Quote from: dooglus on June 05, 2014, 05:02:33 AM

Quote from: organofcorti on June 05, 2014, 03:47:48 AM

It's just you. The signature is actually completely illegible.

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."

I haven't given any though to the distribution of longest runs since this: https://bitcointalk.org/index.php?topic=80312.msg2338366;topicseen#msg2338366

I'll have to try and spin some of the old neurons up and see what happens.

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