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

EDIT: Can you explain this in more detail?

Quote

I'm told that the expected number of rolls before you see a 28 loss streak is around 514 million, but I don't know why.

/.../

Also, using simulation, I tried to figure out the number of rolls you need to make to have a 50% chance of seeing a streak of length N. It looks to me like the number is about sqrt(2) times smaller than the above numbers, and so we need to have seen 410M/sqrt(2) = 290M rolls to have a 50% chance of seeing a streak of length 28.

Since we've seen 357M rolls, we presumably have a greater than 50% chance of seeing such a streak.

This is pretty low quality research I did using simulation. The sqrt(2) thing in particular is very dodgy.

An exact formula can be found here: https://math.stackexchange.com/questions/59738/probability-for-the-length-of-the-longest-run-in-n-bernoulli-trials

and a more useful approximation here: http://mathforum.org/library/drmath/view/56637.html

The answer seems to be 284 million rolls.