Quote:
Originally Posted by NotoriousDJ
Thanks for your help guys. I'll level with you, this is for a game Im designing which requires the probabilities of poker hands (from Royal flush to one-pair or high card) and one of the 'ultimate' goals is to get what I call '5 of a kind' in which it is simply 4 aces and one Joker.
@whosnext I did your first calculation in my first ever attempt at working this out haha:
54! / 5! x 49! (so the number of possible ways in a 54 deck divided by the amount needed and the amount left over) - all together I got 3,162,510 possible dealings in this game. Does that math sound right?
Yes, I and many other people write this as C(54,5) where the C is referred to as the "Choose" function. So you would say this as "54 choose 5". And the formula is what you typed above.
Quote:
Originally Posted by NotoriousDJ
There's another outcome I need help with. What is the probability of dealing a flush consists of 5 cards of the same colour? (regardless of suite)
Do you mean either all 5 red cards or all 5 black cards (with no jokers)?
Let's tally it for red, and then multiply our result by 2 to include black (obviously the prob of 5 black cards = prob of 5 red cards).
How many red cards are in the deck?
How many do we need to select (choose)?
How many ways are there to have a "qualifying" hand (5 red cards)? [Hint: this will be a Choose function.]
Multiply by 2.
Remember the total number of possible 5-card hands that you derived above.
Divide the first number by the second number.