ZERTZ - How to force a win?

Article by: Karina


How to force a win in Zértz


I really love Zértz. I discovered this beautiful game half a year ago, and it was love at first sight. The rules are easy, but the game is hard to master. And the playing time is short.

I've studied Zértz a bit (37 rings where you need 4 whites, 5 greys, 6 blacks or 3 of each to win). And I found that if you play second and your opponent removes a ring to the edge (not a corner ring), you can force a win wherever he/she places the first marble and no matter what color it is. If your opponent starts by removing a corner ring, there are only 13 "safe" places the marble can be placed. If the marble is placed on any of the other 23 places, you can force a win. This was really surprising to me. Of course this theory won't work if Zértz is played with more rings.

I've divided the method into two parts. In the first part you can give away up to six marbles, get two whites by isolation and leave the board empty. In the second part you can give away up to five marbles, isolate another two white marbles and win.

Before I show you the theory, I'll list a few things you have to remember:

Never give the initiative to your opponent, - always force a jump unless you leave the board empty.

Keep a close eye on your opponets marbles when you place marbles, - don't pick a marble that will give away the victory.

Be careful to place the white marble you want to isolate, at the right time.

Don't leave a ring where your opponent can isolate the first marble in part two.

You can force your opponent to jump in the direction you want, by removing rings.

Part 1

In the first part you can afford to give six marbles, for example three blacks, two greys and one white. A total of eight rings can be removed: the one your opponent removes and the seven rings you are allowed to remove in order to isolate two white marbles. The result has to look something like this:

A non-corner ring is removed




So, let's see how it works. And we'll start with the situation where your opponent removes a non-corner ring at the edge and places a marble anywhere on the board. The board will then look like this with one single marble places somewhere: (You may have to rotate or flip it to get a match.)

And when you see this, you'll know that you can force a win. How? I'll show you. First take a look at this diagram:

Let's suppose that the removed ring is at a2 (remember you can twist the board to match your situation). If the marble is placed in the red area, you can isolate two white marbles on a1 and b1. If the marble is placed in the blue area, you can isolate two white marbles on a4 and b5. If the marble is placed in the green area, you remove a3 and places a marble on the green ring just above or below the first marble. If your opponent jumbs into the red area, you go for the red strategy with a1 and b1. And if he/she jumps into the blue area, you go for the blue strategy with a4 and b5.




There are in fact more possibilities if for example the marble is placed on the edge somewhere, but for simplicity we don't include that now. Just focus on the red strategy with a1 and b1 and the blue strategy with a4 and b5.



So, now that you've got a goal, you need to know how to get there. You have to both prepare an isolation area and force a jump onto it at the right time.



In the red strategy you have to remove a3, b3, b2, c3, c2 and last c1. In most cases you also have to remove g1 to force a jump with a white marble onto d1. Click here to see how to do it in the specific cases.

In the blue strategy you have to remove a3, b3, b4, c4, c5 and last c6. In most cases you also have to remove g4 to force a jump with a white marble onto d7. Click here to see how to do it in the specific cases.

In the green strategy you first remove a3 and places a marble just below or above the first marble, and your opponents first jump decides how you continue. Click here to see how to do it in the specific cases.

A corner ring at the edge is removed

If your opponent removes a corner ring, you are not sure to win. Let's suppose the removed ring is g1 (remember you can twist the board to match your situation) and take a look at this diagram:

If the marble is placed in the red area, you can isolate two white marbles on a1 and b1. If the marble is placed in the blue area, you can isolate two white marbles on d7 and e6. If the marble is placed in the green area, you can isolate two white marbles on the ring the first marble is placed and a neighboring green ring. There are more possiblities, but for simplicity we don't include that now.




If the marble is placed on one of the 13 black rings, I don't know how to force a win. It might work, but that depends on where your opponent places the first marble in part two. You can't take that risk. Instead I'll advise you to just place a marble somewhere smart, and continue thinking throughout the game. Good luck!



Let's suppose the marble is not placed in the safe black area. Now you can both prepare an isolation area and force a jump onto it at the right time.



In the red strategy you have to remove a3, a2, b3, b2, c3, c2 and last c1. You may have to use the removed g1 to force a jump with a white marble onto d1. Click here to see how to do it in the specific cases.

In the blue strategy you have to remove c6, b5, c5, d6, d5, e5 and last f5. You may have to use the removed g1 to force a jump with a white marble onto g4. The blue strategy is simply a reflection of the red strategy.

In the green strategy you have to remove five rings in order to isolate two whites on the ring the first marble is placed and a neighboring green ring. Click here to see how to do it in the specific cases.

Part 2

In part two you have to be creative. You leave the board like this if you use the red (left) or blue (right) strategy:

Note that the two pictures are flipped and rotated, and can therefore be handled identically.

If a corner ring is removed and a marble placed in the green area, the board looks like this:

The problem is that your opponent can place a marble anywhere and removes any ring at the edge. This results in many different situations. (27 alternative places to place the ring, and 16 alternative rings to remove gives a total of 27*16=432 different possiblities.) So let's look at the possibilities in general. You can offer up to five marbles and remove six rings in order to isolate two white marbles without loosing the initiative. You can either isolate the two white marbles on the same side or one on each side. This works well, in fact I still haven't found a case that breaks the theory.


Let's suppose you've used the red strategy. Here's a few examples on what to do:

Your opponent places any marble on f2 or g2 and removes any ring but a4, d3, e1 and f1:

Note that in this case you isolate one white marble on each side of the board.

Your opponent You

15. Nf2/g2,nn 16. Ng2/f2,b5
17. xg2Ne2 18. Wd3,b4
19. xd3Nf1 20. Ne1,d2
20. xf1Nd1 21. Wa4,e1 x Wa4, Wd1

Your opponent places any marble on d6 or e6 and removes any ring but a4, b5, c6, d7 and f5:
Note that in this case you isolate the two white marbles on the same side of the board.

Your opponent You

15. Nd6/e6,nn 16. Ne6/d6,b4
17. xe6Nb5 18. Nd6,c4
19. xb5Nf6 20. Wf5,g4
21. xf5Nd7 22. Nc6,c5
23. xd7Nb5 24. Wa4,c6 x Wa4, Wb5

Your opponent places any marble on e5 or f5 and removes a4:

Note that in this case you isolate the two white marbles on the same side of the board even though your opponent removed the uttermost corner on that side.

Your opponent You

15. Ne5/f5,a4 16. Wf5/e5,c4
17. xf5Nd5 18. Ne5,d4
19. xd5Nf5 20. Ng4,d5
20. xg4Ne6 21. Wf5,g4
22. xf5Nd7 23. Nc6,c5
24. xd7Nb5 25. Wb4,c6 x Wb4, Wb5

Have fun!

Karina

Want More?: Zertz Joseki

Circular Routes in Steam

The benefits of the Circular route


Within my own gaming groups I quickly realised the key to winning an Age of Steam game was to upgrade your train quickly as possible so as to make sure that you are regularly delivering blocks for $5-6 by the end of the game – this resulted in me winning a lot of the early games we played (Basically I did the fiscal math as regards Low Expenditure/Small Train Vs High Expenditure/Large Train and having a large train always came out on top).

However the other players within my regular gaming group soon began to realise what I was doing and begun to adjust their play to counteract my strategy by doing the following:

• Taking the locomotive upgrade when opportunity presented it (rather than letting me get it)
• Delivering cubes I might deliver elsewhere before I could deliver them myself for $5-6
• Obstructing my delivery routes by urbanising cities with the colour of cubes I would wanted to deliver further away

All of the above resulted in my delivery options being reduced & therefore my income not increasing as it had done previously.

All this got me thinking about track building, in that there seems to be an objective focused desire to build track towards a city you either want to deliver blocks to or take blocks from. Whilst this is a fine idea, it does create a tendency to leave you with limited options as regards block delivery as the game develops. Basically you end up with linear route along which all your blocks have to be distributed and it is only the end blocks near the end of the route that can be delivered for $5-6, and only then if the city of the required colour is at the opposite end of the route (assuming the route isn’t obstructed by a similar coloured city).

For instance assume you have built the following route connecting cities (A) through to (G) together.

Only blocks on Cities (A) & (G) can be delivered for $6 and only then if the city at the opposite end is the correct colour.

In fact for a 6 train on a linear 7 city route the average potential value a block on each city could be delivered for, destination and same colour city obstructions permitting, would be as follows:

City A $3 ½
City B $2 2/3
City C $2 1/3
City D $2
City E $2 1/3
City F $2 2/3
City G $3 ½

This gives an overall potential block delivery value average for the above network of $2 3/7

Imagine however if you had built a circular route and city (G) links back to city (A)

Now the average potential value of a block on each city could be delivered for, if you have a 6 train, would be as follows:

City A $5
City B $5
City C $5
City D $5
City E $5
City F $5
City G $5

Basically each city, destination and same colour city obstructions permitting, always deliver for $4-6

The explanation given above is very stylised as it makes quite a few working assumptions, but what they do demonstrate is the financial flexibility of having a circular route over a liner one, basically where it might only be possible to deliver a cube from city (A) to City (B) for $1 it is now possible to deliver of the ‘long way’ around the loop for $6.

Essentially any cube that appears on a given city has the potential to be delivered for more income. Having more cube delivery options also means it is harder for the other players to ship away all your high value cubes.

However a simple circular route is far from being completely flexible as in a real game situation it is possible that deliveries might still be obstructed by same colour cities or still not be the ideal delivery value of $6 depending on where the potential delivery city is on the route.

With this in mind there are benefits in utilising ‘cross-cuts’ across the circular loop.

Imagine you have the circular route described above, but that Cities B&G are also linked directly.

 

From city (A) you now have the potential to deliver to both (F) and (C) for $6 where before it was only $4. Deliveries to (D) and (E) from (A) have the possibility of being increased f $4 to $5.


Deliveries from (G) that could have been obstructed by same colour cities at (A) or (F) can now be delivered to (F) for $5 rather than $1 (via the link to city (B).

Adding an additional cross-cuts, for instance from (F) to (C), (B) to (G) and from (A) to (D) – will increase your options even more.


The real life specifics off where you build your cross cuts will off course depend upon what the actual cubes distribution is and what same colour cities you need to by-pass.


Additionally having ‘spurs’ out from you circular route to additional cities, perhaps of a colour not on the Circle or which can act as the source of more cubes to be delivered, provides even more flexibility.

For instance imagine we have an additional city (H) on a Spur from City (D)


With the network described above deliveries from city (H) have the potential to be delivered to any city (Except city (D)) for a value of $6. Conversely if City (H) is of a colour not on the circular route, goods of it’s colour can be delivered from any city of the network (Except city (D)) for a value $6.


The act of building such a circular route, and the benefits it provides, cannot expected to be implemented without interference from other players. For their own purposes, or possibly just to obstruct you, your competitors will be building their own track. A degree of flexibility might then be required if your planned route becomes obstructed, you might either have to pay your competitor money to utilise a link or create a different variation of the planned loop (Maybe even only building a 5 link circular route and supplementing it with some spurs).

In fact, if possible, the sequence in which you build a circular route and it’s ‘cross links’ might benefit from building shorter loops (Which can later become ‘cross links’) which are more appropriate to your train size that point in the game.

For instance if you had a 3 train, you might choose initially to build a route with cities (B), (C), (F) & (G) on it.

 

And once you have expanded to a 4 train you can link to city (A) creating a loop that maximises the potential use of said train.



Finally if you have created your circular route flexibly enough, and if your competitors are linked into it and short of other possible deliveries, they will find it very difficult to justify not paying you to utilise 1 or 2 of your links are order to gain whatever scant income they can.

Credit: BGG user "SkiBoy" (Richard Minson)

More Settlers Strategy

I compiled this from reading a couple Settlers websites:
http://www.catanworld.com/the_games/settlers_of_catan/settle...
This probably the best strategy guide that I found out there, put together by Scott McPherson. Anyone know if he’s on boardgamegeek?

I also read this strategy guide, which was very useful:
http://www.settlersofcatan.net/settlers_of_catan_strategy.ht...

I also put in some of my own thoughts from playing Catan.

Anyone know of more valuable strategy guides to read out there?

Overall strategies:

Wood/brick (leads to longest road)
Build lots of settlements.
Build your future settlements on grain/ore hexes in order to build cities.
Build roads to cut off other players expansion, very useful in cutting off grain/ore players who might not be able to expand as fast as you can.

Grain/ore (leads to largest army)
Robber is a threat – huge target if you are building cities.
Buy development cards to try to get a knight in case robber is sitting on your city.
Only use the knight if the robber is sitting on 1 of your cities, try to save them for this situation to occur.
Focus more on ore than grain since you need 3 ores and 2 grain to build each city.

Try not to put your city on 1 good number and 2 bad numbers, or else the robber can come and make your city worthless.

The grain/ore strategy is generally my favorite strategy to play all things being equal, because it leads to guaranteed cities at the beginning. As long as you have development cards to protect them from the robber, I think it’s a very good strategy to pursue. You can always either expand towards wood/brick by either using the grain/ore to trade to other players since they will likely need it to build cities – which can result in favorable trades for your grain/ore.

Generally you either need the longest road or largest army to win the game, it’s very hard to win without either of them.

Initial settlement placement
Try to get your initial settlements on a total dot count of 11-13, this generally leads to strong resource production. Always put the first 2 settlements on 3 resource hex possibilities (not at the water where there are only 2 possibilities). You don’t want to constrict your resource growth at the start, you can always expand later to the water to grab a port.

Try to spread out your settlements on as many different numbers as possible so that your resource cards don’t come in huge batches – which may lead to robber losses down the road. This is an extremely key point, by doing this you are able to get resources no matter what number is rolled, which leads to steady and consistent building. I saw this approach work first hand last game, my friend had his settlements spread out among basically every number from 4-9 and he thus got resources seemingly every roll of the dice. And his cards came slowly, instead of in big batches.

Review the board at first and try to put a settlement on the rarest resource that you see (either by sheer number of tiles in the game or that the numbers on the tiles are not good), this will become extremely valuable for trading purposes later. Generally it will result in you getting 2 resource cards for your 1 resource card in trading, which can be really valuable for future building.

Expansion/settlements
Build settlements early, since growth is exponential once you get settlements and cities going. This is the most important strategy point – build settlements and cities first, to generate more production later – exponential growth rate.

Also try to go for settlement spots where your opponents are also going for, if you are sure you can get there first, otherwise don’t go for them because it’s just a waste of resources.

Break the longest road if at all possible with a settlement.

Try to get settlements on 3 different types of resources, though if you can’t, put your settlements on:
Wood/brick - settlements
Grain/ore – cities
Sheep are valuable, but generally it seems like sheep are always in high supply, so I generally don’t try to worry too much about getting sheep. It is nice to have at least 1 hex on a sheep, but I don’t worry too much about them.

Generally wood/brick is really valuable early on in the game for building roads and settlements, but then loses some of its value as the game goes along. This is because a lot of people start to build cities using grain/ore. Sheep generally hold the same value throughout the game (or its value goes slightly down), because they are only used in settlements (mainly done early in the game) and development cards (throughout the game).

Expansion opportunity priorities:
1. Go for the spot with the most dots
2. Increase diversity of resources you produce
3. Try to get to a nearby port

Make sure you are not cut off from future expansion opportunities, use roads to make sure of this, watch where your opponents are building towards.

Don’t place settlements just to try to screw others players, only think about yourself first and foremost. If in the process of getting a solid settlement placement you screw another player in the process, then that is great because you accomplished 2 missions in 1 shot.

In terms of settlements/cities, try to put your settlements/cities on hexes that have other players on them as well so that the hex is shared. This can help with keeping the robber off your hexes, since other players are also involved in the hex too.

The riskiest play in my opinion is to completely monopolize a hex (3 cities on 1 hex), this makes you a huge target for the robber, and you better have knights handy to get the robber off that hex in case the robber lands on that hex. I generally wouldn’t recommend monopolizing hexes, because it results in huge swings in terms of the number of cards in your hand, and the robber threat mentioned above. I did this in my last game, and while it did pay off okay (because another player was clearly in the lead the whole game and thus the robber was always on them), I don’t like to do it unless things just work out that way.

Robber/knight tips
If the robber is on your settlement/city before you roll the dice and you have a knight card, play the knight card before you roll so that if you roll the number that the robber was on before, you will get that resource.

Don’t buy too many development cards early on, it constricts your growth rate of resource production. It is much more worthwhile to build roads/settlements/cities because of the exponential growth rate of production if you get things setup early on. Save the development card buying for later once you get your resource production machine running and actually need some knight cards to keep the robber off your cities.

Make sure that you always have less than 7 cards before someone rolls the dice, even if it hurts your trading chances later, in case a 7 is rolled - I have been hit with the robber probably more than anyone else in my gaming group, I know the pain of having a 7 rolled with more than 7 cards in your hand =)

Buy a development card or something else if necessary to avoid having more than 7 cards in your hand before the dice are rolled.

If a 7 is rolled, put the robber on the rare resource hex
Also target cities if possible
Preferably target the current game leader, put it on his rarest resource hex that has a city on it – or try to hurt as many players as possible with the placement. By hurting as many people as possible with the placement, it also helps for later when a 7 is rolled again, so that 1 player doesn’t just target you with the robber if you singled out them the last time.

Count VP points as the game goes along to see who is in first place, and generally target them with the robber.

Trading
Don’t trade with someone if they are about to win the game (ie 7 or 8 VPs) – only trade with people who are behind you or slightly even with you. During the early to middle part of the game it’s generally fine to trade with anyone.

Try to be a part of every trade possible, as long as it helps you as much as your opponent. Don’t just make a trade simply for the fact that you wanted to make a trade – be sure that it helps you as much or more than your opponent.

Ports
Ports are useful – 2:1 ports can be really useful if you can get another settlement on that resource type with a really good number like 6 or 8.

3:1 ports are also useful, they may actually be more useful than 2:1 ports because there is no risk of the robber affecting your port trading ability by someone putting the robber on the hex that is producing the 2:1 port resource (since with a 3:1 port you can trade any resource, but with a 2:1 port it takes one specific resource). And since ports can only be used on your turn, you may want to try to hold out to trade all your resources using your port, putting you at higher risk for the robber.

Placing a settlement near a port at the beginning of the game (but not directly on the port) can be a good idea, because it can give you access in the future to it.

Though try to avoid placing settlements directly on ports early on, as it really constricts your resource production. It is much better early on to have both of your settlements on 3 resource hex possibilities. Later on in the game once your resource production machine is more established you can build a settlement on a port.

Development cards
% deck of development cards is as follows: (this may vary slightly depending on what deck and edition you are using)
Soldier – 48%
Monopoly – 12%
Road building – 12%
Year of plenty – 12%
Victory point – 16%

So generally unless you are going for largest army or just wanted to buy a development card to avoid having more than 7 cards in your had due to the robber – it is likely a better investment to build roads/settlements/cities since they result in guaranteed VPs, whereas it is more of an unknown with development cards. If you are going with the grain/ore strategy I would recommend investing in at least 1 development card to try to get a knight to help keep the robber off your city if at all possible.

Generally, development cards are only a good investment when:
1. You have more than 7 cards in your hand but have no other options to build anything else
2. If you are trying to win with the grain/ore (city) strategy and need knights to keep the robber off your hexes
3. If a lot of development cards have been bought already (and they were soldiers), so there is a better chance that the remaining cards are non-soldier cards

Monopoly card trick
One sneaky trick involves the monopoly card – trading away all of one resource to the rest of the players in exchange for whatever they have, then using the monopoly card to get it all back. So you then have all the resources that you traded for, in addition to the resource that you just traded to the rest of the players. I pulled it off once, and it did work, but my friends weren’t too happy about it =)