You can see the characters of Fruits Basket playing Dai Hin Min both in the manga and anime. Ever wondered what the HECK Dai Hin Min IS? It's a card game, and the rules are pretty simple! I play it with my friends at school often!

What you Need to Play: A full deck of cards, including jokers.

lowest value: 3 4 5 6 7 8 9 10 J Q K A 2 :highest value

Rules: Shuffle your deck of cards and pass them out until all the cards are passed out. You can play with 3 people and up. I wouldn't really advise playing with more than 7 or 8 people, though. If you're playing with only a few people, you might end up holding a rather lot of cards.
The person to the LEFT of the dealer always starts, and the game is played 'clockwise'. That first person can put down 1 to 4 cards. Let's say, for EXAMPLE, that they put down two "5"s. The next person in the rotation has to match the number of cards, in this case, two cards, because the beginner put down TWO "5"s. The person must put down 2 of cards that are greater in value than five, or equal. I made that handy chart above.
Following that chart, the second player can put down: Two "5"s, Two "6"s, Two "7"s, Two "8"s, Two "9"s, Two "10"s, Two "J"s, Two "Q"s, Two "K"s, Two "A"s, or Two "2"s. (Remember, "2" is the highest value card!)
The next person, of course, has to beat the player before them's play. Remember the example? The first person put down two "5"s, let's say the second person put's down two "8"s. Now for the third person. Let's say THEY put down two "2"s. Now let's say we're playing with THREE people. That means it's the first person's turn again. But the only way to beat two "2"s is...two "2"s. Well, let's say the first person doesn't HAVE two "2"s. They can PASS. The turn goes to player number 2. THEY pass. This means that everyone except the person who put down the cards has passed. The cards are put to the side, and that person can now start over any way they want with any number of cards they want. This means player number 3 could now put down 3 "7"s if he wanted.
It went like this:
DEAL
1) two "5"s
2) two "8"s
3) two "2"s
1) PASS
2) PASS
*cards are cleared*
3) three "7"s

Now, if a person who is 'starting' puts down FOUR OF A KIND, it's called a REVOLUTION. This causes the low-high order of cards to reverse. Look at my list/chart. A revolution means that "2" becomes LOWEST, and "3" HIGHEST. Revolution stays in effect until someone has four of a kind again. This is a COUNTER REVOLUTION.
So, what's the object of the game? It's to get rid of all your cards first. Or, at least, not last. The only person left with cards in their hand is the Dai Hin Min, or the "poor man". THe person who gets rid of their cards FIRST is the winner. Oh, and JOKERS are WILD. If someone puts down two "3"s, you can play one "3" and a joker, for example.

An Example Game with Fruits Basket players!
Tohru deals.
Yuki: one "4"
Hana: one "4"
Uo: one "3"
Kyo: one "7"
Tohru: one "9"
Yuki: one "J"
Hana: one "K"
Uo: PASS
Kyo: one "A"
Tohru: PASS
Yuki: one "A"
Hana: one "2"
Uo: PASS
Kyo: PASS
Tohru: one "2"
Yuki: PASS
Hana: PASS
Uo: PASS
Kyo: PASS
*cards are set to the side*
Tohru: four "8"s REVOLUTION!
Yuki: PASS
Hana: PASS
Uo: PASS
Kyo: PASS
*cards are set to the side*
Tohru: three "J"s
Yuki: three "9"s
Han: three "5"s
Etc. etc. Notice after Tohru's REVOLUTION, Yuki and Hana-chan had to put down cards that were LOWER in value.

Okay, so my directions are WAY overly complicated. Easier to understand directions are at TOKYOPOP. Their version really isn't any different from mine, except they mention one version I've never heard of. I've never even seen anyone play it. Some sort of version where if someone's card is a spade, you have to follow all the same rules AND make sure your card is ALSO a spade. etc.

Anyway, if you have trouble understanding my directions for Dai Hin Min (honestly, I'd be surprised if you DID understnad them) there's other pages out there with directions, like TOKYOPOP, which I linked to above.