If reason is untrustworthy and discerning God's actual existence appears to be "a coin toss"...

Mmmmm...Bah.

The wager's scope is limited to the God (monotheism) vs. no God dilemma (atheism) and its logic is false.  Try to prove either that God does or doesn't exist and you're just locking horns with the opposing side in circular arguments.  The scope is skewed.  The given scope is a false dilemma.  No, really, that's what they call it -- a false dilemma.

Religious Choices: Either Believe in God or Atheism.

Whenever you are presented with two possibilities, it is crucial to establish whether those possibilities are contradictions, contraries, or choices.   Presenting two options as if they were contradictions or contraries, when in fact they are not, is the common fallacy of false dilemma--so called because the "dilemma," or hard choice between two options, is "false," because other options than the two offered are possible. This fallacy is also known as the "either-or fallacy" because it makes you think that your options are limited to either one or the other.

Scope

While not summarily dismissing or favoring monotheism, there simply are other pertinent choices available.  There are also polytheisms, nontheisms (religious or other), orthopraxy (as compared to orthodoxy) and even very different definitions of "deity," "divine," and "worship" with which to further broaden the scope.  Beyond that, we're not the only species and planet out there so there's even more diversity.  You've got to remember that what we call religion, deity, divine and all that is greatly colored by our neurological wiring and social tendencies as primates and mammals so I'm sure humans haven't covered the whole territory.

Reason vs. Truth

It's another false dilemma to pit orthodoxy (correct beliefs as truth) against reason (frequently interpreted as pitting monotheism against science, more on that in a moment).

Additionally, reason is subject to different world perspectives, different wiring (a spatial-visual person may provide "off the wall" insights and challenges to common verbal arguments) and even very different meanings given to common words (like "deity," "divine," or "worship").  Reason is subject to a lot of things, including interpretations of facts being mistaken for fact/truth.  All that makes communicating reason across different reality tunnels very difficult but doesn't make reason wholly unreliable.

It's better to teach people how to think & process emotionally in a multidisciplined way than to argue or wager over belief/truth.  It's better for people to live their system(s) of arts and disciplines and/or religion(s) that they call theirs and do it well, with courtesy and respect for others who offer like.

Truth vs. faith?

First of all, faith is not a synonym for religion.  It'd only appear to be if the limit of one's scope is defined by orthodoxy (and you'll notice that many atheists still let monotheistic orthodoxy define their scope).

As for the search for truth, what is it?  What is truth and what types of truth are there?  And what is the search for truth, really?  For one thing, not all religions hold truth as their axis of power and reference.  For another, the search for "truth" seems to be not a thing of logic or reason as much as it is a volatile search for certainty and security.  The search and claims of "the" truth are the number one things people kill, war, maim, and MF each other over (see "Ramp of Moral Improvement," here).  Humans are primates that may all too easily follow alpha types/ideas to the point that a search for security/stability becomes a search for power and control, something that often gets abusive (see power wheels and discussion of, here).  The problem is that most don't understand power enough to differentiate and consciously better build different power metaparadigms, their flags, their basic patterns.  Notice in the last link that the meta power paradigm for abuse is called Power and Control.  Deep topic.  Don't confuse it with an anti-authoritarian or anarchist position!

Anyway, reason and religion are not the only arts and disciplines possible with which to approach most anything.  Let's say you want to pit science against religion -- not only is that myopic but it generally results in scientism vs. religionism and very intellectually dull debates.  Too bad those are the debates that linger and gain the most attention. (Not all religions are at odds with science.)

Sorry about the edits.  I often only access the screen for seconds...I'm watching the grandchildren.