SGOTM 13 - One Short Straw

[Dhoomstriker]

I think only Willem teching it gets it to us in trade.

Cathy: ((1 * 100 / 4) < 20) = (25 < 20) is false, which means that Cathy will trade us Math if she learns it

Note that the "4" assumes that Cathy has met the Unknown AI. If she has not met the Unknown AI, then the odds are even better of her trading Math.

Vicky: ((1 * 100 / 3) < 30) = (33.33 < 30) is false, which means that Vicky will trade us Math if she learns it

Note that the "3" really should be "2" but we are going to assume that 1 more AI (besides Ragnar and the Unknown AI) meets Vicky between now and the time that she learns Math.


So, either of those girls learning Math will be sufficient for us to see it in trade, that is, assuming that the AI_getTechMonopolyValue function does not come into play here. Math gives access to a building (the Aqueduct) and a Wonder (The Hanging Gardens), so it is possible that this function comes into play, but for now I'm ignoring that function and hoping that it won't have a bad effect.

 

[babybluepants]

I've seen the HG block happen many times, but I suspect it doesn't happen on the first turn. Thanks for looking that up, Dhoom. I do agree that we should try what we can to get it in trade (meaning delay as much as possible).

 

[Dhoomstriker]

I've seen the HG block happen many times, but I suspect it doesn't happen on the first turn. Thanks for looking that up, Dhoom.

Actually, I think that the denial for building a Wonder is slightly different code in the same function where the "DENIAL_TECH_MONOPOLY" happens. Specifically, for a Wonder, you instead get the "DENIAL_MYSTERY," as per this bit of code:

for (iI = 0; iI < GC.getNumBuildingInfos(); iI++)
  {
    if (isTechRequiredForBuilding(eTech, ((BuildingTypes)iI)))
    {
      if (isWorldWonderClass((BuildingClassTypes)(GC.getBuildingInfo((BuildingTypes)iI).getBuildingClassType())))
      {
        if (getBuildingClassMaking((BuildingClassTypes)(GC.getBuildingInfo((BuildingTypes)iI).getBuildingClassType())) > 0)
        {
          return DENIAL_MYSTERY;
        }
      }
    }
  }

Regardless, we wouldn't get a "DENIAL_MYSTERY" refusal until after an AI had already completed an Aqueduct, which shouldn't affect us--thus getting Math in trade is probably slightly easier from a Wonder-mongeror than would be a different Wonder-unlocking tech.


Back to the "DENIAL_TECH_MONOPOLY" stuff:
Buildings, Wonders, units, etc unlocked by a tech, particularly units when a "war plan" is on the table, seem to have an effect in the mysterious AI_getTechMonopolyValue function that I keep referring to, which is a little different from an AI refusing due to being in the process of building a Wonder. The caveat with me not knowing what this fucntion does is that this function could make it so that an AI requires more-than-the-normal number of players to "know" a tech before they will trade it around... but I'm not sure... and even if does work that way, I'm not sure that it would matter for Math or not.

I suppose that the best thing that I can do is just set up similar conditions in a test game for the Math tech.

 

[Dhoomstriker]

Unfortunately, it looks like that AI_getTechMonopolyValue function DOES matter. This fact will change the situation to be more like what babybluepants was suggesting:
Willem + Ragnar know Math = Willem will trade us Math
Cathy + Ragnar know Math = Cathy will NOT trade us Math
Cathy + Isabella + Ragnar know Math = Cathy will trade us Math, even if she knows the Unknown AI
Vicky + Ragnar know Math = Vicky will NOT trade us Math
Vicky + Unknown AI + Ragnar know Math = Vicky will trade us Math

 

[babybluepants]

That sounds more like it. Doesn't really change anything, we should still wait if we can. You never know what they all will research.

 

[Dhoomstriker]

Looking closer at that AI_getTechMonopolyValue function, where the still-confusing part for me is the potential for the function to return a value of "0"... somehow there has to be a way for it to be returning "100" instead of "0" for "default" techs, so that we multiply by 100 and divide by 100 but I don't see it... but anyway, ignoring that detail, it seems that:
Math has no Units or Projects associated with it, so only the Buildings matter.

For the Buildings, it seems that there is no additional value for Religious Buildings (or that perhaps it means that each Religious Building type like a Temple is counted once, but by the looks of things they aren't counted at all).

However, for non-Religious Buildings, we add +30.

It looks like Wonders get an ADDITIONAL +50, so really, Wonders, if I understand things correctly, get +80.

Now, 0 + 30 + 80 = 110, which would affect the "iTechTradeKnownPercent" portion of the following formula:
((iKnownCount * 100) / iPossibleKnownCount) < iTechTradeKnownPercent)

Like I said, I'm still confused why we'd return "0" instead of "100" by default, because then I'd think that all Buildingless, Unitless, Projectless techs would have a "iTechTradeKnownPercent" value of "0," meaning that they would never be treated as Monopoly techs. Could this situation be the reason why Alphabet and Monarchy are non-Monopoly techs? I would think that the answer is "no," since Alphabet has a SPY Unit, but then, if we look closely at the section of the AI_getTechMonopolyValue function that deals with a Spy unit, we see:

  case UNITAI_SPY:
    break;

Contrast this fact with a different type of Unit, and we see:

  case UNITAI_ATTACK:
  case UNITAI_ATTACK_CITY:
  case UNITAI_COLLATERAL:
    iValue += bWarPlan ? 50 : 20;
    break;

which seems to imply that there is a value of either +50 or +20 assigned for those unit types and also implies that a Spy unit doesn't get any value added to it.

So, then, YES, I think that the reason why Alphabet and Monarchy are non-Monopoly techs is for the very reason that the AI_getTechMonopolyValue function returns "0" for them.

Okay, so going under that assumption, then I'll stick with my value of "110" for Math and see how it affects the formulas:
Cathy: ((1 * 100 / 4) < (20 * 110 / 100)) = (25 < 22), which is false, which doesn't work because we want to see a true value here for the DENIAL_TECH_MONOPOLY value to be returned

Okay, so I guess I don't quite have it solved, but what we need to see for Math is a number returned by the AI_getTechMonopolyValue function that is somewhere between: X = 126 and 249 (where above I was calculating X = 110), since we have:
((1 * 100 / 4) < (20 * X / 100)) = (25 < (20 * X / 100)) returning true
AND
((2 * 100 / 4) < (20 * X / 100)) = (50 < (20 * X / 100)) returning false


Anyway, it doesn't matter except that we don't have a solid way (yet) of figuring out if an AI will trade us a tech using formulas, but we do have one method that still works: test games!

 

[Dhoomstriker]

Okay, so it sounds like I will be:
1. Talking to Willem and offering him Polytheism
2. Taking Hunting in trade if he will give it to us for Polytheism
3. Keeping our Science Rate at 0%
4. Setting Research to Compass for 1 turn
5. Debating the Currency issue in the future (i.e. as soon as next turn)
6. Working towards getting a Worker and a Settler over to the Iron City location (with the other Worker likely just unloading in Stone City, but it could also go to Paris' Island. It doesn't really have much to in either case, but at least if unloads at Stone City, it can always be ferried over to Iron City after the first Worker and Settler land, so I think that I'll go with the "unload in Stone City" approach, although I won't have to decide until next turn anyway

 

[Dhoomstriker]

Unfortunately, Willem will not give us Polytheism <-> Hunting. He WILL give us Polytheism + Priesthood <-> Hunting, but we DO NOT want to make that trade (well, I don't, anyway), so I'm just going to have to gift him Polytheism.

Sorry about that.

 

[Dhoomstriker]

Okay, I have advanced the turn to Turn 134, 650 BC.

Unfortunately, Willem is going after Monotheism. So, yes, Polytheism was an "on the way there" tech for him.

On the plus side, Cathy still doesn't know Meditation!


I do not really see us wanting to gift Monotheism to Willem, since that tech opens up Monarchy. He will spend 3 more turns researching that tech.


Thus, we are probably at a point where we should just bite the bullet and self-tech Math at a 100% Science Rate.

For reference, our Great Scientist will arrive in 6 turns, while it will take us 7 turns to research Math at a 100% Science Rate.


Gold City will become Unhappy next turn, but the plan is to grow into this Unhappiness so that we can grow as much as possible for a potential Confucian Missionary whipping action, as Confucianism hasn't been spreading much recently.

 

[Dhoomstriker]

So, unless there is an objection, I plan to pass through Stone City on this turn, in order to arrive next to Paris' Island and thus be able to load Settler 6 into the Galley.

In order to be able to do so, I will need to unload one Worker, which I plan to unload in Stone City, so that it can finish work on the Grassland Workshop for Stone City, followed by later heading over to Iron City once space is available in our Galley.


Future planned changes to the PPP:
- Instead of building a 3rd Trireme in Stone City, we will build a second Galley. I've said so before, but I just want to get this point off of my chest so that I can update my local copy of the PPP
- Instead of starting on a Monument in Pig City, we'll build a Warrior (it'll only have a few Hammers invested in it when The Pyramids are built), which may get used for Military Police or as an advance scout, such as for the island to the SE of Iron City.
- I'll probably call the new City "Iron" City instead of "2 Clams" City, since it's easier to think of that way (Marble City also has 2 Clams, for example, so "2 Clams" can get confusing)


Finally, the big decision is: Tech Research.

I'm sold on the idea of Math at a 100% Science Rate. If it's going to take Willem 4 turns just to finish Monotheism (this last turn plus the next 3 turns), then it will take him too long to research Math. If Willem doesn't get Math, we ARE stuck with needing 2 other AIs to learn it in addition to Ragnar, so let's just get it ourselves and start gifting it around (possibly for Hunting and/or Archery if you guys really want those techs).

 

[Dhoomstriker]

Hmmm... Math not only unlocks an Aqueduct and The Hanging Gardens, but it also unlocks two Unique Buildings based on an Aqueduct: a Hammam and a Baray.

That AI_getTechMonopolyValue function looks like it just blindly iterates through all Buildings and Units (you'd think that they'd use some kind of a lookup functionality, like a hash, for performance reasons, but whatever).

The point is that we probably actually have:
initial iValue = 0
Aqueduct = +30
Hammam = +30
Baray = +30
The Hanging Gardens as a Building = +30
The Hanging Gardens as a Wonder = +50
final Value = 170

All of a sudden, we have a value that fits nicely between 126 and 249!


I think that it would be clear to anyone that looked closely that counting a regular Building AND all corresponding versions of it as a Unique Building is NOT behaviour that makes a lot of sense, since, outside of a Mod that enables multiple of these Buildings for a Civ, each Civ can only use ONE instance of each Building. It is nonsense for an AI to "charge" us for the "ability" to build all 3 versions of the Aqueduct when we can really only build one version of it, no matter which Civ we are playing as.

Therefore, I claim that I have found a BUG! Ha! Take that, Fireaxis!

 

[Dhoomstriker]

By the way, I'm holding off on further play until I get some confirmation that people are interested in either:
a) Agreeing with me to go for Math at a 100% Science Rate immediately
OR
b) Wanting to argue for a different approach for Tech Research

 

[Mitchum]

I prefer bbp's approach of researching Currency first while we give an AI or three a chance to learn Math.

 

[Dhoomstriker]

I prefer bbp's approach of researching Currency first while we give an AI or three a chance to learn Math.

At an immediate 100% Science Rate, right?

We have a junkload of Gold saved up (345 Gold), and although we'll lose more than the current 17 Gold per Turn at a 100% Science Rate after settling Iron City, I don't see how we'd need to save up any additional Gold... it takes 12 turns according to the game's current tech bar to finish Currency (but that's because I recently whipped away some Commerce squares) but realistically it will take us a total of 11 turns to get Currency since we will gain more Commerce after having settled Iron City and the in-game tech bar's value is really something like 11.2 turns right now. Since I don't foresee our expenses jumping up to more than 30 Gold per Turn by settling Iron City, we can most certainly finish Currency at a 100% Science Rate.

Presumably, we would then buy-up Gold from the AIs whenever possible, as well as:
(here's the part that we totally forgot about):
getting GOLD PER TURN for some of our excess Resources!

Okay, to be honest, we don't have that many excess Resources floating about, but we do have at least a Clam that we are gifting to Ragnar that could be converted into a Gold per Turn trade. We're also gifting him a Fish but he may reconnect his between now and then.

Similarly, we don't REALLY need to import a Fish from Isabella, although the she may have reconnected her Clam by then (we're trying her a Clam for her Fish) so we might not want to cancel that trade anyway.

Still, it's yet one more point in favour of going for Currency.

If we don't mind being the "jerk on the block," we can also Demand Tribute of Gold and Gold per Turn, although we'd want to do so after increasing our Power by whipping an army during the post-Great-Person-Generation period.


So, what's the worst case? Not enough AIs researching Math for us to be able to get it in trade, of course! That situation would mean: 11 turns to Currency + 3 turns at a 0% Science Rate (assuming that we get really unlucky and the AIs have no Gold to give to us) + 7 turns to Math = 21 turns

We are 9 turns away from completing The Pyramids.


I'm not saying that we can't get Math in trade. In fact, Cathy has a very high chance (she values it at 50) of Researching Math. Contrast that value with Ragnar's value of 10, while he has already gone for Math.

But it is a reasonably-sized risk to rely on the AIs to get Math for us, now that we know that we need 2 additional AIs OR Willem to Research Math. Add to that the fact that certain combos of AIs don't work (i.e. Vicky + Cathy doesn't help unless they meet each other), and it is a reasonably high risk to our plans.


The downsides of Math -> Currency are that we wouldn't be able to get Gold or Gold per Turn from the AIs after learning the first of the two techs (meaning that we would have to spend those guestimated 3 extra turns collecting Gold before going after Currency), and we would have a pretty negligible chance of getting either tech in trade by following that tech path.

However, if we are willing to accept these downsides, then the "safe" play is Math (gift it around in the hopes of getting Calendar soon) -> Currency -> Compass.

 

[mdy]

For every 2 turns we delay maths after we revolt to CS, we delay astronomy by 1 turn. Given that Cathy has only just got writing, so even if she decided to research maths next she would be unlikely to research it in time. The probability of Vicki getting it as well is even lower. The possibility of getting a few extra gold from currency (especially when I doubt this tech will pay off) can't make up for this risk, so I think we have to research maths at 100% next.

- Instead of starting on a Monument in Pig City, we'll build a Warrior (it'll only have a few Hammers invested in it when The Pyramids are built), which may get used for Military Police or as an advance scout, such as for the island to the SE of Iron City.

Why would we want a monument in pigs when we don't have a granary/lighthouse there yet?

 

[Mitchum]

(here's the part that we totally forgot about):
getting GOLD PER TURN for some of our excess Resources!

I've mentioned it at least twice but hadn't made a big deal about it...

I take that back. I just did a quick search and didn't find it. I really meant to say it though...

However, if we are willing to accept these downsides, then the "safe" play is Math (gift it around in the hopes of getting Calendar soon) -> Currency -> Compass.

bbp showed that the extra trade route income is almost equal to the 20% bonus we get on Currency if we research Math first. In my opinion, if we are going to research Currency, the sooner the better:

• Researching Currency first will allow us to get gold and gpt that much sooner.
• Researching Currency first will increase our GNP, which may or may not make Math a 5-or-6-turn tech rather than a 7-turn tech.
• If we have Currency when we're "gifting" Math around, we can actually get some gold for it.
• The longer we delay Math, the more likely we can get it in trade, thus shaving turns off of our overall research, even if we are already partway through Math when we finally get it.

For these reasons, if we decide to research Currency, I think we should go Currency -> Math, not Math -> Currency.

For every 2 turns we delay maths after we revolt to CS, we delay astronomy by 1 turn.

Can you please explain this? I think you're completely discounting the boost to GNP (which increases our beaker count) and the ability to get gold/gpt (which allows us to run 100% science slider more often). As Dhoom said several posts ago, how do we know that adding Currency to our tech path isn't the fastest way to Astronomy. Add to that the fact that we could very easily get Math at a discount (either free or a few turns less depending on when we trade for it) makes me view Currency very favorably.

By the way, having Currency would also give us more margin to avoid a late-game troop strike situation. Granted, if we're warring effectively, gold from capturing cities should keep us alive, but you never know...

 

[Dhoomstriker]

Given that Cathy has only just got writing, so even if she decided to research maths next she would be unlikely to research it in time.

Well, I suppose that I could set up a test game to simulate how long it might take Cathy to research Math. It is certainly going to be a Tech that she has a high chance of going after, since out of all of the techs that she can possibly research next, it is the highest ranked value at "50."

Note that if we are serious about trying to get Math in trade, there is a VERY SIMPLE way of getting Cathy to speed up research: Open Borders with her!

She has The Great Lighthouse and is not using it to its fullest potential.

Borders can always be Closed later.

The probability of Vicki getting it as well is even lower.

Why? This comment I don't understand. Vicky has had access to Writing for a while now. She has a "0" for Alphabet Research, while she weights Math and Monarchy equally. It is very likely that she is chasing after one of these two techs at this stage in the tech tree, giving her a reasonable chance of learning Math.

We can't Re-Open Borders with her yet, so that option is not (currently) on the table.

The possibility of getting a few extra gold from currency (especially when I doubt this tech will pay off) can't make up for this risk, so I think we have to research maths at 100% next.

Correct, the extra Gold will not make up for the risk of the AIs dragging their heels on Mathematics' Research.

However, what the extra Gold WILL do is shorten the time that it would take for us to Research:
Currency -> Math

I actually think that it is reasonable to say that it will take less time to Research:
Currency -> Math
than it will to Research:
Math -> Currency


Why? Well, babybluepants' calculation showed that the bonus Commerce from an earlier Currency would be very similar to the bonus on Research to Currency for knowing Math. To me, that means that either path is equal not counting any bonuses that we get from learning the Techs.

The difference comes into play when you consider that Currency allows us to get lump-sum amounts of Gold amounts and Gold per Turn amounts of Gold, both of which would make Currency -> Math faster ON THIS MAP. On most maps, you won't get so many nice Foreign Intercontinental Trade Routes, so Math -> Currency is generally faster, but here, Currency -> Math will be a more efficient approach.


The discussion, however, needs to about risk. We need to decide how much level of risk we are willing to accept.

(especially when I doubt this tech will pay off)

Of course, there are other factors at play in the discussion, such as an unwillingness to self-tech Currency, that may be influencing the decision.

Why would we want a monument in pigs when we don't have a granary/lighthouse there yet?

The latest test game for Turn 142 (the originally-targeted completion date for The Pyramids) that I shared with you guys has Pig City building: Granary -> Lighthouse -> Monument

I noticed this fact when I set up the test game with Iron City and presented a screenshot demonstrating Iron City's automatic fog-busting upon settling the City. If you look at that screenshot again, it shows Pig City building a Monument.

My local copy of the PPP spreadsheet instead shows: Granary -> Lighthouse -> Warrior

I just wanted to make it clear to everyone that we would NOT be building the Monument in Pig City, despite what the screenshot shows.

The idea is that if there is room for an assumption to exist, then it is probably better to reduce the ambiguity and come out and clarify the possible assumption. That way, we'll all know what is going on and will have sufficient opportunity to argue against any such decision (say, if someone really wanted that Monument, now would be the time to tell me, instead of me feeling that I have to pause play at that future point in the turnset).



So, I would suggest that if anyone wants to push for the Currency -> Math approach (like Mitchum), that they also probably push for ways of stacking the deck in their favour:
1. Pushing to gift Monotheism to Willem (possibly getting Hunting in trade)
AND
2. Pushing to Open Borders with Cathy
AND
3. Pushing to Re-Open Borders with Vicky as soon as we are able to do so

In other words, we'd be aiming to reduce the risk of a somewhat risky approach.


One question would be: would this reduction in risk be sufficient to allieviate our concerns about not getting Math in trade on time?

Another question would be: for those who do not want to self-tech Currency at all, would going "Compass at 0% for a while -> Math only at the last minute" be an acceptable level of risk without doing the 3 points above?

A further question would be: for those who do not want to self-tech Currency at all, would you prefer to implement some or all 3 of the points above, so that a "Compass at 0% for a while -> Math only at the last minute" approach has a greater chance of getting Math in time?

An a final question would be: can we get someone to show the math behind self-teching Currency either paying off or not paying off?

 

[Dhoomstriker]

In my opinion, if we are going to research Currency, the sooner the better...
Researching Currency first will increase our GNP, which may or may not make Math a 5-or-6-turn tech rather than a 7-turn tech.

That's a fair point and a reasonable assumption to make.

I listed a worst case scenario of needing 21 turns for Currency -> Math, without any AIs deciding to research Math within those 20 turns.

A more realistic case scenario would put that total time at 17 turns.

Turn 134 (now) + 17 turns = Turn 151, 8 turns after The Pyramids are completed

So, that's our cost should the AIs fail to get Math: 8 additional turns after The Pyramids come in before we can make use out of Pacifism.


Now, let's put those 8 turns into perspective, because they aren't exactly 8 turns' worth of delaying hiring Specialists.


As I showed with the calculations when we were talking about Generating Great People, we would probably spend this number of turns growing our Cities AFTER The Pyramids are completed:
Paris = 5 more turns
Gold City = 3 more turns, but assuming that we'll have to whip a Confucian Missionary here, it will be 7 more turns
Marble City = 2 more turns
Pig City = 8 more turns

So, what's the difference?

Paris = delayed 3 turns in being able to use Pacifism's bonus
Gold City = delayed 1 turn in being able to use Pacifism's bonus
Marble City = delayed 6 turns in being able to use Pacifism's bonus*
Pig City = 0 turns of delay

* An important point is that we might not actually have 6 turns of delay here. Why? Well, the later that we generate a Great Person in Marble, the more dilution our Scientists will have on the Great Person probability of becoming a Great Prophet. So, preferably, Marble City will be one of our LAST Great People to be spawned. Since it will already have a good number of Great Prophet Points, we will most likely delay hiring Specialists here for quite some time.

In fact, I think that we'll end up delaying the hiring of Specialists in Marble City so much that we will not only have 0 turns of delay, but we will also probably just keep growing Marble City well after hiring Specialists in the other Cities.


Therefore, our "realistic case" scenario for Currency -> Math, where we DO NOT get Math in trade, gives us:
3 turns where Paris doesn't get to use Pacifism's bonus plus 1 turn where Gold City does not get to use Pacifism's bonus.


When I look at the numbers this way, then the risk of going Currency -> Math is actually very low.


Here are some of the benefits that this tech path gives us which are not directly related to the bonuses that Currency gives us, as Mitchum outlined above:
A] We get more time for Confucianism to auto-spread
AND
B] We give the AIs roughly 15 turns to research Math, which, if they do, will still save us about half of the cost (or more) of Math
AND
C] Since the cost of failing to get Math in trade is so small, I would be completely willing to avoid any of the risk-reducing factors that I mentioned in the last message (points 1, 2, and 3 in regards to Opening Borders and gifting Monotheism to Willem). Since the cost is so low, the risk of failing isn't very high, thus I'd probably rather keep the AIs a bit dumber, which is a choice that more people are more likely to agree with

 

[LowtherCastle]

Pigs City should not build a warrior since Stone or other cities can. Pigs needs granary+lh asap (if it doesn't have them yet).

 

[babybluepants]

The Math bottleneck needs to determine our research path, I think. We have to get Math by a certain date - I am assuming this to be approximately T+14. Is this wrong? If it takes us 6-7t to research Math, we should delay for 7t hoping for a trade and maintain enough cash to finish it @ 100%. We could also try to massage to slider to load up the last few turns, in case we can at least make a partial trade later. In other words, I don't think that Currency-Math is a good move, since it would delay this schedule.

The actual beaker cost of Currency is probably about 1/3 higher than the extra TR payoff by 1AD. The payoff is tricky to calculate, though. More base commerce and the cash-making abilities translate into better slider. We also have Rep and a pile of specs coming that will alter numbers significantly. I can take a shot at a careful estimate later today, but I think the reality of it is the payoff will depend to a great degree on how much cash we get in trade and on when we can reasonably expect a Currency trade in the alternative. Neither of those are really known, though we can probably guess relatively low cash payout and relatively late Currency trade, since the AI's seem quite slow. Willem throws a bit of a wrench in things, since I've seen him beeline Currency and even (possibly) trade it at monopoly.