It's a google docs spreadsheet.
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[SPOILERS] Small Wunders and Izzy of Inca: The fat lady sings
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Ok, here's my attempt to calculate the worst case for 2 axes vs an archer and you (Mindy) can tell me if I'm missing something.
 He'll have 40% culture on turn 52, and this is the worst case I'm assuming he has one archer in his capital at full fortify (not crazy). The archer gets an innate 50% (hill) + 25% (city) bonus, plus 20% for CG1. (They no longer get Drill in RBMod.) Most concerning is the 21.7% chance of the first axe doing 0 damage. Chancing of winning with two axes, assuming we follow through and attack again no matter what: Number of hits first axe gets: Total chance that the first two axes kill 0 hits: 21.7% * 2.27% = 0.0049 1 hit: 0.2618 * 0.0764 = 0.0013 2 hits: 0.2092 * 0.4552 = 0.0952 3 hits: 0.1384 * 0.5153 = 0.0782 4 hits: 0.0820 * 0.5938 = 0.0487 5 hits: 0.0452 * 0.7005 = 0.0317 6 hits: 0.0236 * 0.8540 = 0.0202 Dead: 0.0227 ----- Sum: 0.3029 So the total chance of 2 axes winning is 30%, unless I'm missing something. And in practice it's less than that, because I doubt we'd proceed on 0 or 1 hits with less than 10% odds on the second attack. Even if the first axe gets the archer down to 10%, the second one still has a 15% chance of losing! 
Another turn of the same, summed up by this:
 We're over the free limit and incurring unit costs now, which means that retep is paying more, and we're the only two in the world doing so. Until he stops building axes there's no other goal we can have other than not dying. The chances of being relevant in the world picture are gone.
September 1st, 2013, 06:30
(This post was last modified: September 1st, 2013, 06:31 by WilliamLP.)
The craziest news is that Retep razed Bacchus's expansion city! This is where serious C&D would be useful, if we checked the world power at the beginning and end of the turn to see how much he lost. We'll see it on the graphs next turn though.
 He missed a turn with a military build. I wonder what's the matter? Anyway, that news is enough to make it safe-ish to build a settler now, finally. Meanwhile Ichabod planted his third three turns ago.  I thought the tile 1N of Barber was important enough to spend two worker turns roading. It allows units to get back to Turandot in 2 turns, and to control the tile 1W of corn. It also means we can do a surprise strike on Retep's sentry units next turn. The funny thing is, killing those units might help him since it would improve his GNP. 
The moment we've been waiting for is here:
 I haven't played the turn yet, and I intend to think this over a while but the turn should be played within 12 hours to be polite. Mindy, if you see this before that point, any input would be great. Retep chose the north route! He did use combat engineers, but we still have at least 3 turns to play if he goes for Turandot. Probably more because attacking anything on the hill SW of the city over a river would be foolish. His force: 5 axes, 1 warrior to the south. Our force: 4 axes, 3 archers, 2 quechua. Turn 51 add 1 archer. Turn 52 add 2 axes. (Both cities have enough overflow after a whip to 1T an axe next.) The forest 1NW of Barbiere could be chopped this turn if we wanted, or used in defense. 1 Axe in Barbiere has moved already. With the scout, he knows the contents of Barbiere. We have the raw numbers advantage, so anything that trades 1 for 1 is a great deal. So what are the options? Side question: Do we counterstrike? It would be possible to road and attack the scout 2SW and move units from Barbiere there. Quechuas aren't going to be very useful against axes, though not useless as city defenders. But they could be a pillage threat if he just has an archer or two at home. As discussed above the math is horrible for attacking into his capital, always, so I think that's basically off the table. Side question 2: Do we kill the warrior right now? The axe has >99% odds to do so, but it would mean he'd be pretty out of the fight in health (most likely) and position. Chances are (about 90%) that he'd have enough health left to defend against an axe afterwards with more than 50%. Unfortunately he'd only get 1XP from the warrior fight. Main question: What do we do about the invading force? Options: 1. Just let him come in and play zone defense. He could move onto the forest and sit there, but that's not very scary. We could put enough on the corn that attacking over the river would be a bad idea for him. He could also move NE. 2. Guard the forest. Then moving NE is his only choice. We lose fortify bonus in Barber for anything moved out but his numbers don't look that scary right now so we may not need it. 3. Guard the NE grass, let him move E onto the forest. This feels very wrong because what we guard with can't get back to guard Barbiere without leaving a couple of workers hanging. 4. Try to guard both the NE grass and the forest. We could, say, leave the 1 axe in the forest, and 2 axe + 3 archer in the grass. (Unfortunately the 4th axe can't move). If he wants the forest we have 10% fortify so his C1 axe has 11% chance to win, and an unpromoted axe has 4%. The most likely outcome is that he loses 1 axe, and wins the second combat, and has 4 axes on the forest, 1 wounded but promotable. The problem is him attacking into the open field. He'd get (probably) 3 axe vs archer combats which are 95% odds in the open. He'd be wounded but we wouldn't have much to counterattack with, just 2 axes. And we wouldn't want to give him the chance to promote and heal. Right now I'm leaning on #2. We put maybe 3 axes + 2 archers in the forest, which ought to be enough to make it a really bad idea to attack the forest. If he moves NE, we either slam into him with what we've got, immediately, or await his next move when we'd have 2 more axes in play. The trouble with that is that he could go toward either city from there, and the river split makes defending both tricky. So I guess that's my default play unless we think of something else: - Defend the forest with 3 axes + 2 archers. He basically can't attack into that, I don't think. - If he moves NE, option 1 is to slam with 4 axes at basically even odds (minus the C1 he has). We could win anywhere from zero to four battles (see binomial distribution which would be 1 - 4 - 6 - 4 - 1 relative probabilities ). In the worst cases he has some wounded axes and one full health one, we have 4 archers to follow up (one over a river), plus 2 quechuas, plus 2 more axes to deal with him after his next move.- Or... there may be a better option if he moves NE to defend and stall for a couple of turns. I'm not sure. 
So the move:
 3 axes + 2 archers + 1 quechua are on the forest, with 1 turn of road on it. There's no way he'll attack into this unless he just wants to improve his GNP really badly. The archer on the corn might be a mistake because if we attack next turn it has to cross a river, but I was thinking of tactical possibilities where we defend the hill to the north with 2 archers, which are hard to take down. Two workers are on that hill to 1T a road. I deemed attacking the scout to be too expensive. every unit we have may be needed, depending on the RNG. He's either going to go NE or give up. NE means it's time to run a bunch of war sims and do some math.
So Retep, what'cha gonna do with all that axe inside them jeans?
 He ran away, to the square SW of the spice. I see 3 horses in the screenshot. The NE horse is clearly the easiest to claim, 5 turns from our capital. The W horse is obviously a bad idea. Claiming the SE horse would be the loony play, and so the one I'm thinking of making! It's not like we have a lot to lose this game anyway. We have enough overflow to make 2 more axes this turn, if Barber goes into starvation mode for one turn, but now that we don't have to I don't think we will. We're already paying 4gpt in unit costs which is a heavy burden in this part of the game. For where to proceed, it's finally time for a settler I think. It could be too early for a post-mortem of this start, but I think we've already proven that settling Barber was an economic move defensible against the most aggressive possible early rush. And hence Retep's move wasn't to his benefit, unless his goal was to prevent us from being competitive in this game, which he has done. I don't really blame him though - it would have looked differently without copper in our capital but on the other hand we could have built a crap-tonne of archers too. I can't really blame him for it though: he probably thought he had a chance of gaining something. And it's really an unfortunate byproduct of a map that encouraged us both to move toward each other.
September 2nd, 2013, 21:06
(This post was last modified: September 2nd, 2013, 21:08 by WilliamLP.)
 I made a blunder here. I should have moved one axe onto the plains hill forest, to see what was going on, then paused and thought carefully about it. But I moved all 4. I learned a lesson here. So what are Retep's 2 workers doing roading that tile? Ah, he wants to road and 2-move the axe to the Square SW of Barbiere next turn, cutting off reinforcements, and hoping I would think he had given up and pursue him with everything! I sort of fell for it, and didn't see the possibility. There wasn't any reason to move 4 axes to that tile. It's a very cute move, but I'm not sure how effective it will be. Next turn my forces will be 5 axes, 4 archers, and 2 quechuas. That should be enough to kill everything with a favourable ratio, and probably he won't get the city even if I lose 5 axe combats in a row. His other problem is his workers are left hanging. Could he have more units and two worker in the staging forest, to join the fight? I doubt it, since his economy isn't that strong. In other news, we met Slowcheetah who has a scouting warrior on the eastern border of our capital, but that's pretty far down on our list of problems right now. I'm building a settler in Turandot finally. Can we afford to? I'm not sure, but don't think we can really afford not to either. Masonry is next, since Barber at least will need walls if we keep it as the game goes on.
Lurkers: Just to make sure, the second player in a turn split isn't allowed to use promotions the following turn if they are logged in when the turn rolls, and it would be considered a double-move, correct? (And presumably auto-promote cheese would be ruled out too?)
Sorry I missed the big (almost) battle. I would have recommended the same moves; defend the forest and then control the plains-hill-forest.
Absolutely we can afford to build the settler now. -We have almost equal power + the home-turn whip advantage. -We should have culture in 4(?) turns or so in Barbiere. Up to now we've needed to defend at pretty much 1:1. With that culture Retep will need a 2:1 advantage. About that far-reaching horse,....don't have a recommendation yet but as we've seen from Retep's aggression/response we can't defend that city. We were only just able to defend Barbiere with both of our 2 cities dedicated to war and the short travel times that come with home turf advantage. So its easy to say that, if Ichabod is dedicated to taking it, he can. If you're comfortable with the possibiity (likely) of having to turn your entire economy to military to defend that site then go for it. Connecting city that can defend against Retep will allow a move to that horse city if it's still available or the gold city if not. That's my initial feeling anyway. |
