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Subject: What actions are "worth" the 3 Bezants for the cube? rss

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Jared Boyce
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Hello again...

I've played another couple games of Byzantium, and I've found myself often asking the question: "Is ___________ worth it?" This is shorthand for what I really mean, which is "Since a cube costs me 3 Bezants, am I going to get a significant return on my investment if I spend a cube doing ___________?"

I've written down my thoughts here, and I would definitely like to hear other people's thoughts along these lines.

#1: Taking Control of a City

Taking control of a city is always worth it (with the possible exception of the Arab 1-cities depending on the situation). You turn 3 Bezants into 2 or 3 victory points, which is a 1.5:1 or 1:1 ratio. These are the best ratios you'll find in the game for turning money into victory points. Also, if you can manage to control the city for at least one turn, you'll get back your 3 Bezants and more during the income phase.

In the case of the Arab 1-cities, if you hold it for at least one turn the you are effectively spending 1 Bezant (spend 3 and get 2 from income) for 1 victory point, which is a 1:1 ratio and is most definitely worth it.

If you take control of an Arab 1-city and lose control of it that turn, then you are effectively spending 3 Bezants for 1 victory point, and at a ratio of 3:1 it isn't that worth it.

(The chance that someone will bother Civil War-ing you for a 1-city is minimal, though I'd feel remiss if I didn't consider it.)

#1.1: Taking Control of a Byzantine 3-city vs. 2-city on Turn 1

A slight digression from the main theme of this post, something I've spent a good amount of time thinking about is whether or not it's better to take control of a Byzantine 3- or 2-city on the first turn of the game. In terms of immediate maximum benefit, taking over a 3-city gets you 3 victory points while taking over a 2-city only gets you 2 victory points.

However, something to take into account is the expected time of ownership of the city. The longer you hold a city, the more revenue you get from it.

Byzantine 3-city, falls turn 1: you spend 3 Bezants and gain 3 victory points.
Byzantine 3-city, falls turn 2: you gain 3 Bezants (spend 3 and get 6 from income) and gain 3 victory points.
Byzantine 2-city, falls turn 3: you gain 5 Bezants (spend 3 and get 8 from income) and gain 2 victory points.

Comparing the 3-city that falls turn 1 to the 2-city that falls turn 3, the 2-city is the better bet. You effectively gain 8 Bezants at the cost of 1 victory point, and the 8 Bezants are almost enough to get 2 victory points from a mosque or church (assuming that you spend 3 to buy the cube).

Comparing the 3-city that falls turn 2 to the 2-city that falls turn 3, the results are less clear. You are effectively choosing between 2 Bezants and 1 victory point. As explored above, it's definitely possible to get better than a 2:1 ratio (taking control of 2-cities is 1.5:1 and 3-cities is 1:1), though it's also possible to get significantly worse (churches and mosques have a 4.5:1 ratio if you purchase the cube). I think that it's a toss up and is a matter of preference for the player to decide.

#2: Improving a City

If you improve a city you control on turn 1 and manage to hold it through the end of the game, you effectively gain 1 Bezant (spend 3 and get 2 extra income for two turns) and 1 victory point. This is definitely worth it if you can manage it.

If you improve a city you control on turn 1 and manage to hold it through to turn 3 but not to the end of the game, you effectively gain 1 Bezant. However, you gain one Bezant on turn 3 for an investment of three Bezants on turn 1, and it's quite possible that those three Bezants could be better spent on something else during turn 1. Also, this doesn't gain you any victory points.

If you improve a city you control on turn 1/2 and hold it into turn 2/3, you effectively lose 1 Bezant (spend 3 and get 2 extra income for one turn). This isn't worth it.

If you improve a city you control on turn 3 and hold it through the end of the game, then you effectively spend 3 Bezants for 1 victory point. This is a ratio of 3:1, which is worse than most ratios, but it's better than the 4.5:1 from a church or mosque. If you think you can hold the city until the end of the turn, then this is more worth it than churches/mosques.

If you improve a city you control on any turn and lose it that same turn, then it definitely isn't worth it because you lose 3 Bezants with no gain.

Now let's consider the more interesting case... You can improve a city that is not your own city and then conquer it later in the turn. This definitely puts a different spin on things.

If you improve a city that isn't yours, conquer it, and then hold it to the end of the turn, then you break even in terms of money (spend 3 Bezants, get 1 extra from plunder and 2 extra from income) and gain 1 victory point. Overall, you're getting a victory point for nothing, so this is worth it. (If you can hold it for more than one turn/to end of the game then it's even more worth it.)

If you improve a city that isn't yours on turn 3, conquer it, and then hold it to the end of the game, then you effectively spend 2 Bezants (spend 3 Bezants and get 1 extra from plunder) to gain 2 victory points (1 from conquering and 1 from the end of the game). This is a 1:1 ratio and is definitely worth it.

(Also, as an aside, improving a city you don't control and then conquering it is one of the only ways to spend Byzantine money to gain Arab victory points/money and vice versa, so in addition to generally being worth it you have the added bonus of being able to transfer victory points/money between your factions.)

#3: Emperor/Caliph

You spend 3 Bezants for 2 victory points and an Elite unit for a turn, meaning that you're getting a 1.5:1 ratio with a bonus. This is worth it.

#4: Bulgars

If you use the Bulgars to attack a 3-city, then you are effectively spending 3 Bezants to gain 2 victory points (assuming the Bulgars win), getting a 1.5:1 ratio. This is worth it.

If you use the Bulgars to attack a 2-city, then you are effectively spending 3 Bezants to gain 1 victory point (assuming the Bulgars win), getting a 3:1 ratio. This isn't as good as other ratios, but it's better than Churches/Mosques, so if you're limited in options then this may be worth it.

If you use the Bulgars to attack a 1-city, then you are effectively spending 3 Bezants for nothing (regardless of whether or not the Bulgars win). This definitely isn't worth it.

#5: Fortifications

You spend 3 Bezants for no income and no victory points when you could just as easily improve your city, assuming it isn't a 3-city. And if it is a 3-city, then you're still not getting any income or victory points for your 3 Bezants. This doesn't seem worth it. (However, see my admission in #8.)

#6: Churches/Mosques

You spend 3 Bezants for the cube and then 6 Bezants in "construction costs" to gain 2 victory points. This is a ratio of 4.5:1, which is a very poor ratio. This definitely isn't worth it if you have other reliable options. That said, if you don't have other reliable options, then this is a guaranteed way to gain some victory points.

#7: Levies

In general, Levies don't seem to be worth it. I don't have a fully formed way of evaluating whether or not combat is worth it (see #8), but using a (vastly oversimplified) metric of 3 Bezants per cube Levies seem to be a liability.

Assuming you have 3+ Levies, you roll three dice. On average you kill 1.5 cubes from you opponent, costing your opponent 4.5 Bezants. You opponent likely has more than three dice (because of Elite units), meaning that on average your opponent will kill more than 1.5 cubes from you, costing you more than 4.5 Bezants. It's not uncommon in the games I've played for an army to have 3+ Elites, meaning that on average Levies will lose twice as many units as the attacking army, which translates into costing twice as many Bezants.

There is the possibility that a large force of Levies will make the attacker retreat, but that seems highly difficult given that the Levies can lose twice as many units as the attacker and the attacker has the option of removing casualties from the Move box (thereby maintaining his/her number of troops).

There are some cases on the margin where I can see Levies being useful (for example, an army with 5 troops attacks a 3-city) because just taking the attacking army down by one unit significantly increases the chance that army won't conquer the city. In general, though, Levies don't seem to be wroth it.

(I almost removed this section because it isn't as formalized as the previous ones, but Levies are something that's been getting under my skin a bit and I'm highly interested in other people's opinions.)

#8: Combat and Civil War

I don't have a good way of deciding whether or not a particular combat is worth it or not because there seem to be too many variables: immediate victory point/Bezant gain, long term victory point/Bezant gain, taking victory points/Bezants away from an opponent, reducing an opponent's Levies/army, and so forth. And, to complicate issues even more, your own troops are a liability against you in turns 1 and 2 because you have to pay upkeep for them. (Because of this I think it can be good to lose an Elite or two at the end of turns 1 and 2 because you're reducing your overall upkeep and you can just recruit them over again at the beginning of the next turn.)

Because of this, I also can't evaluate Civil War (or fully evaluate whether or not a fortification helps out significantly at all).

Disclaimer

Something that #8 reminded me of (and something that probably should have gone at the beginning of all of this), is that I'm definitely simplifying things/ignoring a number of variables.

For example, when I say that improving a city is strictly better than a fortification (for non-3-cities) I'm ignoring the fact that improving a city may make it more likely for an opponent to attack you because your opponent will get an extra Bezant and an extra victory point from your improvement when conquering it and more long term income as well. Or another example, using the Bulgar action to attack Constantinople/prevent someone else from attacking Constantinople definitely isn't the same as attacking a normal city.

This disclaimer aside, I still think that it's useful to ask the "is it worth it?" question on a simple level because it gives you a starting point for some tactical and strategic planning.

I'm definitely interested in what you all think, so please send some thoughts/comments/questions/feedback if you have any!

Best,
-Jared-
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Jared Boyce
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A follow up to the above...

Something that happened in the game last night that affects the "Are Levies worth it?" question was the Emperor recruiting Levies to help defend Constantinople from the Bulgars. It turns out, after crunching the numbers, that recruiting three Levies to help defend Constantinople from the Bulgars is surprisingly (to me, at least) statistically significant:

11 Bulgars against Constantinople = 50% chance of success.
11 Bulgars against 3 Levies and Constantinople = 34.375% chance of success.

The three Levies make it an absolute 15%/a relative one-third less likely that the game will end when the Bulgars attack. If you're not the one with the most Arab points, then the Levies are definitely worth it.
 
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Michael Van Biesbrouck
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I enjoyed your analysis, but I feel that there is one important bit missing. When you lose control of a city, someone else is gaining VP. The net gain in VP for many of your scenarios may not be worth it.
 
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Greg Low
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Only a starting place for analysis, but a good starting place at that.

The relative value of 3 Bezants from turn 1 to turn 3 is quite a complicating factor.

Another complicating factor is the value of getting cubes out of the casulty pool and into a category that becomes free pool at the end of the turn. It seems to me that every cube to go to a fully returning category could be very roughly estimated to be worth 1.5 bezants per remaining turn.

-Greg
 
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Jared Boyce
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mlvanbie wrote:
I enjoyed your analysis, but I feel that there is one important bit missing. When you lose control of a city, someone else is gaining VP. The net gain in VP for many of your scenarios may not be worth it.


You're definitely correct - my analysis doesn't take into account nearly all of the different interactions.

Any suggestions? Not trying to put you on the spot - just trying to get a more accurate analysis.
 
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Jared Boyce
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talrich wrote:
Only a starting place for analysis, but a good starting place at that.


Thanks! I agree that it's only a starting point. Any suggestions of where to go from here?

talrich wrote:
The relative value of 3 Bezants from turn 1 to turn 3 is quite a complicating factor.

Another complicating factor is the value of getting cubes out of the casulty pool and into a category that becomes free pool at the end of the turn. It seems to me that every cube to go to a fully returning category could be very roughly estimated to be worth 1.5 bezants per remaining turn.


Definitely a good point and something to take into account, and something that changes on turn by turn as you say (especially on turn 3, when you don't get any cubes back).
 
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Inno Van
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According to page 7 under "Income and Maintenance" cities are worth 2 coins each at the end of each year regardless of how many discs they have, and are worth 1 VP each in the final point tally.

Paying a cube to improve a city by one disc doesn't increase income at all. It just makes it more expensive to conquer for others.

Conquering the "cheap" one disc cities is a good option for turn 3 and becomes less appealing with each year afterwards. Meanwhile conquering the 3 disc cities produces double the income the year conquered.

And sadly, you can't fatten up your cities on one side to conquer them with the other. Page 5 notes you can't attack yourself, although a clearer way to say it would have been you can't attack cities with your own color cube on top.



 
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Jim Cote
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talrich wrote:
Another complicating factor is the value of getting cubes out of the casulty pool and into a category that becomes free pool at the end of the turn. It seems to me that every cube to go to a fully returning category could be very roughly estimated to be worth 1.5 bezants per remaining turn.


Exactly. I believe out of every cube that goes into the casualty pool, and any cube that was used for a special action (most?), half of these go into your cube pool for the next turn. So if you spend 6 bezants for two cubes for special actions, one of these will end up in your cube pool (free) on the next turn. I'm not quite sure how to work this back into the numbers, but it is hugely significant.
 
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marc magner
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Innovan wrote:
According to page 7 under "Income and Maintenance" cities are worth 2 coins each at the end of each year regardless of how many discs they have, and are worth 1 VP each in the final point tally.

Paying a cube to improve a city by one disc doesn't increase income at all. It just makes it more expensive to conquer for others.



Actually the rules say p. 7

"Each player now collects income and pays to maintain his armies. Each City Token earns the controlling player two Bezants."

and the Discs you refer to are defined in the rules P 1 under components and p. 2 under starting the game as City Tokens.

So paying to add a city token DOES increase income.

Marc
 
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Inno Van
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>Each City Token earns...

Absolutely correct. This will most probably make the game move up in rating for my group, since we had set it aside in frustration with how short of money was (with our wrong interpretation of the rules).
 
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marc magner
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Innovan wrote:
>Each City Token earns...

Absolutely correct. This will most probably make the game move up in rating for my group, since we had set it aside in frustration with how short of money was (with our wrong interpretation of the rules).


We played last week for the first time and money was tight, so I can imagine a serious negative impact if you constrain it further.

 
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