three card poker bonus (6 cards). 2 x 3 of a kinds, how many winning combinations ????
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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
Quote: avianrandyLast 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.
Quote: andrew888Sorry 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: andrew8881 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!
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?
Quote: andrew888I 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?
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.Quote: andrew888I think the first example has 36 winning combinations.
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.
So for the first example how many winning combinations out of 20,358,520 ?
Quote: andrew888Ok 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).
Quote: avianrandyLast 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.
