Rush Buying Formula

DaveMcW said:

The formula for purchasing units and buildings is:

GoldCost = int( (30 * Cost * GameSpeedPercent)^0.75 * (1 + HurryCostModifier/100) / 10 ) * 10

Cost = The hammer cost on standard speed.
GameSpeedPercent = Modifier for game speed and starting era.
HurryCostModifier = A hidden rush-buy penalty.

Click to expand...

I filled a large spreadsheet comparing the costs predicted by the above formula against actual costs generated in-game, and found that the original formula posted above gives correct results in most cases, but is off for a handful of units and buildings. The formula needs to be slightly tweaked, with a couple of additional integer flooring operations, to:

GoldCost = int( int{ [30 * int(Cost * GameSpeedPercent) ]^0.75 } * (1 + HurryCostModifier/100) / 10 ) * 10

which can also actually be simplified to:

GoldCost = int( int{ [30 * int(Cost * GameSpeedPercent) ]^0.75 } * (100 + HurryCostModifier) / 1000 ) * 10

(And BTW, much thanks to DaveMcW for discovering and posting the original formula! I was having trouble seeing how the purchase cost was calculated until I found this thread, so I'm grateful! )

How do mobilization (33% discount on unit purchases), big ben (15% discount) and mercantilism (25% discount) interact together?

I imagined they'd add up to a 73% discount, so that I could buy a frigate (770g) for 207.9g (or 210 probably).

In fact, it costs 300g.

If the discounts were multiplicative (770g * 0.66 * 0.85 * 0.75) then we'd be buying it for 42.1% of its usual cost, or 324.17g (probably 325 or whatever).

I wonder if the bonuses are applied to different parts of the formula so that, for example, big ben is more powerful than its 15% bonus would appear.

770x(1-(0.25+0.15))x0,66=304,92 rounded off to 300.

Excellent. Thank you Knut.

Sorry for the necro, but it seems that this is still the 'goto thread' for rushbuying.

I noticed that work boats seem pretty cheap to buy, and if I understand the formula correctly with the 25% penalty they should be 300 rather than 240:

>>> (30 * 50) ** .75
241.02852568339551
>>> (30 * 50) ** .75 * 1.25
301.28565710424436

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Also, compared to e.g. a lighthouse (400 gold for 75 hammers) the work boat seems a good deal (240 gold for 50 hammers).

Was this changed in a patch?

I guess DaveMcW is probably not around anymore to modify the first post, but it seems useful to mention. Also, cottages!!!

Can't remember. While the ratio is better for the boat, the lighthouse can sometimes give a much better immediate benefit.

Even if you only have one fish tile, Lighthouse is always better IMO (it's hard to beat +2 food and +1 hammer per tile -- workboat just gets you +1 food). With multiple sea resource tiles, there's no question Lighthouse is better.

Huh, I always assumed lighthouses would only apply to improved resources. Thanks for pointing this out.

OTOH, a lighthouse has worse hammer to gold ratio. I think a lighthouse is 400 for 75 hammers, or 5.3 gold per hammer, while a boat is 240 for 50 hammers, or 4.8 gold per hammer. So, if you want to build one and purchase the other, it might make more sense to buy the boat and build the lighthouse, although you have to work in the lost hammer plus the one or two turns delay between buying the boat and improving the fish, while a lighthouse is immediately effective. For whales/crabs it is a choice between food+happy or hammer, while for pearls it is (a crappy 1) gold+happy vs hammer.

So, it seems that it is a trade-off, but lighthouse as default probably makes more sense than boat as default, even if the boat is one of the most efficient things to buy in the early game hammer-wise (after the worker?).

vanatteveldt said:

So, it seems that it is a trade-off, but lighthouse as default probably makes more sense than boat as default, even if the boat is one of the most efficient things to buy in the early game hammer-wise (after the worker?).

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It just so happens that one boat is priced the same as a lump sum sell of lux, which is why you buy boats and immediately sell sea Luxes. Hard building a fishing boat early is senseless. And yes, lighthouses are multiple times better than boats anyway.

Rush buying lighthouses is a no-brainer in all of my games

I never have enough gold to rush all that I would like, so (generally) do people rush-buy lighthouses before libraries?

I understand that lighthouses are a priority over work-boats for fish, but what about coastal lux? With DoF, as has been pointed out, the workboat pays for itself. You still get the extra food in the meantime, but does rush-buying a lux to immediately sell it make really make sense?

Favoring the lighthouses it that they can’t be pillaged like workboats. It is also worth noting that maybe your cap can build workboat in just a few turns for a new expo.

Only in an expansion with multiple sea ressources.

vanatteveldt said:

Sorry for the necro, but it seems that this is still the 'goto thread' for rushbuying.

I noticed that work boats seem pretty cheap to buy, and if I understand the formula correctly with the 25% penalty they should be 300 rather than 240:

Also, compared to e.g. a lighthouse (400 gold for 75 hammers) the work boat seems a good deal (240 gold for 50 hammers).

Was this changed in a patch?

I guess DaveMcW is probably not around anymore to modify the first post, but it seems useful to mention. Also, cottages!!!

Click to expand...

Work boat has not had any HurryCostModifier since at least G&K, possibly earlier.