Thread Rating:

andrew888
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
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
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
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
tringlomane
  • Threads: 8
  • Posts: 6284
Joined: Aug 25, 2012
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
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
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
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
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
avianrandy
  • Threads: 8
  • Posts: 1835
Joined: Mar 7, 2010
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
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
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
tringlomane
  • Threads: 8
  • Posts: 6284
Joined: Aug 25, 2012
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
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
September 24th, 2013 at 2:51:31 AM permalink
Thanks tringlomane. Very useful information.
andrew888
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
October 9th, 2013 at 10:07:42 PM permalink
I would like to know the odds for a six card straight flush but with 2 different conditions.
The first straight flush is using any six cards e.g. player has 7,10,Q of hearts and dealer has 8,9,J of hearts.
The second straight flush is a player/dealer straight flush e.g. the player has 7,8,9 of hearts and the dealer 10,J,Q of hearts or visa versa.
How many winning combinations for these?
andrew888
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
October 9th, 2013 at 10:56:44 PM permalink
Quote: andrew888

I would like to know the odds for a six card straight flush but with 2 different conditions.
The first straight flush is using any six cards e.g. player has 7,10,Q of hearts and dealer has 8,9,J of hearts.
The second straight flush is a player/dealer straight flush e.g. the player has 7,8,9 of hearts and the dealer 10,J,Q of hearts or vice versa.
How many winning combinations for these?

andrew888
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
October 10th, 2013 at 4:16:42 AM permalink
I think the first example has 36 winning combinations.
miplet
miplet
  • Threads: 5
  • Posts: 2143
Joined: Dec 1, 2009
October 10th, 2013 at 4:22:58 AM permalink
Quote: andrew888

I think the first example has 36 winning combinations.

the second had 72 if counting the royal 6 card. A-6 to 9-A 9 ways 4 suits. And the player or dealer can have the low end.
“Man Babes” #AxelFabulous
andrew888
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
October 10th, 2013 at 11:45:45 PM permalink
@miplet i am fairly sure we are both wrong having looked at tringlomanes previous posts. The 2nd example should be 10 times harder to win as in the example with the 2 x three of a kinds. 6 cards have 720 different permutations so i think there are alot more winning combinations. My math is not good enough to calculate the correct odds. It's a bit shameful to admit to that as i work in a Casino.
andrew888
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
October 10th, 2013 at 11:50:00 PM permalink
The first example would have all the combinations in the second example and alot more.
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
October 11th, 2013 at 8:06:08 AM permalink
Quote: andrew888

@miplet i am fairly sure we are both wrong having looked at tringlomanes previous posts. The 2nd example should be 10 times harder to win as in the example with the 2 x three of a kinds. 6 cards have 720 different permutations so i think there are alot more winning combinations. My math is not good enough to calculate the correct odds. It's a bit shameful to admit to that as i work in a Casino.



The problem is that you are talking hits without talking about the cycle.

In the first example, there are 36 straight flushes out of C(52,6). In the second example, there are 72 straight flushes out of C(52,3)*C(49,3). So, the 2nd example is 10 times harder to win.
I heart Crystal Math.
andrew888
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
October 11th, 2013 at 9:29:54 AM permalink
Ok thanks.
So for the first example how many winning combinations out of 20,358,520 ?
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
October 11th, 2013 at 10:37:37 AM permalink
Quote: andrew888

Ok thanks.
So for the first example how many winning combinations out of 20,358,520 ?



Quote: tringlomane


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



Quote: CrystalMath


In the first example, there are 36 straight flushes out of C(52,6).

I heart Crystal Math.
andrew888
andrew888
  • Threads: 5
  • Posts: 64
Joined: Sep 22, 2013
October 11th, 2013 at 6:09:15 PM permalink
@crystalmath thanks for your help and patience.
beachbumbabs
beachbumbabs
  • Threads: 101
  • Posts: 14268
Joined: May 21, 2013
October 11th, 2013 at 10:27:04 PM permalink
CM is the coolest!
If the House lost every hand, they wouldn't deal the game.
hwccdealer
hwccdealer
  • Threads: 11
  • Posts: 365
Joined: Jun 4, 2013
October 22nd, 2013 at 11:38:58 AM 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.



That must be a Caesars exclusive; the only place I saw that in Vegas was at Casears Palace.

All we have here at Hollywood Columbus is a progressive jackpot starting at $1,000 for AKQ of spades and a cluster of fools that tries to win it when it gets high enough.

Of course, according to the Wizard's site, there are 22,100 possible three-card hands, and the payout on the progressive is as follows (it's a $1 bet):

Straight pays $6 (720 possible hands)
Trips pays $60 (52 possible hands)
Straight flush (not royal) pays $70 (44 possible hands)
AKQ of any suit but spades pays $500 (3 possible hands)
AKQ of spades pays the whole jackpot (starting at $1,000)
The total payout excluding the jackpot is $12,090, so the jackpot needs to be at least $10,010 for it to make mathematical sense to play the jackpot.
  • Jump to: