by agentcom on Mon Aug 19, 2013 6:34 pm
Seems to me that bottom person still has a fairly strong advantage that will be very decisive in a trench game. The reason is that the bottom player has more ability to grab autodeploy bonuses before they reach their bridge. At that point, they can sit back and bombard and use any extra troops to build up their bonus.
I love the non-symmetrical nature of this map, and I think you should keep it. But I think the way it is now needs work. You'd have to somehow make it easier for the person on the top to reach their bridge with enough troops to pass through BUT without making it too easy.
Playing out a trench game in my mind here. I will even give the top player the first turn and see if he's still at a disadvantage. All the rolls are calculated based on the minimum number of troops that will remain after an attack 50% of the time. Though the early rolls may require rolling less than a 4v3, almost all of the later rolls do not, so (except for the early rounds) basically figure that on average you lose 1 troop taking 2 neutrals and 2 troops taking 3 neutrals.
Format:
R1r [Round 1 red's turn]: r4 [red starts with 4] + 1a [plus 1 autodeploy] + 3d [plus 3 deploy] = r8 [red has 8] --> [after attacks the results are going to be something like] r1 [red has 1 on his starting point], [commas separate positions], r5 [red has 5 on his next territ]
R1r: r4+2a+3d=r9 --> r1, r6
R1g: g4+2a+3d=g9 --> g1,g6
R2r: r1+2a=r3, r6-1a+3d=r7 --> r3,r1,r1,r2 (red attacks Gov't Grants and Auburn) --> r1,r1,r1,r4 (red forts to Auburn)
R2g: g1+2a=g3, g6-1a+3d=g7 --> g3,g1,g1,g2 (similar attacks) --> g1,g1,g1,g4 (similar fort)
The game looks identical for the first two rounds because both are going through the same amount of neutrals. Any variation is caused by the dice. This changes in the next round where green has to go through a 3 on Kearney and red only has to deal with the 2 on Colfax. However, this is not going to be enough to slow green down, IMO. Notice that the negative autodeploys on each player's second territ don't matter because they only left 1 there. For this reason those autodeploys are put in brackets from here on out.
Notice that the forts start to look different for both players here. Green (the bottom player) is not forting out of his base because he knows he's going to have to fort back into it for the bombing. At this point that shouldn't affect whether or not he can keep taking territs.
R3r: r1+2a=r3, r1[-1a]=r1, r1+2a=r3, r4+1a+3d=r8 --> r3,r1,r3,r1,r6 (red attacks Colfax) --> r1,r1,r3,r1,r8 (red forts Colfax)
R3g: g1+2a=g3, g1[-1a]=g1, g1+2a=g3, g4+1a+3d=g8 --> g3,g1,g3,g1,g5 (green attacks Kearney) --> g3,g1,g1,g1,g7 (forts out)
In Round 4, green is going to have to deal with another 3 rather than a 2 and they both hit -1 autodeploys that will come into play in round 5.
R4r: r1+2a=r3, r1[-1a]=r1, r3+2a=r5, r1+1a=r2, r8+1a+3d=r12 --> r3,r1,r5,r2,r1,r10 (red takes 15 Tunnels) --> r3,r1,r1,r2,r1,r14 (red forts forward)
R4g: g3+2a=g5, g1[-1a]=g1, g1+2a=g3, g1+1a=g2, g7+1a+3d=r11 --> g5,g1,g3,g2,g1,g8 (green takes Plum Creek) --> g5,g1,g1,g2,g1,g10 (green forts forward)
Now that you're getting the hang of the autodeploys and deploys (deploys go farthest territ forward, I'm going to skip them for a while. Now I'll just show the "board" as it would look after the deploys and autos have been taken into account.
R5r: r5,r1,r3,r3,r2,r16 --> r5,r1,r3,r3,r2,r1,r13 (red takes Donner Pass) --> r1,r1,r3,r3,r2,r1,r17 (... and forts forward)
R5g: g7,g1,g3,g3,g2,g12 --> g7,g1,g3,g3,g2,g1,g9 (green takes Ogalulla) --> g7,g1,g3,g1,g2,g1,g11 (... and forts forward)
R6r: r3,r1,r5,r4,r3,r1,r21 --> r3,r1,r5,r4,r3,r1,r1,r19 (red takes Truckee) --> r3,r1,r1,r4,r3,r1,r1,r23 (forts forward)
R6g: g9,g1,g5,g2,g3,g1,g15 --> g9,g1,g5,g2,g3,g1,g1,g12 (green takes Julesberg) --> g9,g1,g1,g2,g3,g1,g1,g16 (fort)
R7r: r5,r1,r3,r5,r4,r1,r2,r27 --> r5,r1,r3,r5,r4,r1,r2,r1,r25 (red takes Reno) --> r5,r1,r3,r1,r4,r1,r2,r1,r29 (fort)
R7g: g11,g1,g3,g3,g4,g1,g2,g18 -> g11,g1,g3,g3,g4,g1,g2,g1,g16 (green takes Sidney) --> g11,g1,g3,g3,g1,g1,g2,g1,g19 (fort)
In Round 8 things get a little bit interesting. Red will take Wadsworth putting him ready to take Humboldt Bridge if the dice and green allow it in Round 9. However, green instead of forting forward will simply fort backward to make sure that he has enough troops to bomb anything that might come into Humboldt Bridge. In the meantime, he can use any additional troops to keep securing bonuses--an option not open to red.
R8r: r7,r1,r5,r2,r5,r1,r3,r2,r33 --> r7,r1,r5,r2,r5,r1,r3,r2,r1,r31 (red takes Wadsworth) --> r1,r1,r5,r2,r5,r1,r3,r2,r1,r37 (fort)
R8g: g13,g1,g5,g4,g2,g1,g3,g1,g23 --> g13,g1,g5,g4,g2,g1,g3,g1,g1,g21 (green takes Cheyenne) --> g33,g1,g5,g4,g2,g1,g3,g1,g1,g1 (fort)
Now red is at the verge of Humboldt Bridge. But here's what it looks like if he attacks. Theoretically, red is outdeploying green by 1 autodeploy (because he took Truckee a +1 when green had to take Julesberg), and he has the troop advantage, but I don't think that's going to be enough here.
R9r: r3,r1,r7,r3,r6,r1,r4,r3,r2,r41 --> r3,r1,r7,r3,r6,r1,r4,r3,r2,r1,r38 --> r3,r1,r1,r3,r6,r1,r4,r3,r2,r1,r44 (fort)
R9g: g38,g1,g7,g5,g3,g1,g4,g1,g2,g2 --> g4,g1,g7,g5,g3,g1,g4,g1,g2,g2 (red has been bombed off of Humboldt) --> g10,g1,g1,g5,g3,g1,g4,g1,g2,g2 (green forts in for a little bit to make sure he can always take Humboldt)
From there, the game progresses with red never being able to take Humboldt as long as green keeps enough troops on Omaha to counteract this. Gradually, green will gain the advantage and be able to keep striking out into Cheyenne Social Club, at which point he will have the deploy advantage and the troop advantage.
R10r: r5,r1,r3,r4,r7,r1,r5,r4,r3,r5 --> r5,r1,r3,r4,r7,r1,r5,r4,r3,r1,r4 (red retake Humboldt) --> r5,r1,r3,r4,r1,r1,r5,r4,r3,r1,r10 (fort)
R10g: g15,g1,g3,g6,g4,g1,g5,g1,g3,g3 --> g7,g1,g3,g6,g4,g1,g5,g1,g3,g3 (green bombs Humboldt) --> g12,g1,g3,g1,g4,g1,g5,g1,g3,g3 (forts back)
You can already see that green is slowly gaining an advantage here and will be able to continue to bomb letting Cheyenne (his last listed territ--currently a g3) build up until he can take Social Club.
So, what does this mean for the map? It means that at least as far as the bridge the game is weighted in favor of Green (the bottom guy) in a trench game. That's even if you give red the first turn. If green has the first turn the advantage is even more marked. The good news is that the advantage isn't huge. In a perfect world, red should have an advantage going first (because there's no easy way to eliminate the first turn advantage). In order to give red such an advantage, he would just have to reach the bridge with a few more troops ... up to you how you create those extra troops. One idea might be to give red a +1 resource in Reno or Wadsworth, but someone would have to check if that's going too far. That would encourage red to sit and wait near the bridge for a little bit longer.
Counterarguments and responses:
Argument: Well, what if red doesn't send his troops out to be bombed in those later rounds?
Response: I think the result is still the same. green can decide to take Social Club and keep moving forward, which puts him at a deploy advantage even though red went first. If green went first, he's already got this advantage and that will be further aggravated by red waiting around on Wadsworth
Argument: Well you have X attackers and Y defenders and your result is X' and Y'. That doesn't happen.
Response: First off, if you're just saying that dice vary, I agree with you. Nothing can be done about that, but if you put two people with even dice (in this case the "expected dice"), then you should come out about equal (except for the first turn advantage).
If you are making a more nuanced argument about the particular approach I used, then ... I'm sure there are more considered ways to do the dice odds. However, I don't think they will change much. I took the Battle Odds calculations and took how many troops a person could expect to lose rounded up to the nearest whole number. If you want to figure out a way of calculating odds of fractional troops, be my guest. But there could be a critical error here if I underestimated green's losses or overestimated red's. However, I believe that I may have done the opposite if anything.
Overall, once each player has their second and third territs (e.g. Newcastle and Gov't Grants for red), green has to go through 2,3,3,3,3,2,2 and red must go through 2,2,2,3,2,2,2. That means that green must hit a total of 3 more 3's while red hits corresponding 2s. The penalty for this in my calculations is that green loses 3 more troops. In reality, I think the overall advantage is closer to between 2 and 2.5. (I tested this by running Battle Odds of an attacking stack of 40 through territs of those values.)
Argument: The "unfairness" balances out once you get past the bridge.
Response: Maybe. But that doesn't change the analysis for trench games. You'd have to do a whole different analysis for regular games, and I'm not up for it after this long message. The point here, is that the advantage in TRENCH games could be decisive. Even to the point of giving the bottom player the advantage when he starts 2nd.
If you want to do the analysis for non-trench games be my guest. In such an analysis, you would calculate how far in each turn a player could be expected to "reach" (i.e. how far they get 50% or more of the time). Then you would look at how many troops they have left and use that number as the basis for the next turn. Considering that there are limited choices that a player can make along his path, the analysis wouldn't be terribly difficult. (For example, players will probably grab the bonuses along the way. Players will probably not take the decay territs unless they can take the next one. Players will probably not reserve troops to bomb the bridges because players will probably not leave stacks there. &cetera.)
Argument: This should just go back to the Recycle Bin.
Response: You bite your tongue! I'm very happy to see that this is being worked on again.
