EDIT: Can you explain this in more detail?
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.
I get confused between the expected number of rolls for something to happen and having a 50% chance of that thing happening. It feels as if the (alleged) fact that you expect to have to roll 514 million times on average to get a 28 losing streak means that since we have less than that number of bets then we have a less than 50% chance of having seen a 28 losing streak.
But I don't think that feeling is true.
Consider rolling a 6 sided die until you roll a six. The expected number of rolls to get a six is 6.
But if you only roll 4 times, you have about a 51% of seeing a six, even though you've rolled less than the expected number.
Does that answer your question? Basically my intuition around this is off (and yet I bet 50 BTC on it)...