2 posts from 2008

People who were in the game shouldn't predict, obviously!

Teal plays it safe by making his connection and sitting tight. His restack is pretty good: his two 4-stacks are stronger than any neighbors, and his 3-stack has a good chance to be able to connect, depending on red's restack and if it survives blue's turn. The only way he could have restacked better would have been if the territory between red's 3-stacks had gotten the two dice that went to the southernmost territory. In that case, red might have tried his luck at connecting through it (slightly more than 70% chance of working although with a ~55% chance of ending up with a 2-stack between two 1's before restack), but would probably have focused on the north. This did not happen, however, and red takes the obvious move of connecting his 3's. He plays it safe, and this is his only move (he has only a ~15% chance of taking green's 3 with his two, which might be enough for the bolder amongst you).

Here's green's opening, and red's restack:
Red's restack is good, giving him a strong 5-stack to hold teal in check with. It would have been better if the territory next to the 5 had gotten the third die, as that would have given him a stronger and more connected base after teal's obvious move.

Green's end of turn and restack

Green decides to stake his claim to the eastern edge. Although moving his 5 south gives his base a little more depth, it is left next to yellow's 5 and with no other way out. His restack is poor: it leaves his biggest stack weaker than its neighbor, spreads most of the dice out, and two dice are wasted on his useless western territory. Green ends his turn with a large, well-connected base, but one that has too few dice to stop purple, yellow, and brown from taking most (and potentially all) of it away. Purple's end of turn and restack:
You can see that purple had the misfortune of his restack using half his dice on the northern territories, and leaving his border with yellow with only 4 dice, which yellow (possibly irked by the loss of his southern territory) decides to take advantage of, much to the relief of green. Yellow and blue's ends of turn and restacks: Yellow doesn't get the restack he wanted most, all three dice to his border with green. His choice not to take try to take one or both of purple's remainder is probably motivated by a desire not to spread himself out and by a wariness of blue's 4-stack.

Blue plays it safe, leaving purple's 4-stack alone (~71% chance of success) and going for red's 3 (~90% chance of success). His restack is decent, giving him a commanding 5-stack again.

Brown's end of turn and restack:

Brown makes the one move that has a good chance of success and it fails. Alas. His restack offers a shred of hope, giving him a 4-stack, albeit one hemmed in by teal.

Teal's end of turn and restack: Teal moving his 3-stack up through red's center is an obvious move, but pushing his 4-stack out east is not. The chief benefits are that it allows teal to threaten in most of the south and middle, and also acts as a bulwark against yellow or green becoming too strong -- assuming red can mount a reasonable effort in the south, yellow is stuck as a thin crescent of territories, easily split. Looking further ahead, it also means that if red wants to go north, he'll have to either go through teal, or take the long way around through yellow and green. The problem, of course, is that it gives red the opportunity to perform a three-way split on teal: if he restacks well, it would not be possible for teal to connect through him next turn. But teal knows, as does red, that this is a gamble: a poor restack leaves red vulnerable to a teal counterattack, and even a good one ensures vicious conflict with a larger opponent. So what does red do?

Here's red's end of turn and restack (also green's):
Red plays it safe, taking teal's weak south. This move does leave red vulnerable to teal, but teal has no real reason to start a fight other than spite: red is betting that teal will leave well enough alone and focus on easier pickings to the north while red mops up the south.

Green decides to see how the restack falls. The only move that would be particularly attractive is to take yellow's northern territory, but green probably expects it would be better to keep his large stack close in order to deter brown and purple from taking too much territory. The restack is decent; an extra die on the territory between the purple stacks would have been very useful in pushing the connect out into brown's territory.

Purple and yellow's turns and restacks:
Purple takes the two territories between its big stacks and calls it a day. The restack is as good as could be hoped for, but he still ends up with his big stacks hemmed in by teal, green, brown, and blue. This is why the middle is a bad position.

Yellow takes one of purple's territories, but decides not to take the other, effectively ceding it to red. This is probably in order to prevent a bad restack allowing red to split him. The restack is unhelpful, tossing two dice to an interior territory that would have been more use on the northern border, still weak compared to green.

Finally, note red's message: "be nice teal". This is to let teal know that red doesn't have hard feelings about their squabbling and to communicate that he won't attack if teal doesn't. This sort of subtle communication is much better than blunt truce offers as it is more likely to go unremarked by other players (when was the last time a counter-truce formed because one player asked another to be nice?) and also offers red the ability to take advantage of any future weakness in teal without being labeled a traitor.

Blue and brown:
Blue decides to use his 5-stack to take purple's territory, not brown's. One possible is that blue wants to prevent brown from reconnecting through purple: this makes sense, although a brown reconnect could leave him dangerously thin and easy pickings for blue. Note that the reason blue doesn't take purple's 2-stack is that such a move would leave him with no depth and his big stack in the middle of three stacks of comparable strength. Blue's restack is okay, wasting a die on the useless southern bit.

Brown, again, has few options. He plays it safe by restacking, but taking purple's 2-stack and hoping for a good restack might have been a better move. Brown has easily the worst position, and has very little to lose.

Teal's turn:
He finally takes yellow's stray territory, and leaves red alone. Teal has a stronger position after this turn: he has just as much territory, more dice, more room for possible expansion, and has a big stack right next to red's proverbial jugular. Red wants the ceasefire to hold because he doesn't want to lose, teal because taking out red would be more trouble than it's worth.

After this, everyone passes until green's turn:
Green takes his 4-stack into yellow's territory, which is a mistake: he should have used the 5-stack instead. That would present a stronger front to yellow, and the 5-stack probably isn't preventing purple from moving anyway. Green's borders with purple are too strong -- especially after a restack -- and purple's idleness is caused just as much by threats from teal, brown, and blue as by green.

Speaking of excessive timidity, red should have taken the purple 2-stack by now. Blue's stack clearly isn't going anywhere, and red would almost certainly have restacked enough to deter yellow, already distracted by the fight with green. Red's choice not to take green's stray territory makes more sense, given it is unclear how teal would react to an opening like that.

After this, everyone passes until yellow's turn:
Yellow has restacked better than green, and retakes the disputed territory. Note that although green's western base territory is only a 2-stack, it hasn't been touched. Green makes the obvious counter, and ends up like this: Now green has firmly acquired the territory, but at the cost of too many dice. He could have had a similar position a couple turns ago, and those extra dice would no doubt have been very useful.

Now, things finally get a little more interesting again: Brown finally gets bored of sitting around and takes purple's weakest territory. It's hard to say why, other than boredom: brown doesn't try for the unlikely connect. Most likely, he's realized what a bad position he's in, and hoping that a lucky roll of the dice in his favor will turn it around. Fortune, after all, favors the brave. Purple makes the obvious counter, and the ball's in blue's court: Blue decides to sit this one out, and brown loses the critical dice roll and promptly flags. Teal -- fully stacked for the first time -- takes advantage of the confusion and grabs purple's 7-stack. This puts purple in a tough spot: Purple succeeds in a wild gambit, taking out two of green's biggest stacks. Purple had about a 22% chance of winning an 8v8 and then a 7v7 -- about the same odds as winning a 4v5. Please also note that red (inspired by brown's valiant demise?) finally summons the courage to take out green's stray. This is not a good turn for green, and blue and teal mop up the pieces: Red finally takes purple's stray. Although red could have tried to exploit teal's weakness, teal still has room to expand into, more dice, and perhaps most importantly, more depth. Red would stand a good chance, but it's also very possible that a red-teal conflict would weaken them so much that blue, yellow, and maybe green could make a comeback. Red stays true to form, and plays it safe.

Skipping forward a couple of turns: Luck finally works against purple, and he loses a 7v6 against blue, flagging for 6th after green takes the middle of his emaciated territories. Teal continues expanding, and is confident enough to leave an  apparently open 2-stack for blue to grab -- but both teal and blue know that a 2-stack surrounded by 8's isn't open at all.

After another couple turns: Teal and blue have continued expanding, and yellow has unsuccessfully tried to take green's southern territory. Teal is now the undisputed leader: he has red and blue up against the wall, and could easily apply debilitating splits to them. It's possible that blue and red could win against teal, but it's more likely that he would beat both of them, due to more territory, more dice, and better position. At any rate, blue and red are both going to get points from this match, assuming they keep their positions, and therefore have little incentive to rock the boat. Red will take blue's stray, and the fight will be between green and yellow for 4th.

By the end of teal's next turn: Red has flagged for 2nd and green and yellow have both claimed 4th. Blue didn't flag fast enough, losing a territory to teal. Green has been reduced to one territory, and his demise looks imminent.

After green's next turn: He's managed to take two of yellow's territories, who can't seem to win an 8v8 against him. Teal has graciously allowed blue to reconnect. Yellow now has a choice. He can go for the kill (8v7 then 7v3), with a ~67% chance of success, or play it safe by taking green's 3-stack. Yellow, probably spooked by losing all those 8v8's, goes safe: Red, however, decides to take matters into his own hands, and attacks green through yellow, losing the 7v7. Green restacks his next turn, and yellow bides his time. Red attacks green on his next turn, and again fails -- so on green's turn, he can read the writing on the wall, and takes the ~47% chance for victory: He succeeds, yellow gets 5th, and the rest of the board flags to teal.


So how did everyone play?

Brown: OK. He had a tough first turn, doing well neither by the rolls nor the restack. His choice to go into the NW corner can be questioned, but it isn't significantly worse than trying his luck cuddling up to blue's 5-stack. His second turn 3v2 defeat pretty well put him out of the game. It's tempting to chalk his loss up to sheer bad luck -- and indeed, it was very bad luck, in rolling and restacking -- but in the mid-game, he might have tried attacking purple's weak territory a bit earlier before his lack of territory put him too far behind in the dice count. It might not have worked then either, but green and purple certainly showed that fortune does favor the brave: you can't be lucky if you never roll the dice.

Purple: OK. Things might have gone better for him if he'd ignored what I thought and focused on the north, abandoning his south, but it's hard to say, and yellow might well have decided to take advantage of green's weakness instead of heading south, and a good restack or lucky roll would have meant a completely different game (doesn't it always?). He might have tried to consolidate his position after brown flagged, but he too was facing stiff odds, and winning that 7v6 against blue could have propelled him into 4th or 5th.

Yellow: Well. He might have tried to get purple's last southern territory, but that might have sparked a conflict with red he couldn't afford with green breathing down his neck. Yellow was given a very poor starting position, and came very, very close to getting 4th and winning points from this match -- his ultimate defeat by green was a matter of luck, although a not going for the 8v7 in the endgame was almost certainly a mistake.

Green: Poorly. His failure to move aggressively against yellow in the early and mid game came back to haunt him, and the extra territory might have provided the dice to stymie purple's (very lucky) kamikaze attack. Green's two losses to purple were unlucky, but his fortune returned for his defeat of yellow, so it's probably a draw for him on luck.

Blue: Well. Blue had a very starting position, and solid play allowed him to parlay it into 3rd, helped by a lucky 7v6 defense along the way.

Red: OK. Although red came in 2nd, he might have done better if he had been a little bolder with the stray green and purple territories: he could have acquired more territory faster, possibly pushing into yellow, and seriously threatened teal, especially if blue had helped out.

Teal: Well. Teal benefited from the best starting position of the lot, but he combined good skill at consolidating his position and keeping out of the trouble to the east and north, as well as a bold thrust into the middle of the map which cut off red's expansion and helped reduce yellow and green into the minor side squabble they became. In short, cautious enough to get a handful of full, connected stacks, and bold enough to know what to do with them.