive move without resulting in a huge loss (this is useful for tournament play).

Lerpy 1 Oct 09 game C

Moves: 1. X – X / 2. F – Y / 3. T – N / 4. W – L5 / 5. L5 – I5 / 6. N – W / 7. Z5 – V5 / 8. U – T4 / 9. Y – L4 / 10. I1 – T5 and the rest is packing.

Note if violet plays L4 for U, then orange must not use the L4 to block (it’s needed on the right). Use O4 and I2 to block–one less point, but violet also gets one less point so the results are the same.

REFLECTION: Violet Y could also be V5 (the V3 leak doesn’t matter much since orange has already left a V3 spot for himself in top left corner). Then violet gets an extra I3 but (playing through the leak) orange also gets an I3 in bottom right & the results are identical.

Posted in openings, XF Lerpy | 4 Comments »

XF Lerpy du jour #1

Posted by nand on October 1, 2009

Still thinking a lot about this opening recently — I haven’t posted much on it lately simply because I want to give genuinely useful responses (otherwise this risks simply becoming a how-to manual for people looking to win as violet by lifting games from the blog… it happens). Anyway, my suspicion is that versus good violet play it’s hard to do better than a 3-pt loss. But it’s so complex I won’t pass judgment until a lot of lines are explored.

Anyway, for the moment I’m primarily interested in what is in my view the best reply: orange Y with the knob down. So I’ll just start regularly posting games that I think are close to optimal play. If you have suggestions for where orange or violet went wrong, please post comments, as I want to really map this line out.

OK: so this line is the result of some discussion with oldmanc, who agrees with me that the orange N kissing violet F on move 3 is kinda weak. We have both toyed every so often with L5 in that spot instead. I think these games show this may be promising.

Lerpy 1 Oct 09 game A

Moves:

1. X – X / 2. F – Y / 3. N – L5 / 4. Y – Z5 / 5. T5 – W / 6. L5 – I5 / 7. I5 – F / 8. Z4 – N / and the rest is packing.

This could be improved (the screenshot is from a live game): orange plays V5 in place of N, P in place of O4, N in place of P. One point more for orange!!! But violet can also improve on it: U and 1 in place of the P, and P in place of O4. So we’re back where we started, just 62-59.

Lerpy 1 Oct 09 game B

oldmanc thought violet might do better by blocking orange I5. This game suggests the results are more or less the same. It’s a little hard to tell because both sides have to worry about leaks so packing gets tricky.

1. X – X / 2. F – Y / 3. N – L5 / 4. Y – Z5 / 5. T5 – W / 6. L5 – I5 / 7. W – I4 / 8. I5 – P / and the rest is packing (but violet must not play the O4 till orange has used up the I2, otherwise there’s a leak).

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XF lerpy: is the mirror response bad?

Posted by nand on September 5, 2009

In my initial survey of responses to XF Lerpy the first defensive response is the mirror. My instincts tell me this is not a great response, but it’s far from proven. The usual results of mirroring look like this:

XF Lerpy, P in the centre

(Moves: obviously, X-X, F-F, Z-Z, P.) Why, you may ask, does violet immediately move into the centre on move 4? This is because (1) he doesn’t want to let orange get there first and (2) he’s planning to put a nasty piece through the leak on move 5, typically V5 (J11ddrr).

That V5 caused me to dismiss this line as a disaster for orange, but after playing this out a few times I’m less certain. Basically, it’s an important demonstration of the cardinal rule in Blokus: don’t panic even if things look bad, play aggressively rather than conservatively, and keep a few corners active in as many zones of the board as possible. I played 6 games with myself using variants of this position:

XF lerpy with mirror; violet blasting through the centre

Moves: X-X / F-F / Z-Z / P-Y / V-T. I played the Y below first because it’s important to get something going in bottom left & the Y cannot be blocked in a single move. (It’s a question whether violet V5 is premature–violet could try playing W (I2urur) first, for instance.)

It’s hard to tell from playing versus myself — a live opponent may see angles I’m completely missing — but I basically tried to ensure that orange kept a toehold in all 4 corners, cut off the sides where possible, & generally just was maximally persistent & aggressive. The results were interesting: one big loss, 3 small losses, 2 small wins. That’s statistically pretty good, suggesting that though the violet V5 looks really scary this may be a viable line for orange. More to report on this once I’ve worked out some games more carefully.

Posted in openings, XF Lerpy | 4 Comments »

XF Lerpy: initial survey

Posted by nand on September 4, 2009

This is one of the most annoyingly complex openings, & tends to be regarded with exasperation by many players, largely because (1) it’s quite effective; (2) there are a LOT of mid-level players who, once they figure out that this one is pretty solid, tend to play it ALL THE TIME, game after game.  One of my major projects is to dissect this opening to the point where wins are by predictably small, rather than large, margins (rather as with the XF Rubik, XF Tetris-Time and XF Yasu, which are rarely used by experienced players versus other experienced players because the wins are so small they’re not worth bothering with). I have no idea if this opening can be ultimately reduced to a desirably small margin (in my view, 3 points or less) but it’s worth exploring at length.

I think it is worth setting out the plausible orange replies first. These aren’t all the possible replies — I’d be grateful for suggestions of any others I should examine seriously — but they are the commonest, & I think they are worth examining first before testing out others.

DEFENSIVE RESPONSES:

1. Mirror

XF Lerpy, orange mirror

2. F to the left

XF Lerpy, orange F to left

3A. N up

XF Lerpy, orange N up

3B. N left

XF Lerpy, orange N to left

OFFENSIVE RESPONSES:

4. N kissing violet F

XF Lerpy, orange N kiss

5A. Y kissing violet X, knob up

XF Lerpy, Y kiss with knob up

5B. Y kissing violet X, knob down

XF Lerpy, Y kiss with knob down

*

My current thoughts: Mirror (#1) is demonstrably bad, as I will show in a future post. F to the left (#2) is extremely effective against low- to mid-level players, but has fatal flaws that can be exploited by good players; it may nonetheless be worth exploring. N up (#3a) has a major vulnerability (violet can wrap Z5 around the orange X) but may be OK; N left (#3b) I am not very familiar with.

The major lines are #4 and #5A/B. My suspicion is that #4 is not good, because violet simply lays down N (B7drdd) and orange has no corners to work with in the bottom left corner. Thus #5A and B are the best options, the major branches depending on whether violet plays through the hole on move 3 (typically with T5, though V5 is an option) or blocks the Y.  If violet blocks the Y then orange has the option of playing the N in the same way as in #4, or playing something else there (typically T4).

I’ll try to pick away at these openings one by one, though it’s a tough job. Anyway who wants to help out, be my guest 🙂 ……

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Bigwood F #2

Posted by nand on September 3, 2009

I’ve been working out orange lines for this one. There are so many lines that lead off it, depending on orange’s first move, that I think possibly its main strength is just that it’s hard for even high-level players to remember all the variations. I suspect it’s not all that strong an opening, in fact, just a hard one to grasp. So my little project is to limit the lines & make this a manageable game for orange.

My current thought is that the best initial move, no matter which way the violet F is turned, is a mirror. This almost inevitably gets a violet Y plunked into the middle of the board, cutting off two orange corners & threatening to cut off more. Here’s one line of response (the L5 move is, I think, mine; the U I’ve seen from other players):

One response to Bigwood F (variation 1)

One response to Bigwood F (variation 2)

Moves: 1. F – F / 2. Y – L5 / 3. N – U. Orange L5 is key here: if it were Y then a hanging violet N (E3uuru) or L5 (E3uuur) would threaten a cut-off on the bottom. There’s no powerful cutoff move for violet on the bottom left on move 3, so violet is forced to threaten on the right side. But once violet N is played, orange U leaves only three unappetizing options for violet: (1) block with L5 (K10rrrd or K10rrru) sacrificing a tempo & the entire bottom right corner plus creating a terribly vulnerable series of sides in violet’s top area; (2) play a kiss move (probably T5 [K10rr]); or (3) play a move threatening a cutoff (e.g. W [K10ruru]). I think option (2) is the only viable one, & I’ve played games with this line that have gone either way.

Whatever move violet makes on move 4, I think orange’s logical 4th move is T5 (E5uur), which forces a response from violet (in order to avoid orange N [C8uuru] on move 5).

I do not think that violet can afford to ignore orange U & attack on the left on move 4; if he tries this, orange should simply play as aggressively as possible on the top. I can try to be more concrete about this line in a later post, if it seems worth pursuing.

Thanks to Dormys fan club & mike_yosuke for playing a few games with me that allowed me to work some of this stuff out.

[UPDATE: Bigwood tells me that the position in the 1st board is correct but he thinks in the 2nd board violet’s Y is positioned wrongly: it should be at H6uuu. Then obviously the violet N is no longer the obvious option…. in the game we played together BW played X there. Obviously I need to work on a sequel to this post.]

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XN Gerenuk #1

Posted by nand on September 3, 2009

Been away from posting for a while, not so much because I haven’t had anything to say but because I’m been working hard at thinking through openings. I’ve decided to try posting more “incomplete” posts, first because it’s often simply too timeconsuming to work a line out to its end, & secondly because I’m not so much interested in “solving” a line as in guaranteeing that it remains open (i.e. that orange isn’t in such a helpless situation that there’s no point in working it out further). I also was hoping that occasional readers of this blog will suggest moves I haven’t considered, so we can collectively crack some of these lines.

As my first installment in this series, here’s my current thoughts on XN Gerenuk, one of those looks-bad-but-actually-is-kinda-good openings that is a frequent headache. Currently Rubik87 seems to like this one a lot, but you’ll see it frequently employed by many other players. It requires some special handling if orange tries to mirror it — unlike the XF Lerpy, where the mirror option is a clear disaster (I’ll write about this in a later post), the mirror option isn’t too bad a choice for orange here, & much harder for violet to crack.

Anyway, my current thinking is that orange needs to avoid the temptation of cutting off the corners of the N. I think W on move 2 is very promising, as follows:

XN with W response, take 1

The moves are fairly obvious: 1. X – X / 2. N – W / 3. Y – Y / 4. L5 – P. I believe that violet Y is a forced move, though there’s one other option I’ve explored below. Orange P could also be T4 if one believes that the extra cell in orange’s bottom right might be crucial for endgame packing — I dunno. — From this position I think violet is forced to play through the bottom leak, probably W (G5drdr: that’s “cell G5, down, right, down, right” if you haven’t encountered this notation before). Then probably orange L5 (K4dddl), and the game gets messy. Messy is generally a desirable situation for orange, but obviously from this point the game has too many lines to follow in this preliminary post.

Here’s another possible line: I’m not sure who devised the tricky orange F move but it’s a smart one.

XN with W response, take 2

Violet has no good block now that I can see, & not even anything that leaves a nice block for later on. Another messy game. I think it’s crucial violet maintain a threat against both the bottom right & top right, so when I’ve encountered this situation in the past I’ve played F (J8urr), since it’s vitally important that orange be distracted on this turn from closing up the bottom leak off violet Y. This is a really tricky position, & I don’t think it favours either player.

XN with W, take 3

The only other option I see for violet other than the Y through the middle is this W. It looks bad to me, as basically violet has no good 4th move… violet needs to do too many things here: attack on the right side (& close off that leak); attack through the middle (& close off that leak).  I think the only option for violet is L5 (J10rrrd), which leaves orange with the option of Z4 through the centre or L5 on the right side…. tricky situation, & I’d have to analyse it further to see who’s on top.

So, food for thought. The other line I’ve been exploring as a response here is a defensive move (again, not my move, but I’m not sure who devised it). I’ll just post this one here for now & maybe follow it up later (or in the comments). The key is that there’s no nice block for violet at this point, but I don’t think violet can just ignore the orange F & play a “wait and see” defensive move on top as orange has some nasty things he can do below (possibly Z5 [D2ruur]?).

XN with an XF defence

Posted in XN Gerenuk | 5 Comments »

Studies in XF Lerpy #3

Posted by nand on July 15, 2009

With the standard version of this opening (with orange having an X, N, Y cross in the middle of the board) the tendency is for orange to be protective of the holes in his defence. This game shows that this idea may be a mistake.

XF Lerpy with orange deliberately attacking the bottom left corner

Moves:
1. X – X
2. F – N
3. N – Y
4. Y – Z5
5. L5 – W
6. T4 – L4

This is the key moment in the game: violet could (& probably should) attack on the right side rather than play the T4 in the bottom left corner.

7. L4 – Z4 and the rest is packing (since orange cannot waste the 1 attacking violet’s main area, since it’s better to grab I3 in the bottom left).

Posted in openings, XF Lerpy | Tagged: | 1 Comment »

Studies in XF Lerpy #2

Posted by nand on July 15, 2009

Here’s a line I’ve played a lot as violet. It doesn’t have a happy end for orange.

XF Lerpy with orange on the defensive

Moves:
1. X – X
2. F – Y
3. W – N

These last two moves are often reversed. In my view it is essential that violet play W here, even though this means that it is unavailable for the block for the leak off the orange N. Other moves here are too far away from the centre and permit orange to rob violet of too much of the corner.

4. N – F
5. Z5 – L5
6. P – W

Orange could try to take advantage of the leak off orange N here before violet has a chance to seal it off. In my experience this is a bad idea, but I suppose it could be worth a try, & I haven’t analysed it yet. — Unfortunately orange lacks any good piece for the block, i.e. one that both seals off the bottom side & maintains an attack on the bottom left corner. Te W isn’t much use.

7. V5 – Z4

Again, orange could have tried I2 off the N rather than defending, but it’s REALLY late in the day to try this now…

8. T4 – I2
9. Y – 1
10. Z4 – V3 and the rest is packing. Possibly there’s a better packing for either side–this is a screenshot from a real game, so not necessarily ideal play.

Posted in openings, XF Lerpy | Tagged: | 2 Comments »

Studies in XF Rubik #2

Posted by nand on July 8, 2009

I wasn’t entirely happy with my solution to this in the previous post (a 2-point loss for orange), though that line has the advantage of being more or less a forced game: if orange wishes to lose by only 2 points, violet really has to go along & can’t win by any more. Very useful for tournament play.

BUT: I’m not happy with that orange T5 kiss move, since it seems to me obvious that (1) it’s an unnecessary bit of finesse (since violet will not block that corner immediately) and (2) since it’s a close game & violet is really starved for spots for the 1 and i2 pieces, it’s foolish to give him those spots for free.

So, consider these screenshots as part of my continued exploration of this game, diverging at the point where I played T5 in the earlier game. I won’t give blow-by-blow lists of moves, as it’s getting late in the evening & they are mostly obvious (especially since the opening moves are identical to Study in XF Rubik #1), but I will provide comments.

XF Rubik study 2.1

One-point win for orange. Moves from L5-F on: I4-N / T4-L5 / N-I4 / V5-I3 and the rest is packing. Violet N is bad as it’s the only good block for the top — the V5 leaves an I3 hole, enough for orange to eke out a win.

XF Rubik study 2.2

I realized that the orange N in the previous game is the wrong way round, as orange needs to threaten to grab I3 AND i2 on top. So this line shows that violet can get a 3-point win this way. (If orange N is turned the right way then it’s a 2-point win for violet… I haven’t got a screen cap, but will post it later.)

XF Rubik study 2.3

So here’s another variant on the first game, with orange N in the “right” position, & orange deciding to stop the I5 (which I think is a mistake…. orange has a nice i2-1-I4 series off violet I5, & violet can’t make a really big block in bottom right off the I5 anyway). 3-point loss for orange.

XF Rubik study 2.4

A big win for orange if violet continues to circle. Violet Z5 is a mistake–should be Z4 (1 less point for violet, 2 less for orange) but anyway, this is not good for violet — the leak off the violet L5 isn’t enough to do much of anything.

XF Rubik study 2.5

This time I used L5 not F, & the results are interesting (though I have to see what it’d be like if violet blocked in top right rather than playing I4. A close win for orange, even despite the space-eating I5. (I would have to check if blocking the I5 move with P or Z4 and letting violet get I3 on top is better for orange.)

The moves from L5 on: L5-L5 / I4-T4 / T4-N / N-I3 / I5-V5 / the rest is packing.

OK, so take it from here, folks…. I want to know where these games can be improved from either side.

Posted in openings, XF Rubik | 2 Comments »