Puzzle.... number of hands

I am new to poker and want to understand the game well and step by step.

I have been trying to understand how the number of possible 4 of a kind in a deck is 624.

Have found some answers in the internet, but they explain it with maths and I miss the point, when the answer is shown (have a solid knowledge of basic maths, but I just don't get this one). However much I think I can only find 13 hands of 4 of a kind.

Hope some poker-expert here can explain how we get the answer without too much maths or refer a site where I can find the answer?

Thanks in advance.
Kind regards
Leony.

leony1966 said:

I have been trying to understand how the number of possible 4 of a kind in a deck is 624.

Click to expand...

Well you have to realise that 4 of a kind is a 5 card poker hand,

So AAAA2 is not the same as AAAA3

13 different 4 of a kind hands x 48 possible kickers = 624

Hope i kept the math to a min

there are 13 four of a kinds possible like four of each of the following: 2-3-4-5-6-7-8-9-J-Q-K-A

so it goes like this:

2222
3333
4444
5555
6666
7777
8888
9999
TTTT
JJJJ
QQQQ
KKKK
AAAA

but the above are not complete hands without the fifth card so here are all the possible four of a kind hands

22223
22224
22225
22226
22227
22228
22229
2222T
2222J
2222Q
2222K
2222A
33332
33334
33335
33336
33337
33338
33339
3333T
3333J
3333Q
3333K
3333A
44442
44443
44445
44446
44447
44448
44449
4444T
4444J
4444Q
4444K
4444A
55552
55553
55554
55556
55557
55558
55559
5555T
5555J
5555Q
5555K
5555A
66662
66663
66664
66665
66667
66668
66669
6666T
6666J
6666Q
6666K
6666A
77772
77773
77774
77775
77776
77778
77779
7777T
7777J
7777Q
7777K
7777A
88882
88883
88884
88885
88886
88887
88889
8888T
8888J
8888Q
8888K
8888A
99992
99993
99994
99995
99996
99997
99998
9999T
9999J
9999Q
9999K
9999A
TTTT2
TTTT3
TTTT4
TTTT5
TTTT6
TTTT7
TTTT8
TTTT9
TTTTJ
TTTTQ
TTTTK
TTTTA
JJJJ2
JJJJ3
JJJJ4
JJJJ5
JJJJ6
JJJJ7
JJJJ8
JJJJ9
JJJJT
JJJJQ
JJJJK
JJJJA
QQQQ2
QQQQ3
QQQQ4
QQQQ5
QQQQ6
QQQQ7
QQQQ8
QQQQ9
QQQQT
QQQQJ
QQQQK
QQQQA
KKKK2
KKKK3
KKKK4
KKKK5
KKKK6
KKKK7
KKKK8
KKKK9
KKKKT
KKKKJ
KKKKQ
KKKKA
AAAA2
AAAA3
AAAA4
AAAA5
AAAA6
AAAA7
AAAA8
AAAA9
AAAAT
AAAAJ
AAAAQ
AAAAK

so this is 156 different four of a kind hands times it by 4 you get 624 different four of a kind hands.

why times it by 4?

well here is why:

22223d
22223c
22223h
22223s


you get my drift?

oh and Welcome to cards chat:hello:


I did post this in your introduction thread probablt at the same time you were making this thread.
[old link~tb]

Thanks and at last I get it.

Tenbob and Holduplaya,

Thanks so much for taking the time to answer.

Now I get it. 4 cards won't make a hand, it has to be 5 cards. ......... And of course the 5th card counts too, in evaluating the hand when playing.

Thanks again.


L.

Great post Holduplaya, but Tenbob had already answered (and in 4 lines!)

Holduplaya was just going for a record for the longest post. LOL. Someone dodging work for 15 min while he did all that typing or cut and paste.

Boss gone for the day or what?