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xC's Rule #6 and Vermont
skrumgaer wrote
at 9:03 AM, Thursday June 5, 2008 EDT
This month I have been testing xC's Rule #7 in the first round by not attacking with only one-die advantage except for 2 v 1's. As a general rule I have also been following xC's Rule #6, which says that you should move your big stacks closer together. In a recent game I eschewed a 3 v 2 connect but 2 v 1'ed Vermont to bring my "big" 2 in another area closer to my center. Vermont got upset and somehow came up with the idea that xC's Rule #6 is OK unless employed in the first round. (Perhaps what he was really saying is that xC's Rule #6 is OK unless used against Vermont.) I thought I would do a bit of mathematical analysis to a Rule 6 situation.

Suppose we have the following arrangement:

x 3 2 1 2

where the first two and the last are mine and the others are opponent's lands. Under Rule #7 I would avoid the 3 v 2 to connect and wait for Round 2. Under Rule 6 I would do the 2 v 1. Now what do I accomplish with the 2 v 1?

If I did not do the 2 v 1, the expected number of restack dice on my 3 would be 2/3. If I did the 2 v 1, the expected number of restack dice would be only 1/2, but I would have to make only one attack to complete the connect. Also, the stack I would connect with would have an expected size of 1 1/2. And the expect number of opponents' restack dice on the two intervening lands would be reduced because there is only one intervening land. So there is a tradeoff.

I have not discovered anything that would suggested that Rule #6 is not as useful in Round 1 than at any other time.

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Vermont wrote
at 9:27 AM, Thursday June 5, 2008 EDT
Bringing big stacks together is a good idea in theory at certain times, but is highly situational.

A far more potent rule of thumb is to not have multiple bases, especially in the first round when your opponents are looking to make connects and consolidate their own bases.

This is one of the first basic concepts players come to understand as they start to learn the game, and I believe is even mentioned in Grun's guide to new players.

If you do what you've suggested above, you've decreased the odds of dice going to your primary base and your biggest stack, and made sure that if you do get dice in your newly expanded area you are probably only looking at a 2 stack.

You also fail to take into account that you are probably surrounded by other players that are more likely to pick off your stacks since they are weaker.

You also fail to take into account that people aren't 100% rational. If they perceive that you made an irrational attack like the one above (expanding into a second base for no reason?) then you are more likely to have made an enemy.

I would be interested in hearing xC's opinion on this. I bet he would have some clarifications to make, although I could be wrong.

I would like to point out that the two games you tried this plan in you took a 6th and 7th. (or was it two 7ths? I don't remember.) Certainly too small a sample size for anything conclusive, but not supportive to your theory.

And I bet if you ask players what percentage of the time they think the board would warrant expanding a second area in round one, that they would tell you less that fifteen percent.

The mid game is probably the best place to use this type of strategy, but I doubt the percentage goes up all that much.
skrumgaer wrote
at 10:55 AM, Thursday June 5, 2008 EDT
"a more potent rule of thumb is to not have multiple bases"

Sort of hard to follow in Round 1 where you usually start with muliple bases. Like saying "the road to riches is to have unmitigated good fortune".

Expanding from a smaller area versus not expanding from a smaller area does not change the number of new dice you get. It only changes where they go. A weaker stack here means a stronger stack there.

A sample size of 150 games or more is probably needed to make a realistic evaluation of a strategy.
Vermont wrote
at 11:14 AM, Thursday June 5, 2008 EDT
I think you are mixing terminology here. Typically a base implies more than one connected territory, while island is used to refer to a single standalone territory. Granted, there is no kdice "dictionary" so if you want to refer to single territories as bases, you are free to. I just think it dilutes the meaning of that term as it is typically used.

And you are correct. You get the same number of dice either way, obviously. I did not imply othewise, and anyone who's played more than a few games knows how the number of dice is determined.

Choosing to expand an island into a second base means you are less likely to get dice where you want them, and makes your overall dice/territory ratio lower, which definitely has an affect on the likelihood of your being attacked.

But I only have a couple thousand of my own games as anecdotal evidence. I would like some of the other players to comment on this.

I think we all agree that occasionally this may make sense. However, I feel that as a general rule of thumb it's a bad idea.
Cal Ripken wrote
at 12:19 PM, Thursday June 5, 2008 EDT
While XC's and Grun's rules are definitely good to base an overall strategy on, especially for newerer players to learn good techniques, I don't really think you can test their worth as definite concrete rules to follow. There are just too many other variables in a game to suggest that I should always bring my bigger stacks together- or even what defines a bigger stack.
skrumgaer wrote
at 1:04 PM, Thursday June 5, 2008 EDT
to jpc4c:

in particular situations you may want to overrule a rule that you normally follow, but if a rule has value, its value will be seen when many samples are taken. And it is impossible to evaluate a rule without a large sample size. For example, to evaluate a new medical treatment, you need a large random sample of patients. For some patients the treatment may not work because of other special conditions they have, but with a large enough sample you can evaluate whether the treatment is at least suggestable for the typical patient.

Vermont: If you expand an area into a direction you to go, you have increased the probability that a restack will occur in a place where you want it (namely, your new land). No?
skrumgaer wrote
at 1:13 PM, Thursday June 5, 2008 EDT
into a direction you *want* to go
Vermont wrote
at 1:21 PM, Thursday June 5, 2008 EDT
Using the very example you proposed, I would not want any dice on the two one stacks to the right. They're terribly likely to be killed whether they're a 1 or 2. I'd much rather do what I can to get my extra dice into my primary base on the left.
habit1 wrote
at 1:35 PM, Thursday June 5, 2008 EDT
For me, the biggest determining factor in the scenario you proposed would be the size of the stacks around me and where they will be moving in round 1. The only times i make connects with small stacks early in the game are:
1) when I consider those stacks expendable, and the connect will help make a large stack bigger and more menacing.
2) when the players around me will be moving in another direction. This often happens when you connect on a coast and other players are moving to other coasts, or when you are protected by a lake.
3)when there are other small stacks around me. I will connect and assume that the restack will refill them so that the small stacks around me can not attack
Vermont wrote
at 1:36 PM, Thursday June 5, 2008 EDT
Agreed habit, but in this case skrum is growing a second area where he is NOT connecting, and NOT gaining extra dice.
skrumgaer wrote
at 1:56 PM, Thursday June 5, 2008 EDT
Vermont:

There aren't two one-stacks on the right.
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