

I'm in the process of making a set collection game and need some help with calculating relative ranking probabilities.
The deck has a total of 42 cards with 6 suits and numbered cards from 17 in each suit.
Let's assume you collect 5 cards, is it more difficult to collect a straight flush or 5 of a kind? If so, does anyone know how less likely one of these is in comparison to the other? Also, would the same apply for a 4 card straight flush vs. 4 of a kind.
Thanks in advance!

Dan Blum
United States Wilmington Massachusetts

There are 42 ways to get five of a kind: 7 possible ranks, and in each case you have to leave out 1 suit.
There are 18 ways to get a straight flush: 6 possible suits, and in each case there are 3 possible straights (15, 26, 37).
Since there are 850,668 possible 5card hands neither of these is very likely to be dealt.

Curt Carpenter
United States Kirkland Washington

Without knowing the rules, I guess the question should be which is more likely to acquire by random chance, i.e. chance of drawing 5 cards and getting one of the sets in question.
5 of a kind: There are 42 unique sets of 5 of a kind. I.e. for each number, you have all suits except 1, so 7 numbers times 6 ways per number. Straight flush (of length 5): There are 16 unique straight flushes (of length 5), 3 per suit. So straight flush is significantly harder. By random draw at least.
4 of a kind: 7 numbers times 6C2 (15) = 105. Straight flush (of length 4): 24 (4 per suit).

Dan Blum
United States Wilmington Massachusetts

Using similar calculations I believe that there are 3,780 ways to get four of a kind (assuming that the fifth card does NOT match so it is not also five of a kind) and 876 ways to get a fourcard straight flush.



tool wrote: There are 42 ways to get five of a kind: 7 possible ranks, and in each case you have to leave out 1 suit.
There are 18 ways to get a straight flush: 6 possible suits, and in each case there are 3 possible straights (15, 26, 37).
Since there are 850,668 possible 5card hands neither of these is very likely to be dealt.
Super. Thanks. I started going down that line of reasoning, but then began to wonder if I was thinking about it correctly.

Dan Blum
United States Wilmington Massachusetts

curtc wrote: Without knowing the rules, I guess the question should be which is more likely to acquire by random chance, i.e. chance of drawing 5 cards and getting one of the sets in question.
5 of a kind: There are 42 unique sets of 5 of a kind. I.e. for each number, you have all suits except 1, so 7 numbers times 6 ways per number. Straight flush (of length 5): There are 16 unique straight flushes (of length 5), 3 per suit. So straight flush is significantly harder. By random draw at least.
4 of a kind: 7 numbers times 6C2 (15) = 105. Straight flush (of length 4): 24 (4 per suit).
Curt, for the fourcard hands you need to account for the possible fifth cards. (There are 36 in the four of a kind case and either 36 or 37 in the straight flush case, depending on the straight flush.)



tool wrote: curtc wrote: Without knowing the rules, I guess the question should be which is more likely to acquire by random chance, i.e. chance of drawing 5 cards and getting one of the sets in question.
5 of a kind: There are 42 unique sets of 5 of a kind. I.e. for each number, you have all suits except 1, so 7 numbers times 6 ways per number. Straight flush (of length 5): There are 16 unique straight flushes (of length 5), 3 per suit. So straight flush is significantly harder. By random draw at least.
4 of a kind: 7 numbers times 6C2 (15) = 105. Straight flush (of length 4): 24 (4 per suit).
Curt, for the fourcard hands you need to account for the possible fifth cards. (There are 36 in the four of a kind case and either 36 or 37 in the straight flush case, depending on the straight flush.)
Thanks again. The rules are still being worked out. But, for your information, players will be able to basically bid for different cards in an effort to collect different sets and the sets can score victory points. I needeed a general idea about the difficulty of acquiring eah kind of set so as to award an appropriate amount of victory points. The exchange of ideas above showed me that I was generally on the right track, though I wasn't completely sure. Sometimes I've learned some things in trying to do statistics that seem counterintuitive.


