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True value of early trade: a case study

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  • #46
    If you don't have a French keyboard you'll have to use an alternative method to get the cedille. You can either copy and paste it or use the ascii code. You press the alt-key and keep it down while you type the ascii code for the character on the number-pad at the right of your keyboard. Unfortunately I don't have a list of codes at hand, but I'm sure someone can tell you where to find them.

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    • #47
      I have a list of the "additional characters", as they're labeled, but it's from a DOS manual that's about 20 years old. My best suggestion is to try all the codes (127-255); the letters are grouped mostly at the beginning (ç = 135, ù = 151).

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      • #48
        Bump

        (at long last !)

        I just reread it and find
        Aux bords mystérieux du monde occidental

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        • #49
          Originally posted by La Fayette
          Bump

          (at long last !)

          I just reread it and find it interesting
          Aux bords mystérieux du monde occidental

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          • #50
            Originally posted by La Fayette
            LF - as you say interesting and worth reading - thanks for bumping it.

            After reading it a number of things strike me.

            1) The value of trade as a game winner is much better appreciated now than it was then - particularly for early landing.

            2) Discounted cash flow is a useful tool for analysing some decisions in the game, but as you and others have pointed out it is not always appropriate.

            3) The appropriate time value of money (or cost of capital or discount rate) to use in DCF analysis is not clear. You used 2% and 8% in some of your examples; I would go as high as 20%. This seems to remain an open question.

            4) To take account of non cash flows (eg shields and beakers) it is necessary to convert them to cash. For example you used 1 beaker equals 1 gold but this is an approximation that can sometimes be wrong. (The beakers from a trade delivery when you already have sufficient for your next advance are completely lost.)

            5) The attraction of Civ II is that the game contains so many closely balanced trade-offs that we are still discussing strategy years after it was launched.

            RJM at Sleepers
            Fill me with the old familiar juice

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            • #51
              I agree with RJM -- good Bump.

              Great thread.

              Multiple decisions -- from the start -- search or settle? Since the settler/engineer is a “developing unit” (more later) searching with a settler is very expensive in terms of opportunity costs -- thus only search for a bit then settle (and/or maybe build a road first then settle).

              Next decision is the level of search activity. It is an open question to be deferred at this time.

              What to build? the active question in my mind has always been the same from my economics training -- maximize the expected present value of the long run profit stream. This thread has discussed in part the “present value”; the “expected” was touched upon (the notion of risk) and the long run profit stream is assumed as a game win, but might be better defined. For some players, it might be a high score, others, a rapid win. what we have yet to see is the shortest time to collect $30K -- where $30K might be an easy representation of other achievable goals further down the line. (Although the tech activity might be slowed after trade, republic, banking or democracy -- the open questions being growth to fill the continent in question (especially since the ai is poor with invasions), and the value of additional technology may be small in attempting to achieve $30K.)

              La Fayette simplified the discussion by setting aside the uncertainty aspects of risk reduction via building offensive & defensive units. The discussion of “value of conquest” might also be the subject of some other thread. Similarly, I have yet to see a definitive experiment as to the value of conquest vs bribery of ai cities. And finally the relative value of white goods compared to units can be discussed later, but needs to be discussed with a notion of time.

              Yes, an opportunity cost of four camels is five settlers, but the settlers come with carrying costs and the settlers them selves have varying degrees of value. Open nearby sweet spots with specials? -- plant new cities ASAP. Distant marginal sites, or limited (ICS mode) sites -- hmmm less clear decisions. Use the developing unit to actually build roads/irrigate (intensive development vs. extensive development) is another choice of when & how much -- especially with the increased “cost” of unhappiness and with primitive governments, corruption & waste.

              How to use the resources, citizens, for each city & the slider bar for the economy = more decisions.

              I’d like to discuss all of those at some point, but I think that a simple question can be focused upon -- domestic vs foreign trade.

              La Fayette, I think that the initial data can be reexamined with the new trade information that Solo and others have developed. The 16 turn refresh cycle opens up the thoughts of more camels “sooner” so we may not be limited to ‘just’ three routes -- what we have with the fourth and beyond routes is a potential marginal improvement in the ongoing gain of arrows. Similarly, growing our source city (or for domestic trade both cities) and adding infrastructure can improve the arrow count -- thus affecting our answer. On the other hand I recall seeing some where that there is a cap on the initial cash payout of 2/3 of the total beakers required for the next advancement -- thus in the very early game, a delivered camel may only yield 133 beakers/coins if 200 were required for the next advance -- and thus may not be worth any sort of rushed activity.

              In the early to mid -game, this may be less of a concern -- five turns on a road and two turns of boat may yield payoffs of 800 offshore to foreign lands compared to 150 or so for domestic deliveries from the same source of the same demanded product (as exemplified by my current Cfc GOTM). In this second stage, rushing looks to be well worth it and delivery to foreign lands also looks to be the best decision.

              I remember in other games where the payoffs later were much more often netting 1000 to 1400 coins per truck for a serious trip across the world, circa the late tech stage (maybe 65-70 techs or so). Again, rushing & foreign markets look to yield the best results.

              Note that in addition to the turn number, there is a sense of time with the techs discovered (but that is also another discussion.)

              If we were to just simply take turn numbers in question, then we could estimate the “average” interest rate based upon a simple score as the “long run profit stream”. Using some high scoring games as an example, I saw a table where 15,000 looks like a reputable score. With 400 turns, an interest rate of about 2.45% should get close; about 3.27% will get there in 300 turns (about 1900 AD in emperor) , and about 3.95% can do it in 250 turns (about 1850 in emperor). Since the better players seem to get reasonable scores in a shorter time, I think that they are exhibiting better rates of return than 4%.
              Those with lower expectations face fewer disappointments

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              • #52
                Originally posted by Old n Slow
                maximize the expected present value of the long run profit stream. This thread has discussed in part the “present value”; the “expected” was touched upon (the notion of risk).
                I admit it's rather a long time since I learned about DCF but the idea of the expected net present value is new to me and very interesting. I'm used to npv calculations that assume the return is certain or else increase the discount factor to take account of risk.

                Is the word "expected" being used in its statistical sense or does it have its normal English meaning? Introducing a risk factor into the future returns would certainly help with one of the difficulties I have with dcf - that it can give too great a weight to returns that are far distant in the future. ("too great" and "far distant" are of course subjective )

                Incidentally, I wonder if it should be "maximise the present value of the expected long run profit (cash) stream". A real statistician (like Dr Spike?) would have to comment on whether maximising the expected present value ... is the same as maximising the present value of the expected ...

                My brain hurts; I must go away and think about how to apply this to Civ II.

                RJM at Sleepers
                Fill me with the old familiar juice

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                • #53
                  Let me help your brain pain --

                  Iirc, with a few assumptions (constant interest rate, independent distributions, etc.) the math should work through the expectation calculations -- if not it is close enough relative to the other errors that loom. But I think that you are correct. Technically, one calculates the profit for a given period, adjusts that based upon risk and uncertainty, and then discounts the value and sums it up. Yes the “expected” is in the statistical sense, dealing primarily with risk, but equally yes, the “expected” can be expanded to include uncertainty -- one simply adds assumptions and then treats the uncertainties as quantifiable risks.

                  The risk and uncertainties justify in part the war materiel; of course there may be other justifications for such investments…
                  Those with lower expectations face fewer disappointments

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                  • #54
                    How are you going to define the "expected" value?
                    Although sending a camel on a boat to visit another civ will pay far more in both a straight bonus and in long-term trade arrows, the risks of your camel falling prey to barb pirates or even irate enemy civs is far higher the longer the camel is out in the open.
                    Sometimes it will be better to send your caravans to nearby Rome with a shorter shipchain for a smaller bonus than to send it halfway around the world to Babylon for more money but having to enter hostile territory controlled by the Mongols. The long-term prospects of your target city should also be considered when weighing up where to send a freight. The trade-special AI city may seem to be a good destination but given its location on a land-link between three other civs renowned for their bloodthirsty reputations, then might it not be more sensible to send your caravans to a city that does not have the potential for such a large bonus payment, but is likely to grow larger and remain in the game longer, meaning you will have better value from your trade route and not have to reestablish it when the city is destroyed.

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                    • #55
                      Originally posted by duke o' york
                      How are you going to define the "expected" value?
                      Roughly speaking, the expected value is the value of a particular outcome multiplied by the probability of achieving it summed over all possible outcomes.

                      So if your caravan has a 60% probability of making a delivery with a bonus of 100 gold and a 40% probability of being killed on route, the expected value of the bonus is 60 gold.

                      Estimating the probability of achieving the outcomes may not be too easy and if the range of outcomes is infinite you will have to resort to a little gentle calculus.

                      RJM at Sleepers
                      Fill me with the old familiar juice

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                      • #56
                        A little gentle calculus or a little rough guesstimation?


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                        • #57
                          Originally posted by duke o' york
                          A little gentle calculus or a little rough guesstimation?


                          If your guestimation is good enough - go for it.

                          On reflection, most of the infinite sums that come up in Civ II don't require calculus, they are (hopefully convergent) series.

                          The real problem is estimating the probablities:

                          a) when (indeed whether) a caravan will be delivered
                          b) whether the goods will be demanded
                          c) how many trade arrows the city you deliver to will have (particularly an AI civ).

                          The whole thing gets a lot easier when you can deliver on the same turn that you complete to a city that you have delivered to before.

                          RJM at Sleepers
                          Fill me with the old familiar juice

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                          • #58
                            Originally posted by rjmatsleepers

                            c) how many trade arrows the city you deliver to will have (particularly an AI civ).
                            My rule of thumb: one trade arrow for each population point.

                            Add two extra if city next to Whale.

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                            • #59
                              Originally posted by Elephant

                              My rule of thumb: one trade arrow for each population point.

                              Add two extra if city next to Whale.
                              It's a good rule of thumb, but there is always the possibility that the city will build a settler just before you deliver not to mention the possibility that some other civ or barbarian will occupy a key tile at the wrong moment.

                              Of course you still have to use some rule of thumb, however the uncertainites are sufficiently large that it's not worth trying to be too precise with the dcf calculations.

                              BTW can a worker be displaced from an ocean tile when it is occupied by another civ's ship? (I should probably know the answer to this, but I don't.)

                              RJM at Sleepers
                              Fill me with the old familiar juice

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                              • #60
                                BTW can a worker be displaced from an ocean tile when it is occupied by another civ's ship? (I should probably know the answer to this, but I don't.)


                                No

                                SG[1]
                                "Our words are backed by empty wine bottles! - SG(2)
                                "One of our Scouse Gits is missing." - -Jrabbit

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