Talk:Profitability/@comment-4192477-20110723212956/@comment-4102115-20110724090645

Thankyou Adi, that is fantastic work! It has proven many of our hypotheses.

Just a note for you Adi on your comment on repairs - it took me a while to work out your error, but you have misunderstood the concept of ratios. The 1:14 ratio is a ratio, not a fraction. You have given your workings and gone to all that effort to write up an example, but based on a fraction, not a ratio. It would be better to write is as a 14:1 ratio. Meaning for every 15 "actions", 14 times you will click on a $ symbol, and 1 times you will click on a Repair symbol. All your workings are based on 1/14th of the times you click on a symbol it is a repair symbol and 13 out of 14 times it is a dollar symbol, and you used that same reasoning in your example. That is incorrect. If you are to say that it needs repairing 1/14th or 7.14% of the "action" times, then that would mean it is a collection to repair ratio of 13:1. That is simply not the case. Many people have collected thousands of sample points, showing that the average ratio is 14:1, such that 1/15th of the actions are repairs and 14/15th of the actions are income collections.

Other than that misunderstanding, it is brilliant of you to find the code!!! Any chance you could dump the whole program somewhere? Would be cool to see if we can de-bug their issues for them or at least see if we can work out a workaround - if we can see the code that gives the sun-only award, maybe we could work out what to do to force it, etc.

I am just pleased with myself as well, I posted here before my hypotheses that the chance of needing repair worked on an increasing probability scale. I did not pretend to make any attempt to determine the actual values, but suggested it went on a scale of the nature of:

1-7 collections - 0%, 8 collections - 10%, 9 collections - 20% to 17 collections - 100%. From this var formulae we see I was right on the premise, just off on the actual numbers. Pestilence Rex also posted almost the exact same hypothesis as me :)

We can now see that the probability of needing repair after the n'th collection is:

1 - 7 collections: 0%

8th collection: 1/91 = 1.1%

9th collection: 3/91 = 3.3%

10th collection: 6/91 = 6.6%

11th collection: 10/91 = 10.9%

12th collection: 15/91 = 16.4%

13th collection: 21/91 = 23.0%

14th collection: 28/91 = 30.7%

From the 13th to 23rd collection, the probability of needing a repair on collection increases by 7/91 = 7.69%, up to:

22nd collection = 84/91 = 92.3%

23rd collection = 91/91 = 100%

I am too long out of high school to remember how to calculate permutations to work out from that the exact probability of breaking, which we know when calculated exactly is going to give us 7.14 - 7.15%, but thanks to Adi we now know it is around that number and why the probability is not just 7.14% fixed at any collection point.

So for extra padding, that would mean that probability that after a repair/upgrade/build, the chance that you will get a run of 23 collections without breaking is 4248016074842491607040000/91^15 = 0.0017% or 1 in every 57200 repair runs. So for every 800,000 income collections done, you will get 1 x run of 23 collections before needing a repair. Something to look out for eh? :)