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"Everything must go" strategy

bob_32_116bob_32_116 Posts: 438 ✭✭✭
edited March 28 in General Discussion
With Business Day in force, the outcome of some Golden Cookies is "Everything Must Go", which drops the cost of all buildings by 5% for 5 seconds. The instinctive reaction is to immediately buy what buildings you can afford. But.... should you?

This is a situation people will encounter in the next few days, with April 1 coming up. Five seconds is not much time to make a decision, so it's best to have a strategy in mind beforehand.

Scenario:

- The next "best buy" as defined by the cost in cookies divided by the resultant increase in production - what I refer to as "time cost" - is Theme Park, but I do not have enough cookies at bank to buy one. I can afford other buildings but I am holding off because Theme Park is the next best buy.

- I get "Everything must go", reducing the cost of all buildings by 5%. I still cannot afford Theme Park even with the discount, but I could buy Cookiecoin. Should I?

Here is my reasoning:
The time cost of Cookiecoin is currently less by 5%. However the time cost of Theme Park is unchanged, because I cannot buy it right now and will have to assume that when I buy it it will be at the non-discounted price. Therefore the two quantities I should be comparing are:

100% of time cost of Theme Park
vs
95% of time cost of Cookiecoin.

If the latter figure is lower, I should buy Cookiecoin; if it's higher, then I shouldn't buy Cookiecoin right now merely because i can.

I'd be interested to know if others have thought about this and if you can find any holes in my reasoning.
Post edited by bob_32_116 on

Comments

  • bob_32_116bob_32_116 Posts: 438 ✭✭✭
    Always the first to admit when I get something wrong:

    The flaw in the preceding post is it fails to consider the saving from buying Cookiecoin now at a discount rather than buying it later at the normal price.

    I have done the maths, and it's pretty messy... however the outcome is as follows:

    With a discount factor f in place, the "time cost" is multiplied by an additional factor:

    (f-1)P/dP + f

    where P = current production and dP = increased production from buying "best buy".

    The first term is what I neglected to consider in the previous post.

    With no discount, f = 1 and this factor simply reduces to 1.

    With 5% discount in place, f = 0.95. In the end game, P is normally so large compared with dP that the final f can be ignored and we are left with -0.05*P/dP, i.e. a negative time cost. The saving is 0.05 times P/dP times the undiscounted purchase price.

    The implication of this is that when "Everything must go" appears you should immediately buy buildings that are available, beginning with the most costly one.

  • JezJez Posts: 64 ✭✭
    edited March 29

    The implication of this is that when "Everything must go" appears you should immediately buy buildings that are available, beginning with the most costly one.

    Lol! Nice to see it arrived at thoroughly though.
  • bob_32_116bob_32_116 Posts: 438 ✭✭✭
    edited March 30
    I probably need to clarify the bit " buy buildings that are available, beginning with the most costly one." If you have been following optimal buying strategy, the quantity (purchase price)/dP will be about the same for all buildings, so the time saving is nearly independent of what building(s) you choose to buy during the discount period. The only reason for going for the larger ones is that you only have five seconds to spare, so it's better to use the time to buy a couple of large buildings than to try for a dozen small ones.

    If you look at the formula, there are actually situations where it's better NOT to buy some discounted buildings, but those situations would be extremely rare, and probably not worth stressing about.
    Post edited by bob_32_116 on
  • ZeoniveZeonive Posts: 5
    Are you sure this is the optimal strategy?
    As far as I know, you get way more cookies from the "Lucky!" golden cookies if you have a specific amount of cookies in your bank, so spending them would be way worse in the long run (>5min actually).
  • bob_32_116bob_32_116 Posts: 438 ✭✭✭
    Zeonive said:

    Are you sure this is the optimal strategy?
    As far as I know, you get way more cookies from the "Lucky!" golden cookies if you have a specific amount of cookies in your bank, so spending them would be way worse in the long run (>5min actually).

    Hmmm, I haven't done the maths, but I guess it would be a good idea to make sure you always leave a certain number in the bank. It would depend on the circumstances.

    The potential saving from buying at the 5% discount is massive, the more so as the run progresses. A time cost per building of several million seconds is common. At a cost of 1 million seconds, if you can save 5% of that, that's 50,000 seconds, more than 12 hours.

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