Here we go .... another probability problem for those game designers out there that have mathematics majors!

I've got a basic grasp of probability, but am not really sure where to start with this one, so any help would very much be appreciated!

Basically, I'm trying to put together an excel spreadsheet that will give me an idea of various probabilities.....

Assumptions:

a) A pack of cards consists of the following:

Set 1 (6 cards)

Card A x 1

Card B x 2

Card C x 3

Set 2 (15 cards)

Card D x 4

Card E x 5

Card F x 6

Set 3 (24 cards)

Card G x 7

Card H x 8

Card I x 9

Total = 45 cards

b) There are four players and they receive the following cards:

4 cards each at time 0

2 cards each at time 1

2 cards each at time 2

2 cards each at time 3

c) When a player obtains a set (ie one of each of the cards in that set .. eg 1 x A, 1 x B, 1 x C = 1 set), those cards go back into the pack.

So - again apologies for having absolutely no clue about where to start - is there a mathematics professor out there that can explain how I can calculate:

1. The probabilty that at least one player will receive a Set at times 0, 1, 2 or 3?

2. The probabilty that one or more players will receive a Set at times 0, 1, 2 or 3?

3. What is the average number of sets a player will receive by times 0, 1, 2 or 3?

3. How many cards will normally be left in the pack at times 0, 1, 2 or 3?

Can anyone help ......... ?

Thanks in advance for any comments, tips or steers.

Cheers ..... TwoBob

Hello! I have only just begun looking into card probabilities for a game I'm developing, but I have learned quite a bit and can possibly get you started in the right direction.

Here's a great link to poker hand compotations that has helped me get a grasp on the probability of cards. The math is mostly poker-centric, but you can extrapolate a lot of the information you'll need.

The first question I have is...how much probability and statistics do you know or remember from school? I remembered a little about factorials and that was enough to make sense of the information on the web site.

Just to start with the basics, the number of possible 4 card hands from a set of 45 cards is expressed as C(45, 4) and is calculated as follows:

C(45, 4) = 45!/4!(45-4)! = 45 * 44 * 43 * 42/4 * 3 * 2 * 1 = 148,995

This will help you calculate probabilities of a given hand based on the total possible combinations of any given hand.

OK, that's the easy part...