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# DAMPE PROBABILITY

dannyb21892 Feb 15th, 2016 (edited) 85 Never
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1. There's a 10% chance on each dig to get the HP.  Each dig is entirely independent from all others. Therefore the number of digs until the heart piece is a geometric variable with success p=0.1.  And so the expected value (average number of digs) is 1/0.1 = 10.
2.
3. Often people parrot 7 as the average number of digs, but this is not true. 7 is the MEDIAN.  That is, there is approximately a 50% chance each to get the heart piece before or after 7 tries. This can be seen by finding the probability of 6 failures in a row.  0.9^6 = 0.53.  Therefore the probability of getting the heartpiece in 6 or fewer attempts is 47%, and the probability of getting it in 7 or more attempts is 53%.
4.
5. But if 7 marks the "halfway point" where half the time you'll get less than 7 and half the time more, then why isn't 7 the average?  Well that's because half the time you will be getting 1,2,3,4,5 or 6 and the other half of the time you will be getting 7,8,9,10,11,12,13,14,15,16........(insert arbitrarily large numbers here).  Therefore the upper 50% has a larger average to offset the lower 50%.  Consider this as an example:  I try dampe 10 times.  The number of times I had to dig to get the heart on each attempt are as follows: 3,4,5,5,6,8,14,15,16,24  50% of the time I got a number less than 7, and 50% 7 or greater.  But the average is 10.  On a large scale the numbers will work out the same way as this contrived example.  Hopefully this clears it up and kills the argument.
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