That is analogous to the fact that it is exceedingly improbable that you and I are here in this world today by random processes, and the observed fossil evidence, chemistry and known physics says that too. Of course, one may "believe" (btw "belief" is something I avoid) that mere possibility, not matter how exceeedingly unlikely is preferable to acceptance of an Intelligent Designer, but to accept such an exceedingly exceeedingly low probability chance I find, well, irrational.
The probability of 2 ounces of sodium chloride forming a three dimensional crystal with exact alternation of sodium and chloride ions is 1 in 2(6.022*1023), which is overwhelmingly more improbable than your 50 heads (1 in 250)
Further, it is a false choice to say that the choice is between blind chance and a God pulling the strings. There are many shades of possibility, not only between these poles, but outside of them, as well.
Finally, while the "fossil evidence, chemestry and known physics" make it improbable that we are here by random processes, no one, to my knowledge, is proposing that strictly random processes are responsible for use being here.
Lastly, you claim that "belief" is something that you avoid, yet you profess belief in an entity you cannot see, test or know and for which there is no objective evidence. Indeed, you do not use the entire word "God", presumably to avoid the defacement of the name of this entity. That's beyond belief. That's faith, and I don't think there is anything wrong it, but don't kid yourself that you are a rationalist, and your belief in the supernatural theory of ID is based on logic and reason.
But you have admitted that the 50-head toss is just as probable as anyother sequence so it is no more improbable than any other sequence.