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Subject: Art of War as Applicable on the Scottish Moors rss

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Tony Chen
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Nine boundary stones mark the divide between the wild and fierce men of Scotsbury North and the equally wild and equally fierce men of Scotsbury South. Trouble is, every spring, as the melting snow shifts these boundary stones, someone must restore them to their “rightful” places, which are rarely the same as their former locations, and are never the same in the minds of the fair and impartial villagers of Scotsbury North and the equally fair and equally impartial villagers of Scotsbury South. Consequently, as is natural and expected, the best men armed with twigs, clubs and bagpipes from Scotsbury North and South wage war on the sheep pasture for the right to claim and relocate these boundary stones. As the village elder of Scotsbury _____, it is your responsibility to send the right men to fight over the right stones at the right time.

On the Duration of War
When entering a war, it is critical to know how long it may last so as to be better able to carry it out to the end. A typical war between Scotsbury North and South lasts between ten and thirty minutes.

On Luck
Luck can be a determining factor in all wars, and battles on the Scottish highlands are no different. However, a competent village elder will manipulate luck to work in his favor. The number one rated village elder at for example, has a winning rate of around sixty percent.

On the Tradition of Threes
Just as there are three times three stones on the sheep pasture, no more than three men from each side can fight over a particular stone, who must be deployed one at a time, alternatively between the two warring factions.

These men are deployed from the army reserve, the comprisal of which is hidden from your enemy, and which always consists of two times three men. To keep this number constant, after deploying a man, you must (and would want to) recruit another man from the draw pile into your hand.

The men available for recruit for each faction come from two times three clans, each given a color and consisting of three times three men, numbered from one to nine.

To win the war, a faction must either win a majority of the three times three stones (five), or simply win three consecutive stones.

While it is true that adhering to these traditions puts serious limitations on the flexibility and maneuverability of your army (surely sending five men to beat up on your enemy’s three can be very convenient), choosing to do otherwise portends a far greater risk—that of incurring the wrath of the almighty and cursing your village to ruin. Therefore, it is not only wise, but mandatory to honor these age-long traditions that have been in existence since the creation of Schotten Totten by Reiner Knizia in 1999.

On the Strengths and Weaknesses of Individuals
As afore-mentioned, each individual comes from a specific clan indicated by his color: red, orange, yellow, green, cyan and slate blue. Ancestry may be of paramount importance in determining the qualification and worth of an individual in the Aristocratic English society, but not so on the Scottish Moors: each man is judged not based on the family name, but by the weapon that he carries. Thusly, a man wielding a hammer, whether he be of royal blue or plebeian green descent, is worth six whereas a man yielding a cane is invariably worth half the third as much. In general, the bigger a man’s weapon, the higher his strength rating, which varies from one to nine—a notable exception being the bagpipe that is worth two, one less than the smaller weapon that is the twig.

On the Strength and Weaknesses of Formations
The destructive power of a group of three men depends more on how its parts work together than the sum of its parts. On the battlefield, two plus two doesn’t always add up to four. It is vital to know which formations create the strongest triad of warring Scotsmen.

The weakest formation is a wild rabble, a group of men put together randomly in disharmony and disaccord. They are more likely to fight amongst themselves than actually engaging the enemy in combat.

A slightly more coordinated formation is the relay, a group of men of consecutive values.

A stronger and tighter group is a clan, a group of men from the same colored clan. It should come as no surprise that clansmen work better together.

But even stronger is a team, a group of men with the same value.

Ultimately, though, the strongest formation is an ordered clan, which is made up of men of consecutive values from the same clan.

When facing off on opposite sides of a boundary stone, the stronger formation will win, regardless of the individual prowess of the fighting men. However, if the formations are of the same type, the triad with the higher sum of values of its men will win. If this is also the same, then the triad that is completed first wins.

It is important to know that while stronger formations are better, they are also harder to complete.

On Assessing Accurately the Strength of Armies
All percentages discussed in this section will be based on the assumption that all of the useful cards are still in the draw pile and not in the six card hand held by your opponent. Now, the true percentage is fairly close to the given percentage at the game’s start, but becomes smaller and smaller as the game goes on and the drawn pile diminishes (thus increasing the chance that the card you need is in the opponent’s hand instead of the draw pile). Also, these percentages are the chances of drawing the required cards—whether you get to play them together on the same stone is another issue.

I will call men with values whose difference is no greater than two relay partners. And clan relay partners are simply relay partners from the same clan. For example, the clan relay partners of a slate blue six are slate blue four, five, seven and eight. More specifically, the partners with a difference of two are distant relay partners, and the partners with a difference of one are close relay partners. Another example, an orange two has two close clan relay partners (orange one and three) and one distant clan relay partner (orange four).

Men with the same value are team partners. For example, all nines are team partners.

Men of the same color are clan partners.

completing an ordered clan with one man
If the man has four available clan relay partners, the chances of completing an ordered clan with it are 50%. (All numbers from three to seven start in this condition)

If it has two close and one distant partners still available, the chance reduces to 37.5%. (Note that all twos and eights start in this condition.)

If it has only two partners still available, and those two partners are also clan relay partners between themselves, the chance reduces further to 25%. (Note that all ones and nines start in this condition.)

Completing an ordered clan with two consecutive men
If both of their relay partners are still available, the chances are 75%.
If only one of their relay partners is available, the chances are 50%.

Completing an ordered clan with two non-consecutive men
The chances are 50%.

Completing a team or clan with one man
If there are five partners available, the chances are 81.25%.
If there are four, the chances are 68.75%
If there are three, the chances are 50%.
If there are two, the chances are 25%.

Completing a team or clan with two men
If there are two partners available, the chances are 75%.
If there is one partner available, the chances are 50%.

So how do we use this information? If you see a cyan four played by your opponent, this means that your group of cyan five and six has 50% of forming an ordered clan. Or if your opponent plays a red five on a stone and you have a red three in your hand, the chances of his forming an ordered clan with the red five are 37.5%.

On Losing Big and Winning Little
Winning one stone is one stone. Notwithstanding how you won it—by a landslide with an ordered clan of values seven eight and nine (the best formation possible) over a wild rabble, or barely with a team of fives over a team of fours—it doesn’t count any more or any less than one boundary stone.

Suppose that both you and your opponent each have four formations. If they go head to head, the best going against the best, the second best going against the second best, etc, you are likely to win in two out of four formations. However, if you send your best formation to fight his second best, your second best to fight his third best, your third best to fight his worst, and your worst to fight his best, you are likely to win the former three formations and lose only on the last.

Therefore, to win more stones, aim to lose big on a few stones so as to win little on many stones.

On Knowing Thy Enemy
Information is power. This information is revealed to you by the men your enemy deploys to each stone. Let us examine how you can take advantage of this information.

When he deploys his first men to a stone, you can aim to win small, lose big, or both. If he deployed a nine, send something “worthless” like a one or a two. This way, you’ll either end up losing big, or even better winning little (low value ordered clan beating high value team). If he deployed a six, send something to barely beat him like a seven.

When he deploys his second men, you know what formations he is restricted to. We won’t consider wild rabble and relay because those are weak formations that one use only as last resorts. In general, after the second deployment, one is either restricted to team or clan, which can be ordered or not.

If he is restricted to a team of a lower value than you, go for an ordered clan or team, whichever is the easiest (usually the latter), as either will beat him.

If he is restricted to a team of a higher value, go for an ordered clan; because if he does complete his team, that’s the only thing that will beat him, and if he doesn’t, falling back on a mere non-ordered clan (which is usually easier to do than forming a team) will do.

If he is restricted to a clan (potentially ordered) of a higher value, go for a team; because if he completes the ordered clan, you lose no matter what, but if he fails to complete an ordered clan and must settle for a simple clan, a team will beat him. It’s true that an ordered clan would also beat him, but a team does just as much for you and is more likely to be completed.

If he is restricted to a clan (potentially ordered) of a lower value, go for an ordered clan yourself. If he succeeds in completing an ordered clan, then you must have an ordered clan to beat him. If he fails and falls back for a non-ordered clan, you can still use a non-ordered clan (or an ordered clan if you wish) to beat him.

In general, after his second deployment, if his men are of values lower than yours on a particular stone, go for the same formation he has. If they are of higher values, go for the opposite formation (assuming there are only the dual selections of team or ordered clan).

When he deploys his third and last man, his formation is set. If it is definite, or very likely, that he will win, then do not commit valuable men to that stone. Example: he just completed an ordered clan of four five and six, and you played red two and three there. You also have two fours on another stone, and a red four in your hand that you were saving for deployment to either of these two stones. Well, now your choice of stone for that red four is reduced from two to one.

Now suppose that he failed to complete an ordered clan must settle for a clan of four, five, and two. In this case, you have the option to use your red four to complete your team of fours instead of using it to beat him with an ordered clan of two three and four. You can simply use a red seven or above to beat him with a higher valued non-ordered clan.

In general, the third deployment lets you decide whether you must play a certain man to that stone, or you can free that man for service elsewhere (assuming that it can be of service elsewhere).

On Maintaining a Flexible Army
You want to keep your options open, and try not to limit and reduce the number of men that may help you. The less you commit, the more flexibility you will have. You are forced to play one men on each turn, so you must commit somehow. The key is choosing the correct commitments to minimize the damage. Generally speaking, we can spread out our commitment and play one man at many stones, or focus our commitment and play two or three men to the same stones.

When we send multiple men to the same stone, we are committing on all those men plus these men’s partners. For example, if we play two fives on one stone we are committing to a team on that stone and reducing our chances of making an ordered clan with threes, fours, sixes and sevens of the same colors should they be in our hand or drawn later on. However, if we play a single man to each stone, we can avoid making such commitments.

Now, how do we spread out the men to maintain flexibility? Delay deploying men that have multiple purposes. For example, if you have a slate blue two and three, and a yellow three, the slate blue three can be used for either an ordered clan or a team of three. So hold on to that slate blue three, and instead play the slate blue two and yellow three on different stones first. This way, you are still capable of forming either a team or an ordered clan on either stone, plus the flexibility to use the slate blue three for either. If however, you chose to play the slate blue three first, and on your next turn either the slate blue two or yellow three, then you are faced with the disagreeable prospect of having to choose prematurely whether to commit the slate blue three to a team with the yellow three, or to a clan with the slate blue two. In other words, play men that are unrelated to each other on different stones. In this case for example, the yellow three and slate blue two are unrelated because they are not clan or team partners.

However, spreading out the men does have its repercussions. For one thing, and this becomes more relevant later in the game when empty stones are few and men in your hand become less and less flexible, it may prevent your starting a new and better formation because there are no spaces left. For example, suppose there are only three empty stones left, and one of which you don’t want to play in because losing that stone will give him three consecutive stones. Now, you have two sixes, red three and four, and yellow nine and six—respectively chances of making a team, ordered clan, and clan—which are three possible formations and only two spaces to play. By playing any one man to one of these two empty stones, we are giving up on the chances of using one of the two other formations. Why not just go ahead and aim for the two best formations and give up on the clan? Well, going for a better formation and failing may lose a stone, when a simple clan could’ve won that stone for you. Playing multiple men to the same stones can save valuable empty stones for later.

So, when is it good to play multiple men to the same stones? When each of the men played to the same stone are already committed. This way you are not furthering your commitments that much. So how are man/men on the stones committed?

For example, if you have two fives on a stone, those two men are already committed to a team. Or if you have a single eight on a stone, but the seven of the same color is played elsewhere on the board, then that eight is also “committed” to a team because it is no longer viable for an ordered clan. Actually, all stones with two men are committed. Stones with one man are committed if and only if their partner/s are played elsewhere on the board. It's good to play to an already committed stone because you are not furthering any commitments--it already was.

Men that are in your hand may also be committed, if their partner/s are played by the opponent, or played by you in a group of another formation. For example, if you had a red two in your hand, then you are committed to playing it on a team if you already played the red three together with a green three on another stone.

Sometimes you may commit on non-commmitted stones. For example, if you have a two and your opponent two eights on the same stone, then you may choose to commit that two to an ordered clan by playing a three of the same color to the same stone. So when is it worth it to commit on a stone? When the opponent’s man/men on the same stone are also committed/limited. For example, if he played two fives, then you can choose to commit the eight you have there to a team, because you don't have to worry about his beating you with an ordered clan. Or if he played a single seven, but three other sevens are either out on the board somewhere or in your hand, then you can commit your two there to a team, because he likely won't do better than a relay or wild rabble.

In summary, generally when spreading out try to play uncommitted men to empty stones, and when playing multiple men to the same stone try to play a committed man to an already committed stone, or a stone that you are willing to committ because the opposing team on the same stone is already committed. rehash

Uncommitted men to empty stones
Suppose you have a green seven on a stone, you also have the yellow seven, yellow and green sixes in your hand, and two other sevens are already played elsewhere on the board. If you play the yellow seven to the green seven, you are committing to a team on that stone, and most likely (if not absolutely committing, at least heavily leaning towards) a team for the yellow and green sixes in your hand. Now suppose that you play that yellow seven on another stone. Now, your commitments would be an ordered clan on two separate stones (using the sixes in your hand). However, if you play a yellow six instead on another stone, you are making a much smaller commitment. On the two stones, and all the men involved, you are still leaving the options open for both team and ordered clan formation.

Committed man to committed stone
Consider this scenario: you have a red four on a stone, but the red five and two are already played elsewhere. You have an orange and cyan four in your hand, and a cyan three and five are already played elsewhere, while the orange four is still capable of forming an ordered clan. Now, if you play either four to your red four, you are committing to a team on that stone, but that isn’t furthering your commitments too much because it is already being committed to nothing better than a team by the fact that it can no longer form an ordered clan. On the other hand, you are making quite a commitment by playing the orange four because it can still be part of an ordered clan. The best choice would be to play the cyan four on the red four, because neither can be part of an ordered clan anymore.

Now if we put the above to scenarios together, as in we have both situations going on at the same time, what should we do? We can either play a yellow six to a new stone, or a cyan four to the red four. Neither move further commits your men that much, but the latter commits just a tad more: the red and cyan four can no longer form a non-ordered clan. However, the latter move leaves a stone open. Now you may think that a commitment of a single green six may not amount to much, but it may be huge. Suppose case the first that there is this specific stone that you really need to claim to prevent his claiming three consecutive stones. But if you committed the green six elsewhere, you may lose out on a chance to claim the perilous stone with an ordered clan or team you form with the green six. However, if you do play it on the perilous stone, then you are losing out on the option of claiming it with other formations and in danger of losing the stone prematurely if he can prove that he can beat that green six. Now suppose case the second that there is only one empty stone left, and you still have two nines left to play. If you send a yellow six to occupy it you are removing your two nines from play and eliminating your chances of drawing another nine to complete a team.

Uncommitted man to committed stone
Let us consider another example: you have two fives on a stone, a green six and seven on another, and a green five in your hand. You want to hold out on playing that green five, so that drawing either another five or a green eight will allow you to complete the formations on two stones.

Committed man to uncommitted stone
Lastly, consider this: you have a cyan seven played on a stone, and a cyan three and orange seven in your hand. Your opponent has two fives on that stone, and all four other fives are either played elsewhere on the board or in your hand: he can do no better than a wild rabble. The only places where the cyan three and orange seven are useful is with the cyan seven. So you have committed men and an uncommitted stone. If there are many cyan cards left in the draw pile, then you can safely commit the stone to a clan and play the cyan three. If there are many sevens left in the draw pile that are useless anywhere else, then you may safely commit the stone to a team and play the orange seven.

You are willing to committ to the uncommitted stone because the opponent is limited to a wild rabble. If he still has a good chance at forming an ordered clan, and so do you, then you want to hold out on playing a second men to that stone.

Uncommitted man to uncommitted stone
Also, if the orange seven, or any other seven that you draw are possibly useful elsewhere (the sevens are uncommitted), and the cyan three may be also useful elsewhere, then try to hold out on playing these uncommitted men to an uncommitted stone.

On Morale
When it can be proven based on the men already deployed that a completed triad will capture the stone they are fighting for, their village elder can, on his turn before deploying a man, claim the stone. Consequence of suffering such a blow to its morale, the opposing faction will then surrender the stone without putting up a fight, and unable to send any more men to the lost stone/s (Scotsburyans are too proud to be sent to a lost cause as cannon fodder).

This has enormous implications. If you lose a stone before deploying all three men there, you are losing valuable space/s to play, which can be very inconvenient and undesirable. At all time (except in the war’s very end), you will have places and men where you would really rather play later than sooner; and sometimes, hopefully, you will have men that you want to play first and places where it is okay to play to. Having less places to play to means higher chances of being forced to play men in places sooner than you would like, or having men that you want to send but nowhere to play it. Simply, you are losing flexibility when you are shut off from playing to a stone.

Moreover, you need to win either five or three consecutive stones before your opponent does the same, and winning stones earlier can only help. For example, I will win five stones, and my opponent three consecutive stones. If he can claim his third stone before I claim my fifth, he wins. So winning stones faster is huge.

So we know the importance of shattering the enemy’s morale. Now, how to achieve this? Simple: to prove that your opponent cannot beat one of your completed triad, play the men that he will need to beat you. For example, to prove that his red two cannot beat your team of sevens, simply play a red three, or a red one and four. Or, to prove that his one orange five cannot beat your team of ones, and the orange three and six are already out, and there are already three other fives in play, play another five (5th five put into play). Note that these used men can be played by either side. So not only do you have to consider playing something that will shatter your enemy’s morale, you should also consider avoiding playing something that will shatter your own.

On Spacing
Not all boundary stones are equal. Let us number them, from left to right, one to nine. Because of the three consecutive stone rule, stones one and nine are worth the least, followed by stones two and eight. Stones three through seven are worth more, especially stones three and seven. If you claim stones three, seven, and any of the three center stones, you are immune to an opponent three consecutive stone threat. Furthermore, you are putting yourself in a great position to threaten three consecutive stones. If you win stones three five and seven, claiming either four or six will win you the game. If you win stones three four and seven, claiming either two or five will win you the game.

If your opponent looks like he’s going to win a particular stone, it is important to maintain flexibility in stones near it. For example, if it looks like he’s likely to claim stone five, then you want to defer playing in stones four and six, maintaining flexibility there and making it harder for him to claim three consecutive stones.

On the Consequences of Rushing Into Battle
Patience is important. Hold out on making a move before gathering enough information--as you draw more men, and see what men your opponent plays, you can make better decisions on what to play where. The consequences of rushing into battle are twofold: first it limits your flexibility, and second it increases your opponent’s flexibility by giving him important information.

We can buy time by sending expendable, useless men first (or even better, useless men that can be used to prove that we will win in another stone). For example, when the cyan three, and three other twos, are already out, the cyan two is pretty useless. Plus, if your opponent has a cyan three and four, and the cyan five is played elsewhere, playing a cyan two will prove that he can do no better than a non-ordered clan on that stone. However, this comes at a price of sacrificing a stone to your opponent. We can minimize the damage of losing a stone in three ways.

One, choose a stone where losing it won’t give your opponent a great chance of claiming three consecutive stones.

Two, if you are going to lose, lose big, so choose a stone where your opponent is very strong in.

Three, try not to give your opponent flexibility. For example, if you are committing two men to a wild rabble against your opponent’s yellow seven and eight, he is now no longer tied to an ordered clan, but a simple clan will do. If however your opponent has two nines, then he is still committed to a team, unless he thinks he can beat you with a higher value wild rabble. Now, if your two men can form a relay, then it can be very useful. Even if you still lose, you are tying up a nine that he may use elsewhere, and forcing him to commit elsewhere until he draws his nine.

On the Consequences of Shying Away From Conflict
There are times, however, when you want to play men as soon as possible.

One, when your opponent can claim a stone on his next turn, and if you have an expendable, relatively useless man. Play the useless man here to buy time in other areas before the opponent claims the stone.

Two, to claim a stone. To do this, you must first complete your triad at that stone. And if necessary, you must play man/men to prove your enemy’s limitations at that stone. Refer to the section On Morale for why it is important to claim a stone early.

Three, when it appears that the two sides on the same stone may end up being the same formation of the same value, with the tiebreaker coming down to who played the third man first.

On Contradictions
Most of the assertions covered in this treatise are not meant to be held steadfastly. In fact some of them may even contradict each other. We must allow for exceptions to general rules. The climate and circumstances of war are forever changing and unpredictable, and so must our strategies be flexible and adaptable. As the Chinese saying goes, “Nothing is constant except for change.”

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Nick Bentley
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Finally! Somebody who is as enamored of this game as I am, and who's actually taken the time to work out some strategy. Thanks. I put together a big collection of strategy tips for Battle Line, many of which apply just as well to Schotten-Totten. I provide a link to it here, since I think that complements well what you've written:

Big Bulleted Battle Blueprint! (Please Add Your Own Strategy Wrinkles.)

There is sooo much in this little game. Nearly perfect in every way. Like many of my favorite games (eg Hex) much of it's richness is hidden behind a simplicity that makes new players assume there isn't as much inside as there really is. It's my curse to like such games.

The guy who won the WBC battle line tourney this year is a three time winner, and at some point I'm going to try to get in touch with him and try to interview him and see if he's willing to divulge his strategic approach.
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Fabien Conus
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Wow ! What a review !

I am also a big fan of this game. I recently started playing with the "bonus cards" and it is also very fun. It adds even more chaos to the game

Great game, great review.
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