I've written an article about applying statistics to deck building that would (hopefully) be of pretty general use. It even contains a download to a file that will do the math for you
@MikeTheProf so one of the fundamental issues in Vintage deck design is the variability around moxen. Many decks play out completely different when they have a t1 Moxen, White Eldrazi, as both of us are well aware, maybe being the best example. I've been tinkering with your tool but I can't figure out how to calculate for moxen or other variable mana sources.
We’re building Vintage White Eldrazi and we’d like to ensure that we have a two-mana spell to play in our starting hand at least 85% of the time. How many two-mana spells should we play in our deck
This doesn't really answer (or ask I guess) the more important question of how likely are we to play a two mana spell on turn one.
Can I use this tool to I calculate the odds of having at least 2 mana sources, 1 of which is artifact mana? Is there a way to do this without treating moxen as the desired spell, say if I want to calculate odds of turn 1 Thalia?
This particular question is relevant for a statistical tool like this because the answer would point to whether moxen or white sources or the two-drops is the limiting factor.
There's no direct way to do that with the tool, but it's something I'll consider for future updates of the CDF.
In the meantime, I would suggest that you do the two things independently. You could calculate the number of white sources you'd want and (separately) calculate how many "double mana" sources you'd want.
Once you know those numbers, you could then find the likelihood that you'd have a white source with your Thalia (from the Mana Stats tab) and (separately) the likelihood that you'd have a Mox (from the Spell Stats tab). The probability of having both would be (approximately, since they technically depend on each other):
1 - (likelihood of white source w/ Thalia)*(1 - likelihood of a Mox).
That would give you the percentage of hands that either have a Thalia with the white source and a Mox or don't have a Thalia at all.
Hopefully that helps
It doesn't take mulligans into account though, nor does it help you build a manabase
@ribby I've given it some thought and I think I'll add a tab to the CDF tool that does what the website you linked does, but includes mulligans as well. Thanks to you and @wappla for the conversation here
My next article will likely be an update to the CDF and example questions/answers to questions like wappla's (but done without approximation and including mulligans.