The probability of a losing streak of 13 at 50% win chance is 0.5^13 = 0.00012207031 or 0.012207031% or once every 8192 rolls.
I didn't realize the odds were that low, funny that it happens to me often
I think this is more of a psychological thing; I've also found that it seems like when you bet higher, you lose more. However, the sites are provably fair; they can't do this. It's all in the mind, as we tend to care more about our bet when the amount we bet is higher.
Either way, OP, if you were trying to find the odds to try and make a profit off dice, I'd advise against it, as the house always wins in the long run.