In this entry, I discuss the basics of the concept of
probability and how it can be applied in a game of MTG.
The probability of the occurrence of an outcome in an event
is quantified as a number between 0 and 1. The closer the value is to 1, the
higher the chance that the outcome will occur. Calculating the probability that
an outcome, denoted by A, will occur
thus requires knowing two quantities. First, the number of all possible
outcomes of the event which we denote by N,
and second, the number of outcomes among those that are identical to the
outcome that we are interested in which we denote by X. Given these quantities, the probability that A will occur, P(A)=
X/N.
For example, in a mirror match between two RB aggro players,
A and B, let us say that Player A is at 4 life with a Glorybringer and a Goblin
Chainwhirler attacking Player B who is at 9 life with a clean board and 5 lands.
Player A has no cards in hand but has a Chandra in play (which he already used)
while Player B has a Lightning Strike in hand.
Given this situation, Player A is deciding whether to use
the Lightning Strike to kill the goblin, taking the damage from the 4/4 dragon
and falling to 5 life or to shoot the instant at Player A, bringing his
opponent down to 1 life. Player B knows that even if he uses the instant to
kill the goblin, he will still die to another attack from the dragon and tick
up (2 damage) from Chandra in the next turn. However, if he does not kill the
goblin and draws unlicensed disintegration the next turn, then he will be able
to kill both the dragon and the goblin but he will still die to Chandra’s +1
ability since he will be at 2 life from taking damage from the goblin. Based on
what is in the public zones (graveyard, battlefield, exile), Player B knows
that he only has 30 cards left in his library, which include 1 Chandra, 4
Unlicensed disintegration, 1 shock, 1 lightning strike, 4 Glorybringer, and 1 Earthshaker
Khenra. Let us assume that no other cards in the library are relevant for the
next turn cycle. Based on this information, all of the cards mentioned except
unlicensed disintegration will allow Player B to win on his turn if he chooses not to
use the lightning strike to kill the goblin and shoots the instant to the dome instead. Thus,
the outcome we are interested in is Player B drawing a card that wins him the
game in his next draw step. There are 30 possible outcomes since there are 30
cards left in the deck and of these, 1 Chandra, 1 shock, 1 lightning strike, 4 Glorybringer,
and 1 Earthshaker Khenra fit the outcome that we are interested in. That’s a
total of 8 cards. So, the probability that Player B will draw a card that wins him
the game is equal to 8/30 (26%). On the other hand, the probability that Player
B will draw an unlicensed disintegration is only 4/30 (13%). Thus, we can say
that Player B is twice as likely to draw a card that wins him the game if he casts
it at the opponent instead of the goblin than he is to draw unlicensed to keep
from dying. Based on these numbers, it is sound judgment for Player B not to
kill goblin and instead shoot the lightning strike to the dome.
But what if Player B does so, and then draws Unlicensed Disintegration?
He dies the next turn and when he looks at his next card, it’s one of the 4
Glorybringers in the deck which would have won him the game had used the
lightning strike to kill the goblin. Well, this of course can happen. In fact,
based on our computation, it will happen about 13% of the time in the said
situation. However, this does not mean that Player B’s decision to spare the
goblin and burn its master instead is incorrect. In fact, if you were placed in
this exact same situation for 100 games and you choose the same play over and
over again, you will definitely win about twice as many times as you will lose.
Thus, in any single game, the actual outcome of a decision will vary, but playing
smart by using the concept of probability consistently is good magic that will have
noticeable rewards.
May the shuffler be with you!
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