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PJ_SCOTT_35
Member Posts: **3** ✭

I want to know when I should ascend for the first time

I have about four quintillion cookies and 157 prestige

I have 250 cursors 230 grandmas 200 farms and mines 160 factories 150 temples and banks 110 wizard towers 100 shipments and alcmey labs 60 portals 50 time machines 40 antimater condensers 30 prisms

I have about nine trillion cookies per second in 850 hours

43 percent achevements and upgrades

I don't know when to ascend for the first time

Any suggestions ?

I have about four quintillion cookies and 157 prestige

I have 250 cursors 230 grandmas 200 farms and mines 160 factories 150 temples and banks 110 wizard towers 100 shipments and alcmey labs 60 portals 50 time machines 40 antimater condensers 30 prisms

I have about nine trillion cookies per second in 850 hours

43 percent achevements and upgrades

I don't know when to ascend for the first time

Any suggestions ?

1

## Comments

434✭✭✭If you prefer you can wait a bit longer and earn more prestige so you can buy more of the cheaper boosts. But you'll get back to where you were in no time so if I was playing for the first time again I'd ascend now.

3✭651✭✭✭Description:As I have said elsewhere, I think the best time to ascend is when the ratio current production over average production, which generally decreases with time, falls to equal the production boost that will occur from prestige points at the end of the run. The latter of course increases with time.

I therefore generated a formula to calculate the current difference between these quantities. Then I took the time derivative of this. Dividing one by the other gives an estimate of the time for this difference to fall to zero.

Assumptions:- Passive play is assumed, i.e. production is coming only from buildings and various upgrades.

- Production is assumed to be constant, which is a good approximation near the end of the run.

- Existing prestige level must be much higher than 1; therefore the formula is useless on the first run, and probably not very accurate on run 2, but should be fairly good on later runs. the formula is really designed for the "end game" which is when all the upgrades have been bought.

Some notation:B = current prestige boost, i.e. the factor by which the prestige multiplier would increase if I ascended right now.

R = ratio of current production to average production for this run

P = current production (including wrinkler hoarding)

Cp - cookies baked from previous runs

C = cookies baked so far this run

T = time duration of this run so far

t = time from now till the end of the run

Now to the formula:

*** formula corrected Feb 06***

t = (R^3-B^3)/[P/Cp + 3P^3*T^2/C^4 * (PT-C)]

Be careful with the units. The game screen displays production in cookies per second, but T is displayed in hours and you probably want to see the remaining time expressed in hours as well. That means you need to convert T to seconds by multiplying by 3600, plug that into the formula, and then convert the resulting value for t to hours by dividing by 3600.

I have only just put the formula into my spreadsheet, so its validity has not actually been tested yet. However it gives 14.2 hours remaining, on top of the 262 already passed, so the figure is believable.

153✭✭651✭✭✭A possible use for my formula is deciding whether the "best next buy" is in fact the best. A prism may represent the best value in terms of increased production vs cost; however if you are going to have to wait 24 hours to afford that prism, and you expect the run to end in 14 hours' time, you will never get the benefit from that prism, and it might be better to buy something smaller that you can afford now, to get at least a small production boost.

153✭✭651✭✭✭463✭✭✭651✭✭✭27.2 hours. I then popped the wrinklers and finally got wrinklerspawn, which effectively gives 5% boost in production. Estimated time remaining is now59.6 hours.A nice illustration of how critically the best time to ascend depends on what upgrades you have.

1,182✭✭✭✭08619-6956956318-03154

463✭✭✭141✭✭✭absolutelywasting your time.Literally dunk the points you'd give onto my other account, this one has zero value to me and will literally cease to be relevant come~~May~~~~June 1st~~~~June 18th~~June 19th: @CookiewoodstockHi, I'm Barry Scott. Bang, and the signature is gone.

651✭✭✭Has anyone else done this? Ascending with no prestige give no increase in production, but as far as I can see it does not cost anything either, except for the time taken to ascend and reincarnate repeatedly, time during which no production can take place. It seems slightly ridiculous that I may at some point find myself doing 80 dummy runs, simply to get that particular achievement. It will also quickly become tiresome.

1,182✭✭✭✭08619-6956956318-03154

651✭✭✭At this stage of the game, my production is such that it will take me hardly any time at all to get that first HC, but thanks anyway for the warning.

434✭✭✭651✭✭✭Having commenced a new run since then, it's become clear that his formula is highly inaccurate in the early stages of a run, even I am already approachingthe maximum number of buildings, and is really only valid near the end of the run. This is because R falls much more rapidly in the early stages of the run than in the later stages (see "The mathematics of Cookie Clicker"), leading to a gross underestimate of the time remaining.

Accordingly I decided to try and improve the formula.

Generating a precise equation for the time t at which B and R become equal leads to a horrendous 4th-degree equation in t, which I don't think I am capable of solving. However, if we make the simplifying assumption that the rate of change of B will remain constant at the present rate, it leads to a manageable 2nd-degree equation.

Here is my revised formula, for anyone who is interested:

t = (-b+sqrt(b^2-4ac))/(2*a)

where

a = P^2/D

b = (B-1+C/D)P

c = BC-PT

and D = 3B^2*Cp

The quantities C, Cp, P, T and B are the same as in my earlier formula.

Using this formula gives a value of t = 324 hours remaining for my current run, which is now 72 hours old. I think this is a somewhat more realistic estimate than what's given by my earlier formula, which gives only 13.8 hours remaining. (The duration of the last run completed was 544 hours.)

In case you people are wondering, yes I do have a life, but I also have a fair bit of free time. :)

153✭✭651✭✭✭In other words, the longer you leave it, the longer each dummy run takes... but also, the fewer of them you need to do, so it's not immediately clear when the best time is. After 20 ascensions, 80 dummy runs are required to get the achievement. After 60 ascsensions, only 40 are required. Will each of the later ones take twice as long as each of the earlier ones? That depends on how many cookies you expect to have after 60 ascensions. As they say in the classics, I'LL HAVE TO THINK ABOUT IT.

651✭✭✭Pursuant to the above post, I calculated the quantity C^(1/3)/P * (100-A) for each of my runs already completed, where

C = total cookies

P = final CpS

A = no. of ascensions

This should give an estimate of the time it would take to do all the dummy runs to reach the 100-ascension achievement (there is an additional constant involved, but this does not matter for the purposes of comparing values between runs).

This quantity shows a steady decrease up to and including Run 16, after which it slowly increased again, suggesting that the end of run 16 would have been the best time.

The increase seem to be levelling out between runs 19 and 20, so I'm going to see what happens with the next couple of runs. It may go down again. If there seems to be a continued upward trend, then I'll do the runs straight away, otherwise I'll wait.

I think the reason for the initial decrease was because in the early runs I was getting building upgrades and kittens at each run that I had not acquired on earlier runs. Now that I am in the end-game that's no longer the case, so I expect the dummy run time to keep increasing - but let's see what happens.

Of course eventually if I waited until I had nearly 100 runs, there would be only a few dummy runs to do, so the time must decrease sharply at the end. Waiting makes no sense though, as you have to do all those "normal" non-dummy runs, without the benefit from the achievement.

153✭✭Just hit the 100Dec. Now ascended twice since, each one taking c.7min.

651✭✭✭651✭✭✭The numbers are not important, only the shape of the graph. As you can see, if you are going to do the dummy runs at all, the earlier the better.

The cookie multiplier per run was set at the rather low value of 1.2, to make the graph clearer. the larger this multiplier, the closer the peak of the graph is to 100.

Is the time spent doing dummy runs worth it? You bet it is. At my current stage of the game, each new achievement boosts overall production by 2.3%. In other words, getting that achievement should shorten each subsequent run by about 2.3%, which currently equates to 10 hours or more.

153✭✭Fifteen thousand hours and still learning...

434✭✭✭57✭✭153✭✭651✭✭✭153✭✭651✭✭✭Installing the Quadrillion Fingers upgrade in the permanent upgrade slot increases the production so much in the early stages of the next run that after about a day's playing you are already back up to the level you had reached at the end of the first run, which took me 435 hours (18 days). This is the single biggest lift to production in the game.