Monday, 7 October 2013

Cookie Clicker - Chain Cookies

I did an little analysis of cookie clicker before to explain how the late game is dependent on clicking.  Well, here comes some more, and it's really good news - kind of.

Generating cookies in end game was heavily dependent on alternating between Frenzy and Lucky cookies to get massive quantities of cookies when the duration of frenzy overlapped with the effect of a lucky cookie.  I ignored chain and click frenzy because they were rare and basically bad.  But they aren't bad at all any more.  Let's talk about them for a moment.  I'm going to talk about these new calculations using 12B Cps, which is about how much you will have with the current upgrades in the game assuming you are at end game and just trying to get your last 10 or so condensers before acquiring your last 20 or grandmas with 250 heavenly chips.

Click frenzy multiplies your click value by 777 for 26 seconds.  Thanks to a new upgrade, your click value is 5% of your Cps plus 4 plus 132.6 times the number of non-cursor objects you own which will be around 900-ish so that's 119344.  If your Cps is 12B then your 5% of that is 600M so... oh, right, your click value is 5% of your Cps.  In a quick test I think it's pretty reasonable to click 5 times a second for 26 seconds - we'll call it 25 because you probably miss a second realizing you've hit the rare event - so that's 125 clicks at 5% of your Cps is 6.25 times the 776 bonus you are getting is 4850 seconds of production.  That's a lot.

Of course, like lucky, click frenzy can overlap with a frenzy, which would multiply its effect by seven because your click value is just a fraction of your Cps.  Unlike lucky, though, you need the frenzy to last beyond the instant you get the click frenzy or it may just apply partially.  If you click frenzy with 12 seconds left of frenzy then you get times-seven for 11 or 12 seconds and no times-seven for the remaining 14 seconds.  Thanks to Markov chains and uniformly distributed probabilities, I can say that 39% of your click frenzy time will be under the effect of a frenzy.  So the total value of a click frenzy is about 16,243 seconds of production.

That's a lot and not to be missed in the calculation even though it is infrequent.  At this level, assuming you have the requisite cookies in the bank to maximize your lucky clicks, you are producing about 18.9 times your Cps while actively playing without considering Click Frenzy.  Click Frenzy brings that up to 26.6 times.

What about chain?  Chain used to have a 10% chance of stopping every chain cookie that appeared after the fourth one, and at maximum gave 13 chain cookies, the last of which was worth 6.66 trillion cookies.  That sounds like a lot but it isn't.  At 12B Cps a lucky cookie is worth 14T without an overlapping frenzy, over 100T with one.  Since just over 50% of lucky cookies have overlapping frenzy, the chain is prety miserable.  Especially since a chain only has 43% chance of paying that much.

But the 13 digit limit has been upped to 17, which is 66 quadrillion.  To compensate the chance of ending went up to 13% and if the cookie gives you more than 25% of your current holdings then the chain automatically ends.  Of course that means if the cookie gave you 24% of your current holdings then the chain might continue, and the next cookie would be worth about 240% of your current holdings, with no limit by Cps.  Does that sound insane?  Sure it does.

So, if you have 12B Cps you ought to have over a quadrillion cookies in the bank.  Since one quarter of that is 250T, a cookie with a value of 666T would automatically end the chain.  Still, that means getting 740T cookies out of the chain.  That's more than 60k seconds of production, which is the first time I've felt the need to abbreviate the number of seconds of production an event generates with a "k".  Of course each link in the chain is only an 87% chance, so the value of a chain cookies is actually only 17,923 seconds of production.  But that's still a lot.  The chance of getting a chain cookie is only about a half percent, though, so that only brings out total production up to 27.5 times your list Cps.  More, but not a lot more than the value without chains.  But what if you stored up 2.67 quadrillion cookies so that the 666T cookie did not automatically end the chain and instead had an 87% chance to lead to the 6.66 quadrillion cookie?

Instead of averaging just shy of 18k seconds of production, the value of a chain cookie expands to just shy of 156k seconds of production.  This increases your golden cookies adjusted Cps to 34.3 times your list Cps.  That's about 25% more than if you didn't save up the massive bank.

But all of this math has always had the unstated assumption that you were not in grandmapocalypse mode.  That makes sense because your cookies used to come from frenzied lucky cookies.  You can't even get frenzy in the grandmapocalypse, and more than half the time you are going to get a cookie that is actually bad.  How could this possibly be good?  Well, it increases your chances of getting a chain dramatically from half a percent to 9.3%.  Of course get can get clot which can halve your lucky cookies and click frenzies.  You can get ruin which loses you 10 minutes of production.  All of this adds up so that if you have minimum frenzy/lucky cookies in the bank with 12B Cps then turning on the grandmapocalypse reduces your cookie production from the 27.5 times list mentioned above to only 17.7 times list.  That's not good.  What about if you save up 2.66 quadrillion cookies and activate the grandmapocalypse?  Then your production, instead of the 34.3 times list mentioned above is 104.5 times list.  That is good.

Okay, let's just go over that again.  If you have 12B Cps, and you all in full on grandmapocalypse with all upgrades, then the actual amount of cookies you take in per second of play is not 12B but 1.2T.  That means if you play for an hour you'll rack up 4.3 quadrillion cookies.  Of course, what that really means is that if you play for an hour you'll get an average of 24 chances at a 9.5% shot to get a 25% shot at getting 7.4 quadrillion cookies.  The rest of what is happening is kind of miniscule by comparison, accounting for only about 6% of your total income.

But if you can average 4.2 quadrillion in an hour, then you could reasonably bank 26.67 quadrillion cookies so that you could hit a 66 quadrillion chain.  That would multiply your income by about 8.1 times, meaning you could average more than 32 quadrillion an hour.  Even 100B Cps would account for less than 5% of the total cookies per hour at this level.  The breakpoint is actually around 466B Cps.  At that amount you should ditch the chains and return to lucky/frenzy.

At the beginning I said this was all good in a way.  The way it is good is that all we care about is making a lot of cookies.  But this kind of destroys the game.  You don't need hundreds of condensers or kittens or new upgrades or forthcoming dungeons.  All you need is a psychotic hivemind of old ladies and a couple of quadrillion to kickstart your efforts.  Once you have that, your Cps basically doesn't matter anymore.  Plus progress is unbelievably random.  It is quite possible that one person will hit two max chains in an hour while another person goes on hours and hours without getting a single one.

You can see how that is a problem.  Wait did I say you can get more cookies?  Oh yeah, no problem.

And speaking of no problem, it took a couple of days between when the 13 digit limit was removed and when the 17 digit limit was implemented.

Count those digits again

6 comments:

  1. I am the cookie master!!

    http://i.imgur.com/V3SDH1y.jpg

    Of course, the game is way easier when you cheat.

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  2. I only have 56 chips but I'm at 33B CPS while working towards my last few condensers. It sounds like I've done something very wrong.

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  3. I decided to click red cookies until I got a cookie chain. Thank you for the advice that generated 74070 cookies!

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  4. Is that screencap your own Humbabella, or something you found?

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  5. Nick: I think my 12B is wrong, but I can't figure out how. The spreadsheet I was using seems to be right (and matches the real game I was using to make it) but that number just doesn't feel right.

    Sky: That is actually my own real game. In the brief period where you could get cookie chains of unlimited size I got myself some very big ones. (The game is "tool-assisted" by which I mean I had a console window open with a countdown to the next golden cookie spawn - basically cookie clicker DBM. "Tool-assisted" to distinguish from "The cheats" as shown in Chris' screenshot above.)

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  6. I found a similar game: http://drmeth.com

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