andrew888
Joined: Sep 22, 2013
• Posts: 52
September 22nd, 2013 at 10:09:58 PM permalink
The secondary jackpot is won by getting 2 x 3 of a kinds. How many winning combinations of 2 x 3 of a kinds in a 52 card(1 x deck) game?
andrew888
Joined: Sep 22, 2013
• Posts: 52
September 22nd, 2013 at 10:18:00 PM permalink
i.e. there are 20,358,520 combinations. How many 2 x 3 of a kind combinations?
tringlomane
Joined: Aug 25, 2012
• Posts: 6270
September 22nd, 2013 at 10:53:13 PM permalink
I'm guessing you mean player has three of a kind and dealer has three of a kind?

Possible 3 of a kinds for player 1: 4*13 = 52

Possible 3 of a kinds for player 2: 4*12 = 48

Total Combinations for player 1: C(52,3) = 52*51*50/(3*2*1) = 22100

Total Combinations for player 2: C(49,3) = 49*48*47/(3*2*1) = 18424

Probability of Player/Dealer 3 of a kinds:

52*48/22100/18424 = 0.00000613 = 1 in 163,129.166
andrew888
Joined: Sep 22, 2013
• Posts: 52
September 23rd, 2013 at 1:28:12 AM permalink
Player could also have 1 x 8 and 2 x kings and dealer 1 x king and 2 x 8 (as an example). This would also win the secondary jackpot. Making any 2 x 3 of a kinds from the 6 cards. This is common in Cambodian Casinos with a six card straight flush as the major prize. Thanks for the info. Does it still apply considering my example?
andrew888
Joined: Sep 22, 2013
• Posts: 52
September 23rd, 2013 at 5:48:30 AM permalink
Sorry wrong info in my last post. To win the second jackpot(10%) player needs 3 of a kind and dealer 3 of a kind. So the info you gave me is what i needed. I would still be interested in the odds for 2 x 3 of a kind in 6 cards. I have been considering setting up 3 x jackpots similar to a slot machine. All progressive. Straight flush in 6 cards, 2 x 3 of a kinds and a straight flush in 5 cards. To see all three jackpots increasing every day might be interesting.
avianrandy
Joined: Mar 7, 2010
• Posts: 86
September 23rd, 2013 at 6:56:28 AM permalink
Last time I was at Horseshoe Cincy,they had Million dollar 3 card poker.In order to win the million,you had to have a 6 card royal flush in diamonds.All other 6 card royal flushes paid 100K.It was not progressive,just set paytables.
andrew888
Joined: Sep 22, 2013
• Posts: 52
September 23rd, 2013 at 8:39:48 PM permalink
Quote: avianrandy

Last time I was at Horseshoe Cincy,they had Million dollar 3 card poker.In order to win the million,you had to have a 6 card royal flush in diamonds.All other 6 card royal flushes paid 100K.It was not progressive,just set paytables.

1 Million dollars is a nice payout but the odds of winning are more than 20 Million to 1.
tringlomane
Joined: Aug 25, 2012
• Posts: 6270
September 23rd, 2013 at 9:15:30 PM permalink
Quote: andrew888

Sorry wrong info in my last post. To win the second jackpot(10%) player needs 3 of a kind and dealer 3 of a kind. So the info you gave me is what i needed. I would still be interested in the odds for 2 x 3 of a kind in 6 cards. I have been considering setting up 3 x jackpots similar to a slot machine. All progressive. Straight flush in 6 cards, 2 x 3 of a kinds and a straight flush in 5 cards. To see all three jackpots increasing every day might be interesting.

For two triplets anywhere in six cards (e.g. p1 = 882; p2 = 228):

Combinations for 2 triplets:

Choose 2 ranks from 13: C(13,2) = 13*12/2 = 78

Ways to choose 1st triplet: C(4,3) = 4

Ways to choose 2nd triplet: C(4,3) = 4

Total combinations for 2 triplets in 6 cards: 78*4*4 = 1248

Total combinations of 6 cards: C(52,6) = 52*51*50*49*48*47/(6*5*4*3*2*1) = 20,358,520

Probability: 1248/20,358,520 = 1 in 16,312.916

Note this is 10 times more likely than forcing a player/dealer 3 of a kind. Because there are 72 permutations to arrange two triplets that lead to player/dealer 3 of a kind. 6 for the first tripet x 6 for the second triplet x 2 for being able to give either triplet to player 1. And there are 6! = 6*5*4*3*2*1 = 720 permutations to arrange any set of 6 cards in order.

Quote: andrew888

1 Million dollars is a nice payout but the odds of winning are more than 20 Million to 1.

Definitely and it's a harsh bet with over an 18% house edge!
andrew888
Joined: Sep 22, 2013
• Posts: 52
September 24th, 2013 at 2:51:31 AM permalink
Thanks tringlomane. Very useful information.
andrew888
Joined: Sep 22, 2013