The NeonUtil utility bot has an incredibly useful streak estimation function (neon global).
I won't be going into how to use the command, because they've got a great guide in their support server, but I'll give some further recources that you can use to expand upon global's results. The common global gives you results in both; average Streak & Tierate, I'll talk about what you can do with these.

The chance of surviving your next battle is simply 1-1/Avg_Streak, so your chance of surviving the next 500 battles would then simply be (1-1/Avg_Streak)^500.

If you turn this function around, you'll get the function for calculating the n-th percentile of your streak! And thus the median, which is honestly a more accurate depiction of a "normal" streak, rather than your average.

$$ \displaylines{ \textbf{P}_{n}(s)=\frac{\log\big(\frac{100}{n}\big)}{\log\big(\frac{s}{s-1}\big)}\\ \textbf{P}_{50}(s)=\text{Median}(s)=\frac{\log\big(2\big)}{\log\big(\frac{s}{s-1}\big)} } $$

We can also calculate your average streak Exp, even considering tierate! Although I do admit this isn't really math, it's more of a glorified for-loop at this point.

$$ \displaylines{ g(x)=200\;+\\ \{ h(x)>100000:100000,⌊h(x)⌉\} \\\\ h(x)=\\ \{x\bmod1000=0:250\sqrt{x}\;+12500,\{ \\ x\bmod500=0:100\sqrt{x}\;+5000,\{ \\ x\bmod100=0:50\sqrt{x}\;+2500,\{ \\ x\bmod50=0:30\sqrt{x}\;+1500,\{ \\ x\bmod10=0:10\sqrt{x}\;+500,0 \\ \}\}\}\}\} \newline\newline f(s,t)= 50+ \sum_{n=1}^{\infty} \; \Biggl[ \bigg( \frac{s}{s+1} \bigg)^{n-1} \cdot \frac{100\cdot t}{1-t} +\bigg( \frac{s}{s+1} \bigg)^{n}\cdot g(n) \Biggl] \newline\newline f_{avg}(s,t)= \frac{f(s,t)\cdot (1-t)}{s+1}} $$