Chain Cookies again.

I will refer you to my previous discussion of them to understand the basics of chain cookie analysis. Essentially I am analyzing the choice between having Elder Wrath on and not having it on. For a brief time that answer was that you wanted elder wrath to take advantage of huge cookie chains. That is no longer the case.

A few things have gone into this. First of all, the way of deciding when to spawn a cookie has changed. The Update notes say that they are now more random, which strikes me as an odd things to say. The graph on top compares the new probability distribution with the old one by number of seconds passed. The lower graph is the cumulative distribution. On both, the blue line is the new system and the red line is a uniform distribution, as it used to be. As you can see, but about halfway through the time between the minimum and maximum times it is already nearly 100% certain that a cookie will have spawned.

Nothing against Orteil - actually, big thanks to Orteil for making such a great game and for inspiring me to work on my own projects - I just disagree with the idea of "more random." To me, uniform distribution is as random as it gets. If the goal was to prevent the prediction of cookie spawns then this change makes them less predictable in the sense that we can no longer get the time remaining to spawn from the variable it is stored in, but it is more predictable in the sense that the window in which the spawn will happen is much narrower and the spawns are more clustered around a certain number of seconds. Personally I think the old method was better, but if a check is to be made every tick then uniform distribution could be easily recreated by just using the right check.

Because of the way the cookie spawns cluster, the chance of getting a lucky cookie while your frenzy cookie is still going on is very close to 100%. If you can click the cookie within 1.5 seconds of it spawning then you'll only miss your high value lucky cookie about 2.3 out of every 1000 times. Now 80% of your click frenzy time will be during frenzy time - up from 39% under the old system. That dramatically increases the value of golden cookies while not under elder wrath, to about 48 times your listed CpS.

Anyway, I wanted to talk about chains. Every chain generates at least 5 digits. Starting with the fifth, the chain has a 1% chance to end randomly, and it will also end if it is more than 25% of your current holdings or more than 6 hours of your current production. As I discussed the last time I wrote about this, it's a little tricky to set a cut-off when each successive click multiplies your returns by ten. If you get a chain that is 26% of your current holdings then it ends. If you get one that is 24.9% then it doesn't, and then the next one is 249%, which is a lot. Similarly, 6 hours of production is plenty while nearly 60 hours is pretty fantastic.

I asked a for a friend's CpS to benchmark my numbers. The number I was using was 885.8B. At that CpS you qualify for a 77 quadrillion chain without wrath or a 66 quadrillion chain with wrath. To get that you need at about 27 quadrillion in the bank as well, but that's easily attainable. When you have 885.8B CpS, though, 77 quadrillion isn't all that much. A lucky/frenzy combo will be worth 7.5 quadrillion, and you get those every four and third minutes like clockwork.

My big spreadsheet matches my intuition. Giving up on those big lucky cookies, as well as those insanely huge click frenzies, just isn't worth it to pick up extra chains. Because the chains for wrath use 6's and the ones without use 7's, you could have enough CpS to qualify for a 17 digit chain with wrath on and only a 16 digit chain without wrath. But even then no wrath is better. Chain cookies, after all, are only a small part of that 48 times return when not on wrath. The majority is lucky cookies.

Personally I'd like it if wrath was better now that there are things attacking you during the wrath. It seems like if you have to defend yourself you should be getting more reward.

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