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bob_32_116
Posts: **395**Member ✭✭✭

Towards the end of a run, the question arises whether it is worth continuing to purchase buildings. Even though the extra production is small as a fraction of the total, it is still extra production, so there is no reason not to get it.

UNLESS you have Chocolate Egg. This releases extra cookies equal to 5% of the cookies at bank at the time of purchase of the egg.

People have realised that it's generally a good idea to purchase the egg at the very end of the run, and before doing so to invoke the Earth Shatterer aura then sell all buildings, which will dump 85% of their purchase price back into the bank.

What if the end of the run is some time off though? Those cookies you have in the bank will bring you an extra 5% at the end. On the other hand, if you use them to buy buildings now, at the end you will get back 85% of what you paid for them, and you will also have extra in the bank from the increased production. Should you buy, or just keep them in the bank?

Let's do the analysis:

Number of cookies available in bank = C

Time cost of buildings = T

Fraction of cost recouped by selling = f. If Earth Shatterer is active, f is equal to 0.85.

Estimated time till end of run = t

Buying buildings with those cookies will generate extra production dP = C/T

By the end of the run this will give extra cookies in the bank equal to Ct/T

From selling back those extra buildings I will also get back f * C

Total = C(t/T + f)

This is to be compared with what I would have had if I had just left the cookies in the bank, which is simply C.

(This is only approximate. It neglects the cost of invoking Earth Shatterer, which requires a sacrifice of one of the most expensive building, and therefore costs more if I have more buildings. It also ignores the fact that T increases a little with each extra building bought. Each of these decreases the total cookies at the end, but not significantly for the purpose of this analysis.)

I should therefore buy buildings only if C(t/T+f) > C

This transforms to

t > (1-f)T

= 0.15T with Earth Shatterer

People probably were aware that there was a point at which buying more buildings was no longer useful, but they may not have realised just how early this point is. For example, my current value of T is about 380 million seconds, which is not unusual towards the end of a run where I am at 290 prisms. To make it worth buying more buildings, my run would have to continue for another 57 million seconds or thereabouts. That's over 15,000 hours!

In other words, if I did have Choc Egg unlocked I should have stopped purchasing buildings long ago. As it happens I don't have it; I cashed it in some time ago before I read the information about how the thing works.

The message here is pretty clear. When Choc egg is unlocked, estimate T and also t, the number of hours remaining for the run. I have an algebraic formula to estimate t, but otherwise just using the duration of previous runs as a guide. Once t becomes less that 0.15T, which may be earlier than you think, stop buying buildings and just let those cookies pile up. (There may be an exception if you are aiming for a milestone such as 300 of some building which will give you an extra achievement and more milk.)

UNLESS you have Chocolate Egg. This releases extra cookies equal to 5% of the cookies at bank at the time of purchase of the egg.

People have realised that it's generally a good idea to purchase the egg at the very end of the run, and before doing so to invoke the Earth Shatterer aura then sell all buildings, which will dump 85% of their purchase price back into the bank.

What if the end of the run is some time off though? Those cookies you have in the bank will bring you an extra 5% at the end. On the other hand, if you use them to buy buildings now, at the end you will get back 85% of what you paid for them, and you will also have extra in the bank from the increased production. Should you buy, or just keep them in the bank?

Let's do the analysis:

Number of cookies available in bank = C

Time cost of buildings = T

Fraction of cost recouped by selling = f. If Earth Shatterer is active, f is equal to 0.85.

Estimated time till end of run = t

Buying buildings with those cookies will generate extra production dP = C/T

By the end of the run this will give extra cookies in the bank equal to Ct/T

From selling back those extra buildings I will also get back f * C

Total = C(t/T + f)

This is to be compared with what I would have had if I had just left the cookies in the bank, which is simply C.

(This is only approximate. It neglects the cost of invoking Earth Shatterer, which requires a sacrifice of one of the most expensive building, and therefore costs more if I have more buildings. It also ignores the fact that T increases a little with each extra building bought. Each of these decreases the total cookies at the end, but not significantly for the purpose of this analysis.)

I should therefore buy buildings only if C(t/T+f) > C

This transforms to

t > (1-f)T

= 0.15T with Earth Shatterer

People probably were aware that there was a point at which buying more buildings was no longer useful, but they may not have realised just how early this point is. For example, my current value of T is about 380 million seconds, which is not unusual towards the end of a run where I am at 290 prisms. To make it worth buying more buildings, my run would have to continue for another 57 million seconds or thereabouts. That's over 15,000 hours!

In other words, if I did have Choc Egg unlocked I should have stopped purchasing buildings long ago. As it happens I don't have it; I cashed it in some time ago before I read the information about how the thing works.

The message here is pretty clear. When Choc egg is unlocked, estimate T and also t, the number of hours remaining for the run. I have an algebraic formula to estimate t, but otherwise just using the duration of previous runs as a guide. Once t becomes less that 0.15T, which may be earlier than you think, stop buying buildings and just let those cookies pile up. (There may be an exception if you are aiming for a milestone such as 300 of some building which will give you an extra achievement and more milk.)

Post edited by bob_32_116 on

2

## Comments

395Member ✭✭✭If you have Choc Egg unlocked and are at the stage where you should be saving cookies rather than buying buildings, this also means that there is no reason to pop wrinklers since you cannot do anything with the cookies they release. They should be left until the very end of the run before popping, unless of course you want to invoke Elder Pledge which will pop them whether you like it or not.

294Member ✭✭395Member ✭✭✭http://forum.dashnet.org/discussion/14628/the-mathematics-of-cookie-clicker#latest

I could have put this discussion there, but I thought it merited its own thread. The thing is, CC is ALL maths. Or mostly.

395Member ✭✭✭That's quite a change, considering that I am only at 263 prisms and 5009 buildings in all. At the end of the previous run I had 292 prisms and 5305 buildings. It seems strange just doing nothing and watching cookies mount up in the bank, after so long being in the habit of waiting for the next building to become affordable and then buying it

At some point I shall have to decide when it's worth trying for the 300 prisms at the end of the run. That will mean selling all buildings except the prisms, buying the prisms and then selling everything again, so I'll lose 15% on the prisms but 30% on everything else. the achievement will give me about an extra 2.3%. I did the calculations at the end of the last run and found I did not have enough assets to reach the 300 prism mark, and I don't think I could do it this run either, but I'll know for sure when I get to the end of the run.

395Member ✭✭✭The hardest lesson to learn, and I remember saying this once before on the forum, is that sometimes the best way to get the most cookies in the shortest time is to simply do nothing.

Fortunately there is more to life than Cookie Clicker. :)