Reposted, because I know Frank could appreciate it

Stories about games that you run and/or have played in.

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Username17
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Re: Reposted, because I know Frank could appreciate it

Post by Username17 »

Here's the deal with probabilities of getting a card in an 8 card hand:

If your favorite card is, for example, only one card in a deck of 60 and you draw 8 cards, then your first card has a 1 in 60 chance of being the card in question & a 59 in 60 chance of not being the card in question.

But here's the thing: no matter how it came out, the next card is being drawn from a 59 card deck. If the first card was the magic card, then of course the second card has a zero in 59 chance of being the right one (of course, who gives a damn, you already have the card!); and if the first card was not your favorite card your second pull has a 1/59 chance of being the magic card. And so on for each of 8 pulls (the 8th having either a 1 or 0 out of 53 chance).

So the chances of pulling the card in question are:

1/60 + 59/60 * 1/59 + 59/60 * 58/59 * 1/58 + 1/59 + 59/60 * 58/59 * 57/58 * 1/57 ... ...59/60 * 58/59 * 57/58 * 56/57 * 55/56 * 54/55 * 53/54 * 1/53.

Sound complicated? It is. Fortunately, there's an easier way to do it. Did you notice how there are really only two possibilities, drawing the card and not doing that? Right, all probabilities always add up to 100% because something happens no matter what card you pull. We can use that.

We can use it because the chances of not pulling our favorite card are very explicable. It's just:
59/60 * 58/59 * 57/58 * 56/57 * 55/56 * 54/55 * 53/54 * 52/53 = 52/60 = 13/15 or 87%

So your chances of not getting your card are 87%, what do you think your chances of getting your card are?

-Username17
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