Man, I got introduced to the card game "Set" tonight. OMG... I'm addicted! It was like a Mensa game of the month or something, I hear. You pair up sets of 3 cards by similarities & differences of the shapes on the cards. You can get a taste of the action at Setgame.com, but it's not intense like when you're playing against other people, and you only get to do 12 cards. But yea, I assure you that the actual card game is hardcore! I chose to play this game over mahjong! That's how fun this game is.
*Ok, I couldn't get this game out of my head, so I decided to do some probability calculations on it. Haha, yea, I know I'm a dork. =P But I forgot like everything I learned in statistics class, so it took me awhile, and I'm kinda iffy about my results, but here they are: The deck consists of 81 unique cards, with 4 attributes to be matched. There are 1080 favorable outcomes out of a possible 85320 (81 nCr 3) combinations. Therefore, if you picked 3 random cards out of the deck, there's approximately a 1.27% chance that it's a set.
...Seems a little bit off, and the numbers don't seem right when I use them to calculate other probabilities. I checked my work though and I can't find any mistakes. Feel free to check me: Each of the 4 qualities has 3 possibilities (3^4 = 81 cards). A set can be formed by having every quality be completely Same (S) or completely Different (D). Each character place in the 4-character sequence represents one of the four qualities. The number of ways to win, with corresponding qualities is: {SSSS=Ø, SSSD=27, SSDS=27, SSDD=54, SDSS=27, SDSD=54, SDDS=54, SDDD=108, DSSS=27, DSSD=54, DSDS=54, DSDD=108, DDSS=54, DDSD=108, DDDS=108, DDDD=216}
This was working on the assumption that every time you add a quality, the number of favorable outcomes is multiplied by 3 for Similar and 6 for Different. For example, if there were only 3 qualities, there would be 9 combinations of SSD; using the formula, there are 27 combinations of SSDS and 54 combinations of SSDD, etc. Ok, so starting with the most simple possible setup, a 9 card deck of 2 qualities (3^2), our winning outcomes would be: {SD= {A1,A2,A3; B1,B2,B3; C1,C2,C3} =3, DS= {A1,B1,C1; A2,B2,C2; A3,B3,C3} =3; DD= {A1,B2,C3; A1,B3,C2; A2,B1,C3; A2,B3,C1; A3,B1,C2; A3,B2,C1} =6}
**Oh wait, they linked to another guy's partial mathematical calculations on the site, and they seem to agree with mine. So maybe I wasn't off after all. Man, and his way was so much easier too, grrr... 81*80*1/6 =1080
*Ok, I couldn't get this game out of my head, so I decided to do some probability calculations on it. Haha, yea, I know I'm a dork. =P But I forgot like everything I learned in statistics class, so it took me awhile, and I'm kinda iffy about my results, but here they are: The deck consists of 81 unique cards, with 4 attributes to be matched. There are 1080 favorable outcomes out of a possible 85320 (81 nCr 3) combinations. Therefore, if you picked 3 random cards out of the deck, there's approximately a 1.27% chance that it's a set.
...Seems a little bit off, and the numbers don't seem right when I use them to calculate other probabilities. I checked my work though and I can't find any mistakes. Feel free to check me: Each of the 4 qualities has 3 possibilities (3^4 = 81 cards). A set can be formed by having every quality be completely Same (S) or completely Different (D). Each character place in the 4-character sequence represents one of the four qualities. The number of ways to win, with corresponding qualities is: {SSSS=Ø, SSSD=27, SSDS=27, SSDD=54, SDSS=27, SDSD=54, SDDS=54, SDDD=108, DSSS=27, DSSD=54, DSDS=54, DSDD=108, DDSS=54, DDSD=108, DDDS=108, DDDD=216}
This was working on the assumption that every time you add a quality, the number of favorable outcomes is multiplied by 3 for Similar and 6 for Different. For example, if there were only 3 qualities, there would be 9 combinations of SSD; using the formula, there are 27 combinations of SSDS and 54 combinations of SSDD, etc. Ok, so starting with the most simple possible setup, a 9 card deck of 2 qualities (3^2), our winning outcomes would be: {SD= {A1,A2,A3; B1,B2,B3; C1,C2,C3} =3, DS= {A1,B1,C1; A2,B2,C2; A3,B3,C3} =3; DD= {A1,B2,C3; A1,B3,C2; A2,B1,C3; A2,B3,C1; A3,B1,C2; A3,B2,C1} =6}
**Oh wait, they linked to another guy's partial mathematical calculations on the site, and they seem to agree with mine. So maybe I wasn't off after all. Man, and his way was so much easier too, grrr... 81*80*1/6 =1080
posted by Dear Daniel at 12:08 AM
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