I did some calculations and came up with an interesting, and perhaps surprising, result....
It's been stated quite a few times that it's best to keep a minimum cookie balance in the bank in order to get the benefit from Lucky Cookie. Conventional reasoning runs as follows:
- Lucky Cookie releases 15 minutes' worth of production in cookies, or 15% of cookies-at-bank, whichever is less. - therefore to get the full benefit, the number of cookies in the bank must be at least equivalent to 100 minutes (6000 seconds) of production.
This seems to say that if you have less than this amount in the bank, even if you have enough to buy another building or upgrade, you should hold off buying it and leave the cookies in the bank. Is this the best strategy though? I have decided that it's not always the best.
By spending those cookies now, you are missing out on potential benefit of Lucky Cookie - but you are buying increased production from your building, and getting it now rather than later, so there is a trade-off.
Let's do the analysis:
Assume I have the optimum number of cookies in the bank to take advantage of LC. This number is 6000*P where P is the current production. If I get LC it will give me 900*P.
Instead of that I can use the 6000*P cookies to buy a building or upgrade. Let's assume the time cost of the next best buy is T. Then the increased production I can purchase is 6000P/T (This is the definition of "time cost").
I can get this increased production later anyway, but by getting it now I get the benefit for 6000 seconds longer than I otherwise would. Hence the number of extra cookies I get by buying now is (6000^2 * P)/T
The condition for leaving the cookies in the bank rather than spending them is therefore
900 * P > (6000^2 * P)/T i.e. T > (6000^2)/900 = 40,000 seconds
Most people are probably more concerned with getting the most out of Cookie Frenzy/Lucky Cookie combination, which yields seven times as many cookies. How does this change things?
The maximum yield from CF/LC is now 7 * 900P
The optimum cookies-at-bank is also multiplied by 7, i.e. 7 * 6000P
this increases the critical value of T by 7, i.e.
T > (7*6000)^2/(7*900) = 280,000 seconds.
What does this mean? In the earlier stages of the run, you are better off buying that building or upgrade and not worrying about missing out on the benefit of Lucky Cookie. Later on, it's best to keep that minimum in the bank.
If you keep track of the time cost of each item you buy, you'll find that in the later stages of a run the time cost is typically well over the million second mark, and at that time it's definitely best to plan for CF/LC combinations.