Hi all,
I'm quite new on this forum although I've been reading your posts for some time before registering.
I'm designing a card game where all players have to bid cards from their hand to collect those cards with which they can make good scoring hand of 5 cards. at the end of the round each player will have (in a 3 player game) about 1/3 of the deck. The deck consists of 55 cards of 5 suits with 13, 12, 11, 10 and 9 cards each numbered from 1 to x, where x is the # of cards in the respective suit. The reason for the unequal # of cards in each suit is to eliminate the chance for a draw.
Now for the statistical question, I know some statistics and some chance calcutaions but most is done intuitive. For the scoring at the end of the round I opted to use the rarity of the combination for determining which hand wins:
(from top to bottom)
1) 5 of a kind.
-There are 9 possible combinations (remember only the numbers 1-9 are present in each suit).
2) straight flush of 5.
-There are 35 possible combinations (9+8+7+6+5)
4) straight flush of 4.
-There are 1970 possible combinations (10+9+8+7+6 = 40 of these there are 10 combinations where only 1 possible card is needed to makes it a straight flush of 5 (1 to 4 or 10 to 13 f.e.) and 30 combinations needing 1 of 2 cards (2 to 5 etc.) so 10 * 50 (55 - 4 (the cards making up the straight) - 1 (the possible card making it a straight of 5) + 30 * 49 (55 - 4 -2 (the possible cards making it a straight of 5 ) --> 500 + 1470 = 1970.
3) 4 of a kind.
-There are 2300 possible combinations (((9 * 5 (for each combination of 1-9)) + 1 (4 cards with 10)) * 50 (55 - 4 (the 4 cards that make up the 4-of-a-kind) -1 (the card that will make it a 5-of-kind)))
So 5 of a kind wins from straight flush of 5 wins from straight flush of 4 wins from 4 of a kind, to me this seems intuitively wrong (being from a scientifical background I know that feeling intuitively wrong means, as much as not, statistically correct). this derivation from the "normal" poker-like scoring can probably be attributed to the unequal suits in the deck.
Are my calculations (or rather, is my approach) correct? Is more number crunching needed to take into account that each player can choose their 5 card hand from about 18 cards in their hands?
If those that have a firmer grasp on statistical calculations than me could help me here I would be greatly appreciated.
Arjen
