TLDR: Defending archers in castle territories hit on 4 and up, cavalry can maneuver to a territory up to 4 territories away, castles cost 8 (6 for Berlin) but don’t grant dice re-rolls. Thoughts?
The post might seem quite long, but the second half (everything after the conclusion) is not essential to understanding my reasoning.
Cavalry and archer buff: Hi fellow BGGers! I've played Risk Europe a couple of times now and like it a lot, but I feel there is very little strategy involved in the choice between archers and cavalry, as the only difference between them is a tiny "statistical" one (see end of post for more details).
Therefore, I thought it would be nice to add a layer of strategy and flavor, by having defending archers in castle-territories hit on 4 (instead of 5) and up, representing that they have the high ground, and allow you to maneuver your cavalry to territories up to 4 territories away (but you cannot maneuver any other units if you maneuver your cavalry to territories 3 or 4 territories away, as the game only allows you to maneuver from 1 territory to 1 other).
Castle strengths and weaknesses: Furthermore, I really like that castles allow for unit recruitment in non-castle territories, supply line protection (the castle-territory can’t be disputed by a single enemy infantry), and forcing your opponent to reveal their intention to attack your castle a turn in advance (they need 2 king’s orders to buy a siege weapon and maneuver it to an adjacent territory before invading your castle-territory - unless they have Kiev or an adjacent city or castle, or build a castle in an adjacent territory and recruit a siege weapon there within a single spend order).
However, I don't think castles will be used for such strategies all that often. Namely, early in the game, a castle can force an opponent to buy a siege weapon (instead of more cost-effective units), but the siege weapon is 2 coins cheaper than the castle and gets its rank 1 attack, whereas the dice re-roll the castle grants will not be of much help if you only have a couple of defending infantry and nothing else. Furthermore, late in the game, your opponents will likely already have siege weapons, and the decision to build a castle will simply depend on whether the castle is more cost-effective than, e.g., 4 cavalry units, which I don’t think it will be (unless you don’t have any units left to purchase). Namely, the dice re-roll the castle grants is rather situational and I find it hard to estimate how many additional hits it will yield for large armies, but I am skeptical it will generate more than 3 additional hits per round, which is what it has to do to beat the 4 cavalry in terms of cost/hit (also, I don't like that the re-roll can be used to help the defending cavalry, even though they shouldn’t benefit from having castle walls).
Castle re-balance: Therefore, I reduce the castles’ cost to 8 coins (6 for Berlin) and re-balance them by removing the re-roll. How does this affect castles' balance? Let's discuss:
By itself, the castle does not provide any units or hits in combat and only requires a siege weapon to be attacked, meaning that is has worse cost/unit and cost/hit ratios than any unit. On the other hand, castle-archers have a better cost/hit ratio than any other unit, and a better cost/unit ratio than any unit but infantry. Hence, when adding sufficient archers to the castle, the combined cost of the castle + archers will be lower than that of an army consisting of a single siege weapon and additional cavalry and infantry units in such numbers that the siege weapon + cavalry match the archers’ hits/round and the infantry make up the difference in units between the two armies. Specifically, this is the case for 9 or more archers (again, see end of post), meaning that you need to have bought almost all available archers and have them defending your castle for it to be cost-effective.
Impact on balance of all changed rules combined: Archers and cavalry are buffed (higher hit-rate in castles and higher mobility, respectively), so are siege units comparatively less useful? I don't think they are, as castles are cheaper and will therefore be built more often, making siege weapons more important for capturing enemy territories. Furthermore, balancing slightly changes for Berlin , London, Paris, and Kiev, which players should take into account when choosing their initial cities. Moreover, because you only have infantry at the beginning of the game, the starting castles will be slightly easier to conquer, which I hope will motivate players to engage in combat a little sooner, instead of waiting until all territories are claimed. Lastly, when playing the advanced rules, kingdom mission 4 needs to be rebalanced: to complete it, you need to control 4 castles instead of 3, as castles are now cheaper.
Conclusion: So, does this add an interesting layer of strategy to the game and allow castles to live up to their potential, or does it make the game unbalanced and add unnecessary complexity? Please let me know think! Thanks in advance for your thoughts and opinions
Alternative castle rules: I also like the idea of lowering the castles’ cost even further to 6 coins (4 for Berlin), but only allow players to build a maximum of 2 castles over the course of the game (in addition to their starting castle). Furthermore, when the castle is built, it is placed upside-down and is only flipped over at the beginning of the next round (when everyone picks two new king’s order cards). As long as the castle is upside-down, the castle can be used to recruit units (including getting 4 infantry from the fortify bonus action) and requires a siege weapon to be attacked, but archers still hit on 5 and up. That way, building a castle cannot be used to boost your archers just before being attacked (in the same round) and requires some foresight/strategy. These latter rules are to compensate for the fact that a castle costing 6 coins is already cost effective at only 5 archers defending it.
The "show your math" part:
Under the rules I proposed, a castle + 9 archers costs 26 coins, has an average number of 4.5 hits per round (excluding the general attack rank 4) and consists of 9 units. Furthermore, an army of 1 siege weapon, 4.75 cavalry units and 1.92 (1+11/12) infantry units also provides 9 units and 4.5 hits per round, but costs 26.16 (26+1/6) coins. Hence, at a cost of 8 coins, a castle becomes more cost-effective than the attacking army at 9 or more archers.
Furthermore, a castle + 5 archers has an average number of 2.5 hits per round (excluding the general attack rank 4), which is the same as an army of 1 siege weapon, 1.75 cavalry units and 0.92 (11/12) infantry units and costs 16.16 (16+1/6) coins. Hence, at a cost of 6 coins, a castle becomes more cost-effective than the attacking army at 5 or more archers.
Cavalry vs. archer statistics: Although cavalry have the best cost-to-hit ratio, (non-castle) archers hit first (which reduces the cavalry's numbers before they can hit back) and have a better cost-to-unit ratio (which is important in the general attack rank and for absorbing hits). I have worked out some (~20) examples on paper and my results seem to suggest that the differences between the two are really quite small. In large armies (of equal value), cavalry pared up with infantry (roughly 1:3) have a slight edge over archers pared up with infantry (1:1/1:2), but in (very) small armies and when insufficient infantry are available, archers have the advantage over cavalry. Furthermore, when pitting armies of unequal size/value against each other, the fact that archers can hit the enemy before their cavalry can strike back becomes a bigger advantage. Lastly, when you have no infantry available to support your army, because you have already deployed all infantry in your reserve elsewhere on the map, archers are also a better choice than cavalry.
1 archer + 1 infantry vs 1 cavalry probabilities: The archer has a probability of 1/3 to hit the cavalry before it can strike back. The cavalry has probability to hit of 2/3, so the probability for the cavalry to not get hit by the archer and hit the infantry is 2/3*2/3=4/9, which is slightly more than the probability of the archer to hit the cavalry of 1/3=3/9. However, when the archer hits the cavalry, he wins outright, whereas when the cavalry hits the infantry, the general attack phase ensues (1v1), in which both the archer and cavalry have a 50% chance to win (actually the defender has the better odds, but I'm not taking that into account). Furthermore, if both the archer and cavalry miss their shots (2/9 prob.), the archer + infantry have a much better chance to win the (2v1) general attack. Hence, the archer + infantry beat the cavalry most of the time.
1 archer + 2 infantry vs 1 cavalry + 1 infantry probabilities: I'm not going to work out the details, but the gist is that the best scenario for the cavalry team, that is, the cavalry hits and the archer misses, has a probability of 4/9. However, in that scenario, the general attack is 2v2, which is a 50/50 (if they both score 1 hit, the next round is 1 archer vs. 1 cavalry, in which the odds favor the cavalry slightly). However, in all other scenarios, the cavalry team is outnumbered in the general attack and is more likely to lose. Hence, 1 archer + 2 infantry beat 1 cavalry + 1 infantry most of the time.
2 archers + 1 infantry vs 1 cavalry + 2 infantry probabilities: The cavalry team has a chance of 8/27 to end up 3v2 in the general attack , whereas the archery team only has a chance of 7/27 to outnumber the cavalry team in the general attack. However, that includes a chance of 2/27 to go 2v1 and a chance of 1/27 to go 3v1, both of which grant much higher odds of winning to the larger team than the 3v2. Therefore, I think the archer team still wins the majority of the time.
(Infinitely) Large armies: When the number N of units approaches infinity, you can use statistics instead of probability to estimate which army compositions are strongest for large armies, as the number of hits equals the expected number of hits (deviations only scale with the square root of N). Furthermore, you can ignore the general attack rank, as that can costs you a maximum of two unit per round and battles typically last 5 rounds or less in the examples that I studied. Hence, you can sequentially let the archers fire, and subtract the hits from the opposing team (first from the infantry units, until there aren't any left), after which the cavalry’s hits are subtracted from the opposing team and the archers go again. My results are that a cavalry+infantry army in a ratio between 1:2 and 1:4 is superior to any other army composition. My intuition is that a 1 cavalry : 2 infantry army might have too few infantry when armies are small enough that the general attack plays a significant role (which causes you, on average, to lose another infantry unit per combat round) and that a 1:3 army is better than a 1:4 army for minimizing lost infantry units, especially when fighting armies that are much smaller than yours. Hence, I recommend 1 cavalry : 3 infantry composition for large armies, which is exactly a 1:1 value ratio.
- Last edited Fri Jan 12, 2018 1:55 pm (Total Number of Edits: 2)
- Posted Wed Jan 3, 2018 10:11 pm
RANCHO SANTA MARGARITA
Re: Adding strategic/flavor differences between archers and cavalry + castle rebalance and statistics
A couple of options to think about:
Attacker rolls 2 dice (max) into a castle defense for tier IV.
Defender can reroll >any< 2 dice during tier IV.
Attacker receives -1 to each die rolled during rank IV during a castle siege.
At the beginning of each ranked order attack, defender scores 1 automatic hit.
Theres a bunch of fun ways to spin the castle bonus depending on how you want your mod to feel.
- Last edited Fri Jan 5, 2018 2:22 pm (Total Number of Edits: 2)
- Posted Fri Jan 5, 2018 2:21 pm
Re: Adding strategic/flavor differences between archers and cavalry + castle rebalance and statistics
There is some good reasoning regarding the cavalry change, I like the idea of being able to manoeuvre up to 3 territories away, something akin to the Riders of Rohan but then it occurred to me, as the Riders rode across the land they passed through enemy territory and then charged headlong into the Forces of Sauron saving Gondor. What does that tell us?
Cavalry should be able to expand after moving a long distance. I can see the thinking behind 3 territory manoeuvre but by then the initiative is lost and the opposing player can redeploy forces to deal with an imminent charge next turn.
How about the following options
- Forces comprising cavalry can manoeuvre up to two spaces and expand in one action.
Regarding the archers I have to say I don't like them hitting 50% of the time. That's waaaay too powerful! Think about this logically, why would archers hit more often simply because they are high up. Surely targets are harder to hit if they are moving quickly and spread out as opposed to firing at ground level. In any case I just don't think defending archers need this extra boost. Leave the current rules in play, defenders will often reroll their archer dice (as rank 4 only receive 2 dice) and you're more likely to recruit archers to castles. Instead it should be more difficult for attacking archers to kill defenders behind the wall. Therefore attacking archers could hit on a 6 which is how we play it.
Also we don't allow rank 3 cavalry attacks during the Siege until late on. This is a copy of my own interpretation below.
A couple of simple changes adding some much needed theme to siege warfare.
Both players should skip Rank 3 cavalry attacks as the castle walls and gates are a better defence.
However if all remaining units in the defending army have been killed the defending player can call upon the Rank 3 attack representing a ‘sally forth’ in a last desperate attempt.
If all remaining units in the attacking army have been killed then the attacking player can dismount any number of cavalrymen (replace with standard foot units) and they will perform Rank 4 attacks.
Note cavalry units do not receive castle benefits.
Castles provide an elevated platform and a commanding view of the battlefield as well as increased protection for the defenders. Enemy archers targeting defenders behind the wall hit on a 6 during Rank 2 attacks. If the defenders lead a sortie with the remaining cavalry then attacking archers hit on a 5 as per the standard rules.
- Last edited Thu Jan 11, 2018 2:04 pm (Total Number of Edits: 1)
- Posted Thu Jan 11, 2018 2:02 pm