Re: Just-Dice.com : Play or Invest : 1% House Edge : Banter++

Quote from: Light on June 05, 2014, 09:46:19 AM

Quote from: dooglus on June 05, 2014, 09:29:24 AM

No, not really, and apparently I'm misremembering anyway.

I was told "The expected value for 28 or more losses is 410,427,273" without explanation. I've asked for the reasoning.

I believe what you're looking for is described in these two pages.

http://math.stackexchange.com/questions/383704/probability-of-streaks
http://www.askamathematician.com/2010/07/q-whats-the-chance-of-getting-a-run-of-k-successes-in-n-bernoulli-trials-why-use-approximations-when-the-exact-answer-is-known/

Not to be rude, but I'd say the maths is beyond the capabilities of most and as it is a recursive function it would need a computer for large values. Hope this was what you're after. Either way it's interesting reading.

Yes, it's very complicated and somewhat annoying. I have found that the nicest explanation of the distribution of run lengths is here: http://gato-docs.its.txstate.edu/mathworks/DistributionOfLongestRun.pdf

I'm ok with "expected run lengths for a number of rolls", but I haven't come across "expected number of rolls for a given run length", so I'm interested in the derivation. Can you point it out in the pages you linked?