What is the application of probability in our daily lives?

Well, I play a trading card game known as Magic: The Gathering. The basic goal of the game is to construct a deck out of different kinds of cards, and then pit it against an opponents deck, and (hopefully) win. Most people just take all their favorite cards and put them in a deck.

This is fine, but if you want to succeed in tournaments, you need to do some statistical math. For example, one rule is that you can only have a maximum of four cards of the same kind in the deck (with the exception being basic lands, which make everything tick). Another rule is that the deck must be a minimum of 60 cards (40 in special cases).

Right off the bat, just with these two rules, we need to do some calculation. Many decks have cards that work together in special ways, or combinations. For a tournament player, it is essential that s/he can calculate the odds of getting the right cards so that the deck functions properly.

This is why most decks are cut down to meet the 60 card minimum- it offers the best chance of drawing the needed combinations as quickly as possible. So, lets say that you have a three card combination. If the decks main focus is on completing this combo, then most players will put in four copies of each necessary card in the deck.

Quick math tells us that 4/60 = 1/15, in other words, you have a one in fifteen chance of drawing one copy of the four of any one kind of card if you draw one card at random. At the beginning of the game, players draw seven cards, which constitutes their initial hand. Assuming you make the first play (thus, you do not draw a card on your first turn), you have a 7/15 chance of holding one copy of one type of card.

Using this probability, you can find how quickly you should be able to summon your combo. Another important use of probability is the Mana Curve. Remember when I said lands make this game tick?

Well, lands produce mana, which is where the term "Mana Curve" comes from. Mana is like a currency within the game. You need a certain amount to play other cards.

In order to maximize the effectiveness of a deck, it needs to fit the Mana Curve. So, back to probability. In this game, every time it is your turn, you draw a card, and you are allowed to play one land per turn.

Every turn, a land can be used to produce mana once, but then you typically have to wait until your next turn to use it again. This being said, you should ideally have your Mana Curve set so that you could use all of your mana every turn, so that you get the most magic for your mana, so to speak. Now, tournament players often use cards that accelerate their mana curve, but most decks fit into this perfect set of numbers that have been calculated out: 24 lands, 9 cards that cost 1 mana, 8 that cost 2, 7 that cost 3, 6 that cost 4, and 6 that cost 5+.

The reasoning for this is simply that 24/60 = 4/10. This basically means that you are virtually guaranteed to be able to play a land card every turn until turn 5, where upon things are no longer certain, but at least you've had four turns to marshal your initial forces. The key to making sure that you can play for maximum mana output every turn now lies in being sure that the things that cost the right amount show up in time.

This is achieved through probability, too. Now, you know that you will have 7 cards to begin with. 7*9=63, so you know that if you have nine cards that cost one mana, you will have virtually a %100+ chance of being able to play (unlike having only 8, because 8*7=56, and 56/60 isn't equal to 1+, or a sure bet.

However, the odds are still arguably good). The same logic is used in finding the other numbers. The key to winning in tounaments often comes down to if you can increase your own tempo and mana curve, and disrupt your opponents, thus making probability crucial to winning.

Hope this example helped!

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