3rd Commander (EDH) and Probability for Deck Construction: Applications of the fraction 1/5.

Hopefully, you don’t try to rig your deck through cheating.  This is for the people that are interested in making their MTG a game of chance.  It’s only natural to want to select certain cards, and often cards can be grouped, such that in a 100 card Commander deck, or any deck for that matter, there are certain formulas that can be used to determine things such as how many lands one is likely to get in their opening hand, or how many elves one is likely to have by turn three.

1/5

Let’s start with the basics.  The first blog was on the fraction ½.  Now, we will start with the fraction 1/5.  In a Commander deck, there are 100 cards and a Commander.  Consider that 99 cards might as well be 100 cards.

Where might this fraction, 1/5, be useful?  1/5 is useful for any number of scenarios.  For example, you might want to have 1/3 mana, but 1/5 mana accelerators.   That is, if you have 20 out of 99 cards, that fraction is equal to roughly 1/5.  Keep in mind this is probability so the fractions need not be exact, and one should round numbers where it is appropriate.  For, example, just because one can use a rounding technique doesn’t mean that it should be used.

Consider this, if one in every 5 cards is a mana accelerator, then you have a 20% chance of drawing a mana accelerator.  In an opening hand one has 7 cards.  Thus, because 7>5, chances are you will have one mana accelerator in your opening hand.  The formula would be 20/99*7=1.4 mana accelerators.  Thus, since 1.4<1.5 it is probably best to consider that you will probably only have one of these cards.

First, consider 7 or 8 cards.  If 1 out of every 5 cards, or roughly 20% of your deck is mana accelerators, you can multiply 7 or 8 by 1/5.  In the case that 8 cards are drawn, 20/99*8=1.6.  Thus, in that situation it is likely that you will have 2 mana accelerators through rounding.

Consider on turn 1 you have ~1 mana accelerators, as has already calculated.  That means that on turn 4 you have ~2 mana accelerators because 20/99*10=2.02.  That is, in a normal scenario, it is likely that you will likely have 10 cards by turn 4, and 2 of those cards will likely be mana accelerators.

This figure for mana acceleration can also be factored in with the amount of land you have in your deck, especially considering how many lands it takes to cast a mana accelerator.  For example, if you have 1/3 lands in your deck and Llanowar Elves, which costs 1 mana, if you have that in your opening hand, then you will probably be able to cast that in your opening turn.  Doing so would essentially make it so that it would be more likely to make a 2 mana play on your opening turn.  In fact, Llanowar Elves is one of my favorite cards.  There are some cards like it, such as Fyndhorn Elves that accomplish the same thing.  Thus, it is possible through including cards like Llanowar Elves and Fyndhorn Elves to improve the chances that you will be able to cast 2 mana on your first turn and so on.  In the case of other games, such as Extended, instead of putting both Llanowar Elves and Fyndhorn Elves in your deck, you can simply  include up to 4 Llanowar Elves cards.