I use Sodium Persulfate as an enchant at a maximum temperature of 50 C. 

My experience with glass heaters is that they break if they are not fully submerged or if they are removed while it is warm which makes me feel that glass is fragile and has tendency to break easily. 

I see that ceramic heaters are cheaper compared to titanium ones. I wonder if the enchant corrodes the ceramic material? Does a ceramic heater break if it is not fully submerged or removed while it is warm? and are they resistant to mechanical shock from a drop or hit?


Question: If you attempt to predict a Roulette wheel $n$ times, what's the probability you'll get $5$ in a row at some point?
Answer: You have a six-state system.
State 1: Not on a run.  Either you haven't started, or the last guess was wrong.
State 2: The last guess was correct.
State 3: The last two guesses were correct.
State 4: The last three guesses were correct.
State 5: The last four guesses were correct.
State 6: You have a 5-in-a-row.
The transition matrix is 
$$A=\left(\begin{array}{cccccc}
1-p&amp;p&amp;0&amp;0&amp;0&amp;0\\
1-p&amp;0&amp;p&amp;0&amp;0&amp;0\\
1-p&amp;0&amp;0&amp;p&amp;0&amp;0\\
1-p&amp;0&amp;0&amp;0&amp;p&amp;0\\
1-p&amp;0&amp;0&amp;0&amp;0&amp;p\\
0&amp;0&amp;0&amp;0&amp;0&amp;1
\end{array}\right)$$
The initial vector is $\vec{v}=(1,0,0,0,0,0)$
To find the probabilities after $n$ rounds, calculate $\vec{v}A^n$