User:Dark ruler ha des

Calculating the odds
It is hard enough to make a deck, but if you want to make your deck the perfect deck, you must calculate the odds of drawing a card you need in the beginning of the duel. To make the odds of drawing that card higher you can use "Deck Thinner". But these cards take up place that could be used for more usefull cards. How to calculate these odds? well we use a simple formula: $$r/n + r/n-1 + r/n-2 + r/n-3 + r/n-4 + r/n-5 = x $$

r= The number of copies included of the same card.

n = The number of cards included in your deck.

x= the number that you have to multiply by 100 to get the percentage of drawing that cad during your first turn.

The more cards you include in your deck the lower the percentage and how more copies ( wich is limited by 3 or may be even lower if the cards are limited) how higher the percentage.

Having every card at his maximum limit you can include in the deck has also a negative effect. If you have 3 copies in your deck of the same card, chances of getting the same card twice in your first turn will be higher. This can be very anoying because you would probably just want to use 1 of them instead of 2. The formula to calculate how the odds are of drawing a card of wich you already have a copy in your hand during the first turn can be calculated by the above formula but after you draw the card aplly r= r-1. For example:

$$3/40 + 2/39 + 2/38 + 2/37 + 2/36 + 2/35 = 0.345666097 $$

0.345666097*100≈34.6% of chance drawing a card included 3 times in the deck twice in your first 6 cards. This formula depends on when you draw the card.

To simplify the above formulas:
 * if you add a copy of a card to your deck you'll increase the chance of drawing it during your first turn by 16%. Having one copy of a card in your deck it chances are 16% of being drawn in your first turn.


 * if you draw your first card, the chance of having it once more in your hand during your first turn is the percentage of the first formula minus 14%. For example: the odds of drawing a card included 3 times in a deck(containing 40 cards) during your first turn is 48%. If this was the first card you drew, the possibillity of having the same card in your first turn is around 34%.