Cactus Game Design Message Boards

If I'm understanding you correctly, then the greyed out lines are:

The first line is the probability of getting the number you inputted for X
The second one is the probability of getting less than X
The third one is the probability of getting less than or equal to X
The fourth one is the probability of getting more than X
The fifth one is the probability of getting more than or equal to X

X is the number of successes, which for a hand is the number of copies you get.

Finally I want to say that this program is slightly inaccurate for Redemption since Lost Souls don't take up draws (you replace them) and that makes it somewhat more complex to get the actual probabilities.

Quote from: ChristianSoldier on September 12, 2013, 11:54:47 PM

Finally I want to say that this program is slightly inaccurate for Redemption since Lost Souls don't take up draws (you replace them) and that makes it somewhat more complex to get the actual probabilities.

In that case, using the previous example, could you calculate the probabilities at 49 population size (7 less representing the souls being replaced)?

I'm thinking it will work, but I'm not sure.

To find the probability of drawing an arbitrary number of LSs in the opening hand (including redraws):

First start with the probability of drawing 0 LSs. This can be done by using the program, putting the deck size as the population size, putting the number of successes as #LS, the sample size as 8, and the number of successes as 0. In MKCs example of a 56 card deck with 7 LS, this is 0.317 (31.7%)

The probability of drawing exactly 1 LS, you start with the probability of drawing exactly 1 LS in the first 8. For this you can use the calculator as MKC mentioned, with number of successes = 0. Then multiply that by the probability that the top card is not an LS (which is going to be 42/48 in the 56 card example), since out of 48 remaining cards, there are 6 LSs, and 42 non-LSs. In the example, 0.423 is the probability that exactly 1 LS is in the first 8, and multiplying that by 42/48 (.875). .423*.875=.370 = 37%

Now it starts tricky. For the probability of drawing exactly 2 LSs, you either have to draw 1 LS in the original 8, have the top card be an LS, and have the next card not be an LS, or you have to draw 2 LS in the original 8, and have both the next two cards not be LSs. For the first case, it will be .423*.125*42/47=.047 (4.7%). In the second case, we start with the calculator and #successes in sample = 2 (.207), and multiply that by 43/48*42/47 (probability that top card is a non-LS AND that next card is a non LS). This is .166 (16.6%) thus the probability of drawing exactly 2 LSs = 4.7+16.6 = 21.3%

Possibilities 3-7 get decidedly more complicated (but also more rare, as based on the previous calculations, the probability of drawing 0, 1 or 2 LSs is ~90%. I could probably come up with an Excel spreadsheet at some point, I suppose, if anyone is interested.