Hey it's you!

You might be able to help me with this...

If someone was to say "ha there's no way there's ever been a losing streak of 28 or more bets on any dice site ever at 49.5%" and I say "oh yeah?  I bet it has happened on Just-Dice alone!" and then someone else says "I bet you 49 BTC that it didn't happen" and I say "OK then!"...

What are my odds of winning?

Suppose that there are 357,937,388 bets at 49.5% and that they were all made by the same person.

What's the odds that it contains a losing streak (p(loss) = 0.505) of length 28 or more?

We know that the odds of a losing streak of length 28 happening in your first 28 rolls are 1 in 1/0.505**28 = 203,161,501.  That makes me think I have a greater than 50% chance of winning.

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.  That makes me think I have a lesser than 50% chance of winning.

So what are the odds of winning?

"Some of this actually happened."