Which Progressive Should I Play?
MediocreMan
If you are just looking at most likely to hit - not ev wise
Quote: MediocreManAt my local casino, Pai Gow Poker, Ultimate Texas Hold 'Em, and Three Card Poker all have separate progressives. To win the progressive on Pai Gow, you have to have a 7 card straight flush with or without the Joker. For the UTH progressive, you need to flop a Royal Flush (your hole cards and the first three community cards). For Three Card, you need to be dealt Ace-King-Queen of Spades. So if I'm playing ideal strategy, which of the progressives am I most likely to hit? My gut tells me I should spend my time on Three Card, but I'm horrible at math and wouldn't have a clue as to how to figure it out.
MediocreMan
MOST LIKELY TO HIT:
I love the smell of card math in the morning, just did a question on another thread.
Okay, so this is actually fairly simple. The UTH Progressive is a Dealt Five Card Royal, nothing more or less. 1 in 649,739
The Three-Card Poker is easy:
(3/52) * (2/51) * (1/50) = 0.00004524886 = 1/0.00004524886 or 1 in 22100.0042874
And, you know what? I don't even have to look at the Pai-Gow Poker one to know that the Three-Card is the way to go.
Quote: WizardofnothingMission, was the math really necessary/. Asking about a 5 card out of five card hand or a 3 card out of 3 hand vs a 7 card out of 7 card, no need to even put the calculator out for that one
Maybe not for you. Most people don't understand these things intuitively. Though there's a little twist in the 3 card that it has to be spades, while the UTH can be any of 4 suits. But still not close.
Though the 7 card can use the joker to win it in any suit (8*7*4ways or 224/154143080 or 1 in 688,138), so that makes a lot more possibilities to win, so close to the UTH but an order worse than 3CP.
Quote: Mission146MOST LIKELY TO HIT:
I love the smell of card math in the morning, just did a question on another thread.
Okay, so this is actually fairly simple. The UTH Progressive is a Dealt Five Card Royal, nothing more or less. 1 in 649,739
The Three-Card Poker is easy:
(3/52) * (2/51) * (1/50) = 0.00004524886 = 1/0.00004524886 or 1 in 22100.0042874
And, you know what? I don't even have to look at the Pai-Gow Poker one to know that the Three-Card is the way to go.
Just a tad off.
1 in 649,740 and 1 in 22,100 exactly, respectively. No decimals. :-)
Pai Gow = 7 card royal
UTH = 5 card royal
3CP = 3 card royal
You should see that these games encompass one another... It's obvious which one(s) are easier and which are harder. In order to get the 7 card royal, you must also have a 5 card royal. In order to get the 5 card royal you must also have a 3 card royal. The easiest one will be the fewest number of cards... 3CP.
edit: Re-read the OP, he said A-K-Q of SPADES, so I guess this would change it just a little bit:
Pai Gow 7 card straight flush (w/ wild): 0.00000127, or about 1 in 780,000
UTH flop royal flush: .0000015, or about 1 in 649,740
3CP As-Ks-Qs = 1/52*1/51*1/50 = .01923 * .01961 * .02000 = .0000075, or about 1 in 133,250
...this is "assuming" the OP meant any 7 card straight flush, but I think we all know it means a 7 card Royal Flush, which would be about 1 in 3,000,000 (natural) or about 1 in 1,500,000 (w/ wild) I think.
Quote: HunterhillFor paigow he said 7 card Straight flush not a royal .
Yeah, you're right. That makes it even better, doesn't it, by a huge amount. So 7x more likely than I thought.
EDIT from above: "Though the 7 card can use the joker to win it in any suit (8*7*4ways or 224/154143080 or 1 in 688,138), so that makes a lot more possibilities to win, so close to the UTH but an order worse than 3CP." Correcting for SF rather than Royal (including Royal) makes it 8*7*4*7 or 1568/154143080 or 1 in 98,306.
