Elements the Game Forum - Free Online Fantasy Card Game
Opponents, Strategy and Decks => Strategy => False Gods => Paradox => Topic started by: Bloom on July 27, 2012, 05:17:43 pm
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So I'm just wondering for my own personal intrigue, what the odds of Paradox drawing his first Deja Vu 18 cards in. He has a 100-card deck. 16 of them are Deja Vu's. Now just with this picture, one could assume that He was using all of his time quanta on Hourglasses but that wasn't the case. The first HG was played turn 3. Then the next turn 5. The last came the same turn as the first Deja Vu.
(http://img819.imageshack.us/img819/7332/51969222.png)
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84/100 * 83/99 * 82/98 * 81/97 * 80/96 * 79/95 * 78/94 * 77/93 * 76/92 * 75/91 * 74/90 * 73/89 * 72/88 * 71/87 * 70/86 * 69/85 * 68/84 * 67/83 * 16/82
I don't want to multiply that out, but the first 17 fractions represent the cumulative odds of drawing a non deja vu card from the deck, which starts out with 84 non deja vu cards and 100 cards total; both obviously drop by 1 each time a card is drawn. The last fraction, 16/82, represents the odds of drawing the first one of the 16 deja vus as the 18th card.
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Plugged what dragon typed out above into WolframAlpha and it came out as 0.006051..
Though I feel that his calculation is wrong, because it multiplies nineteen fractions when we are only drawing 18 cards (???).
I think the proper equation is 84/100 * 83/99 * 82/98 * 81/97 * 80/96 * 79/95 * 78/94 * 77/93 * 76/92 * 75/91 * 74/90 * 73/89 * 72/88 * 71/87 * 70/86 * 69/85 * 68/84 * 16/83 (http://www.wolframalpha.com/input/?i=84%2F100+*+83%2F99+*+82%2F98+*+81%2F97+*+80%2F96+*+79%2F95+*+78%2F94+*+77%2F93+*+76%2F92+*+75%2F91+*+74%2F90+*+73%2F89+*+72%2F88+*+71%2F87+*+70%2F86+*+69%2F85+*+68%2F84+*+16%2F83), which gives 0.007406..
Just to check, I'll use the tool used to get stats for opening hands (http://stattrek.com/online-calculator/hypergeometric.aspx) and plug in 100, 16, 17, 0. What this does is find the odds of getting 0 Deja Vu in the first 17 cards - which is what should happen if the first Vu is card #18. Hypergeometric Probability: P(X = 0) is 0.03841811..
Finally, multiply by 16/83, which is the chance of drawing the first Vu as card #18.
Result is the same - 0.0074.. - so you had some interesting luck today. 75% of a 1% chance :P Though I ignored automulligan, which shouldn't make too much of a difference.